Johanna Lenne-Cornuez

"Where is modern man's place?

Keywords:

While scholars have analysed Rousseau's critique of Locke on the one hand and the controversial place of the woman in Emile on the other, this essay argues that Emile's Book V must be enlightened by Rousseau's critical dialogue with Lockean philosophy.

Notwithstanding the fact that Rousseau's Emile owes a great deal to Locke's Thoughts on Education, there is an irreducible distance between each of the two authors' art of 'forming a man'. According to Rousseau, Locke fails in making the child truly generous. For lack of forming a citizen in the full sense of the term, Rousseau's governor forms a man: a being who is aware of his place in humanity. Neutralizing man's identification with his social place makes the natural feeling of compassion possible again. However, human self-consciousness cannot easily replace patriotic self-consciousness. Virtue requires a sense of belonging to a community. Therefore, Rousseau blames Locke for abandoning his pupil at the most perilous moment: the age of marriage. In the absence of a political community, the common ego will be that of home. Rousseau's philosophy addresses a challenge to those who wish to form a modern man, both independent and beneficent, even though his own solution remains unsatisfactory inasmuch as it sacrifices women's liberty.

critique of Locke's gentleman", in Beyond the State and the Citizen, Miroslav Vacura (ed.), Prague University of Economics and Business/Oeconomica Publishing House, Prague, 2020, p. 79-109. 3 the age of enlightenment, see [START_REF] Trouille | Sexual politics in the Enlightenment: Women writers read Rousseau[END_REF]; on feminist post-cold war reception of Rousseau, see Spector 2011: chapter 8). Surprisingly, however, there has been little attempt to replace Book V in the overall scheme of Emile. The relationship between men and women has been well examined from the point of view of the dynamics of love and its sublimation (see [START_REF] Bloom | Friendship and Love[END_REF][START_REF] Habib | Le consentement amoureux[END_REF]). Yet, another perspective can be adopted, interpreting the woman's place in the light of Rousseau's project to train a modern man who is both free and truly beneficent.

Book V of Emile opens with a critique of Locke's Thoughts on Education: '"Since our young gentleman," says Locke, "is ready to marry, it is time to leave him to his beloved."

And with that he finishes his work. But as I do not have the honour of raising a gentleman, I shall take care not to imitate Locke on this point' (E 357/692; see Thoughts §215). While scholars have analysed Rousseau's critique of Locke on the one hand and the controversial place of woman in Emile on the other, this essay is meant to show that the final moment of Emile must be enlightened by Rousseau's critical dialogue with Lockean philosophy.

Rousseau blames Locke for abandoning his pupil at the most perilous moment: the age of marriage. But though the author of Emile is careful not to imitate Locke in this, he implicitly reveals his debt to Locke's advice in other pedagogical matters. Scholars have discussed the reception of Locke's Thoughts in Emile from the point of view of its empiricist foundations (See Schøsler 2000) or of the problem of authority in the pedagogical relationship (See Marks 2012aMarks , 2012b)). However, Rousseau's main critique of Locke concerns the 'art of forming men'. Going back to the thread of the raising of Emile, I will first assess the extent of Rousseau's debt to Locke and then measure the irreducible gap between the two authors.

Through study of Rousseau's critical dialogue with Locke, I will determine the function of Book V of Emile in the eyes of its author and expose the challenge that Rousseau's philosophy poses to those who wish to form a modern man even though his own solution remains unsatisfactory.

I.

In what way does Rousseau 'imitate Locke'?

The denial of Locke's legacy

In the Preface of Emile, Rousseau pays a paradoxical tribute to Locke: 'In spite of so many writings having as their end, it is said, only what is useful for the public, the first of all useful things, the art of forming men, is still forgotten. After Locke's book my subject was still entirely fresh, and I am very much afraid that the same will be the case after mine' (E 33/241). Translated in 1695 by Pierre Coste, Locke's Thoughts on Education were met with great success in France. Rousseau's judgment of his predecessor's book could be seen as a denial of Locke's legacy. In many ways, Rousseau's pedagogy is in the wake of Locke's.

Indeed, Locke operates a reversal of the traditional relationship between the teacher and his pupil. Against the pedants, Locke does not try to fill his student's head with brilliant knowledge in order to establish his own authority. Not only does Locke revoke the patriarchal justification of absolutism in politics, he also dismisses the absolutism of parental authority, a stand which Rousseau endorses (DI 58/182). Education based on coercion is judged as being both against nature (lacking respect for the child's liberty) and counterproductive (leading only to the pupil's disgust for knowledge). Locke helps change the image of the child, who is no longer a faulty being in need of physical discipline. In most cases, education is the cause of the wickedness of children (Thoughts §1).

Thus, the art of the tutor is based on attention to the child's nature (Thoughts §118).

Unlike most of the treatises on education, where teaching is the central object, in Locke's, it is secondary: only what will be really useful to the adult's life and necessary to his morality will be taken into account (Thoughts §147 91;103;117;197;255;279 / 317-319;338;358;473;551;584). Why did Locke, according to Rousseau, fail in 'the art of forming men'?

The art of forming men

To find this out, one must first determine what it means for Rousseau to form a man. Under false paternal foresight, the child is educated according to the social place for which he is destined (E 40/251). This behaviour is imprudent for two reasons: not only is human existence naturally characterized by its vulnerability to the mobility of things, but modern society also confronts man with unstable social conditions. Education, according to Rousseau, aims to emancipate the individual from an identity defined by his status and position in society: 'On leaving my hands, he will, I admit, be neither magistrate nor soldier or priest. He will, in the first place, be a man. All that a man should be, he will in case of need know how to be as well as anyone; and fortune may try as it may to make him change place, he will be always in his own place' (E 41-42/252).

By learning the use of his organs, his senses, and his faculties (E 42/253), Rousseau's pupil will not be a slave of fortune. Like the Stoic sage, his happiness will not depend on unforeseen external circumstances. It is primarily for the sake of the child that Rousseau democratizes his education: 'In the natural order, since men are all equal, their common calling is man's estate and whoever is well raised for that calling cannot fail to fulfil those callings related to it' (E 41/251). Man's estate not only has a descriptive meaning but a normative one. The individual's humanization depends on his separation from an exclusive identification based on his social place. In the unequal society of Rousseau's time, the antidote to the injustice of relations consists in not confusing man with his rank or social status. Neutralizing man's identification with his social place makes the natural feeling of compassion possible again. The instability of social conditions may be mere fiction, necessary for the moralization of those who, through their status, feel invulnerable. Of course, Rousseau anticipates the decline of European monarchies (E 194/468), but he does not go so far as to believe that the abolition of privileges would put an end to unequal inheritance. The rich man has already replaced the nobleman in his inhumanity (E 195/469).

Thus, Rousseau chooses a rich pupil, because 'in proportion to the number of those in the two stations, there are more men who fall than ones who rise'. But even though conservation of wealth is guaranteed (which is most often the case), the challenge of education is to neutralize the prejudices of wealthy social classes: 'we will at least be sure we have made one more man' (E 52/267).

The being whose social prejudices make him insensitive to the miseries of others is not a man in the full sense of the term. In Rousseau's opinion, Locke failed to 'form a man', that is, an individual both autonomous and emancipated from unequal prejudices. Yet, is

Locke not the first to have raised a modern individual, both independent and rational, whose judgment is autonomous and whose identity is dissociated from his social status? On the one hand, the theological order of the Second Treatise of Civil Government establishes the natural equality of men; the knowledge of natural law by reason provides the antidote to the despotic laws perpetuating the privileges of birth. Government? According to Rousseau, even if Locke's gentleman would become a man who no longer places his honour in his inherited status, he would not depart from an illegitimate selfesteem. Far from believing in the real loss of prestige of titles of nobility, Rousseau believes that inequalities, unjust in that they are based on inheritance, will continue. Injustice is not abolished by the fact that social hierarchy does not rely as much on status as on wealth.

Abolition of ranks would not prevent perpetuating an unequal principle of distinction based not on the real merit of men but on the permanency of their inheritance. This inegalitarian society might even be more unfair as its true principle remains unthought-of. The Lockean individual's property is 'apparently' legitimated by his work, which is therefore, in this sense, the basis of his own merit. But this apparent economic principle masks the misery of men who are left with no place to subsist in and who are at the mercy of the landowners (E 99-100;193/330-333;467;see Bachofen 2002;[START_REF] Balibar | Le renversement de l'individualisme possessif[END_REF][START_REF] Céline | Rousseau et la critique de l'économie politique[END_REF].

II. The honour of man

What is merit?

Honour must be democratized: the esteem to which the individual is entitled should not be attached to his birth rank, but to his actions. Individual merit is substituted for aristocratic honour. The esteem that distinguishes men through their merit must therefore be based on the equal respect to which everyone is entitled, regardless of social positions. As

Rousseau says: 'Man is the same in all stations. If that is so, the stations having the most members merit the most respect. To the man who thinks, all the civil distinctions disappear' (E 225/509). On the basis of natural equality, the merit of the individual is dissociated from the prerogatives of birth. But Locke does not go so far as to attribute merit to individual work, regardless of the fate of his fellow men. Merit resides in virtue; relationships with others cannot be ignored. It would be unfair to suggest that Locke's education forms a selfish individual with no consideration for his neighbour. On the contrary, the major challenge of Locke's pedagogy is to hold the child's desire for domination and exclusive appropriation in check by encouraging him to be courteous, sharing, and liberal (Thoughts §104-100).

However, in Rousseau's eyes, Locke fails in the very task he has set. First, politeness and civility of manners cannot be sufficient criteria for determining the real merit of a man.

On the contrary, this postulate turns to the advantage of the people because it is not guilty of dissimulation and hypocrisy. The rich child proves himself to be 'politely imperious'. Under his 'vain formulas of politeness', he thinks he is 'the owner of the universe' and sees others only as servants to submit to his will (E 86-87/312-314). Locke does not make it possible to achieve an education leading to true charity. Behind his facade of politeness, the gentleman will consider himself the centre of all things and will address to others the exorbitant request to be loved by them more than they love themselves. According to Rousseau, Locke fails in making the child truly generous. The latter's humanity masks a self-interested calculation in which others are not considered in their own right. Indeed, in order to train the child toward liberality, Locke suggests the following expedient: to reward the child for his generosity.

Rousseau's sentence is final: this will 'make the child in appearance liberal and in fact a miser'

(E 103/338).
What is problematic in Lockean liberality is not that the child calculates and centres everything around himself, which is only natural, nor that Locke directs the child's interest with rewards. In the eyes of Rousseau, the problem is twofold: on the one hand, the child does not have any independent criterion to evaluate what he gives (he relies entirely on the opinion of others); on the other hand, he does not empathise with the poor and their needs (he is still unable to put himself in the place of his fellow man). 'Alms giving is an action for a man who knows the value of what he gives and the need that his fellow man has of it. In the child, who knows nothing about that, giving cannot be a merit. He gives without charity, without beneficence' (E 103/338). What can Rousseau's governor do while waiting for the child to have autonomous judgment and to extend to other beings his amour de soi? The tutor must make his student feel that 'honour' lies in the very act of generosity 5 . Far from a condescending aristocratic honour, but also from a feigned generosity with no awareness of the need to give, the example of the charitable governor makes his pupil eager to render himself 'worthy' of the same 'honour'.

Duty of charity, debt of the rich

The honour of man, more precisely of the rich, therefore resides in the duty to give alms, which is inseparable from virtue. In the New Heloise, this duty is based on the evangelical word: every man, insofar as he is truly human, identifies with the sufferings of his 'brothers'. Against Voltaire,6 who deprives 'a poor man of his quality as man by giving him the contemptuous name of tramp' and who likes 'to flatter the harshness of the wealthy' (NHV,2 441/539), justifying the refusal to assist the poor, Rousseau states through Julie's voice that it is inhuman to stifle natural pity. The principle of universal benevolence is coupled with a social criticism: only those who believe that 'positions and ranks' are 'exactly correlated to talents and personal merit' could think that the poor must be left to their fate (NH 440/538). He who is aware of the injustice presiding over social distinctions will find in this accommodating reasoning only a cruel pretext for exonerating oneself from one's duty as man.

In Emile, Locke is at the centre of Rousseau's critique. Admittedly, the former has the merit of tempering the child's libido dominandi with generous habits. However, not only can Locke's method not achieve its goal, his gentleman also remains blind to the fact that the universal duty of humanity towards his fellow men is coupled with a duty of the rich towards the poor. According to Rousseau, the former have a debt towards the latter. The child's question is answered by the charitable governor: 'My friend, this is because, when the poor were willing to let there be rich men, the rich promised to sustain all those who do not have the means of life, either from their goods or from their labour' (E 104/339). These words echo the pact proposed by the rich in the second part of the Discourse on Inequality (DI 53-54/177; see Beyssade 1992). The social state, having instituted unequal appropriation of land, and perpetuating this injustice by inheritance, leaves the supernumeraries without any means of subsistence. Thus, poverty is not a vice of which the poor are guilty but the result of institutionalized usurpation. In the absence of a political solution, the rich owe a debt to the poor for their subsistence. The child knows, however, that his master has never personally usurped -or thus promised to return -anything. He again questions: 'Then did you, too, promise that?'. Rousseau's governor then teaches his pupil the idea that the debt is not individual but social. Even if the individual is not personally guilty, the rich man enjoys privileges and advantages that make him indebted to the poor: 'you owe others more than if you were born without property, since you were favoured at birth' (E 195/469). Thus, the tutor responds to the child: 'Certainly, I am master of the wealth that passes through my hands only on the condition attached to its being property' (E 104/339).

The modality of appropriation for Rousseau must be highlighted. While, in the the invention of money (Macpherson 1962: 203-220). However, in the eyes of Rousseau, nothing can overrule the first condition. If appropriation by some makes it impossible for others to meet their needs, then the former will cause irreducible harm to the latter (DI 52/175; E 193/467). No one can renounce natural self-love amour de soi. In the lesson preceding the one on liberality, Emile has learned that there is no more land available and that property is inherited (E 99/332). Thus, the condition of legitimate appropriation is turned into a debt for landowners to those who cannot live off either their goods or their labour.

Natural place, fictional place

Does Rousseau not force a feeling of guilt upon the rich? (See Orwin 1997; and the response of Larrère 2002). This would be the case if the author did not provide a criterion of judgment distinguishing natural needs, regardless of social prejudice and public opinion.

Locke fails to provide his pupil with such an independent criterion of evaluation. On the contrary, Emile, even before he is able to identify with his fellow man, learns the rule of esteem of things and arts, by relating these to natural self-love. While Locke's governor teaches his pupil only what will be useful to him as a courteous and merchant gentleman, Rousseau's governor pushes Emile to master the rule of 'real utility' (E 186/456).

The hypothesis of the state of nature neutralizes the confusion between the individual and his rank or social status. However, this neutralization is not without ambiguity and Rousseau immediately perceives its ambivalence. The individual must not confuse his own self with the place which he inherits, but can he rightfully think he is independent of all relations? The autonomous individual would then reclaim his social position even more exclusively than before, comforted in the certainty that he occupies his place through the virtue of his own merit. Humanization of man would be nothing but deception. Against an illusory dissociation between the individual's identity and his relations, Rousseau makes the feeling of the subject's place in his relations the central issue of his education. Whatever his social condition, Emile will always be in his own place. Though fortune may try to make him change places, he will not lose his own because he has one which is not determined by the contradictions of the social system and because he knows how to maintain himself in it.

This place is that of man in the natural order. To be in one's own place is, first, to know oneself through the appropriate relations of human nature. But how can one know the natural place of man? Rousseau's originality is to bring to light the need for fiction. Not only does the author invent a fictional pupil who serves as paradoxical proof for the possibility of a natural education (see Citton 1994), but the pupil is that of nature only through his identification with the character of a novel. In fact, 'the surest means of raising oneself above prejudices and ordering one's judgments about the true relations of things is to put oneself in the place of isolated man and to judge everything as this man himself ought to judge of it with respect to his own utility' (E 185/455). Dismissing all authoritative lessons, the governor merely makes sure that Emile will identify with Robinson Crusoe. The latter not only possesses the status of 'conceptual character' who demystifies the economic and social order (Spector 2013), he is also a 'hero' with whom the child must identify. One's natural self-relation requires the mediation of a fictional character in whose place the child puts himself in order to assign rules to his foresight.

While the state of nature in Rousseau's Second Discourse was a myth, and natural man an origin forever lost, natural education makes use here of Daniel Defoe's novel. Before the empathic self-expansion which will put the pupil in the place of those who suffer (E 223/506), another way of 'putting oneself in the place of' is necessary for Emile's education.

The novelistic identification is powerful. Emile pretends to be Robinson, imagining himself both in his place and at a distance: he 'thinks he is Robinson himself' but at the same time assesses the merits of 'his hero's conduct' (E 185/455). This childish game is amoral: the pupil learns what is useful to his own well-being. But this identification is propaedeutical to morality: by putting himself in Robinson's place, the child learns to put himself in the place of every man, as he occupies, through his belonging to mankind, a place in the order of things. Thus, this place banishes social prejudices which would stifle natural pity. From

Robinson's place, fiction puts reality back in order and subverts the order of social places (see Bachofen 2009; Spector 2013). Emile's economic training teaches him the internal logic of the established order and gives him an external point of view from which it can be judged.

Emile has a criterion at his disposal for evaluating things and arts according to their real utility. He can then be honoured to give to the poor: there lies his own merit. This merit is commendable because it has an objective value, determined by human needs.

The virtue of the honest man is redefined by Rousseau as 'active beneficence' (E 251/545). Thus, Emile fills man's place by relieving the suffering of people. Admittedly, the empathic self-expansion leads him to sympathize also with the sorrows of the rich. But, thanks to a judgment which emancipates itself from social prejudices, Emile feels that the pains of the rich bear no comparison with those of the poor (E 225-226/509). Thus, the governor ensures that, for Emile, 'the interest of the indigents [will] always be his. Let him assist them not only with his purse but with his care. Let him serve them, protect them, consecrate his person and his time to them. Let him be their representative; he will never again in his life fulfil so noble a function'. Rousseau subverts the titles of nobility: 'the practice of virtue' is 'to make heard the voice of the unfortunates' (E 250/544). Emile's hero is no longer only Robinson but Don Quixote, no matter how ironically and cynically the men of the world will undoubtedly view him.

Why does Rousseau's work not end there? Why not let Emile go, now that he can be in his own place everywhere, whatever fortune may be, and that he occupies 'a position place 7  among men' (E 235/523) and distinguishes himself only by his beneficence? Why can he not remain 'a knight errant, a redresser of wrongs, a Paladin'? Why can Emile not be the virtuous cosmopolitan? By having broadened the gap between Locke's and Rousseau's educations, the necessity of Book V of Emile may seem even less obvious than it already was.

III. The affective conditions of an effective virtue

To fill one's place in the physical and moral order according to the constitution of one's sex

Upon preliminary analysis, Book V is justified in the eyes of Rousseau by the pre-Freudian importance given to libido in the development of the pupil. Man must not only provide for his subsistence but also for the need to love and be loved. Emile must not 'fill his place in the physical and moral order' only according to 'the constitution of his species' but also 'of his sex' (E 357/692). While the marriage of a gentleman is determined by family alliance strategies, Emile does not value himself or others according to their wealth or their condition. By leaving his gentleman 'to his beloved', Locke gives in to the paternal nobiliary demands: marriage will by definition be arranged according to a criterion that is extrinsic to loving desire. On the contrary, Emile still needs his governor in order to judiciously use 'the right of nature,' which is to 'begin by loving each other before being united' (E 400/756).

Equality, which is granted in the choice of spouses, is however abolished once the union is sealed. Far from promoting Locke's equal parental authority (TCG VI §52), Rousseau states the woman's natural dependence on her husband. The author of Emile wishes to promote what could retrospectively be called difference feminism: the 'women's party' implies in his eyes the valorisation of the merits of each sex (E 363-364/701). For Rousseau, the peril lies in making marriage an alliance of interests, which could then lead to libertinage (E 388/739).

In the monarchical high society, the noblemen and the wealthy city dwellers have perverted the sacrament of marriage by reducing it to an apparent union masking a dissolute life and the annihilation of moral virtues (See Larrère, 2010). On the contrary, love can sustain virtue on the condition that it sublimates sexual desire through reciprocal esteem (E 398/752). 7 Rousseau's terms in French.

But was Emile's virtue not already acquired at the end of Book IV? The Profession of Faith of the Savoyard Vicar seemed to have saved the young man from an imminent danger of 'moral death' (E 264/562). Thanks to the projection of a divine order, man is assured that his virtue is not 'foolish' (E 292/602). Virtue, unlike kindness, requires, if not a form of selfsacrifice, an effort, which makes it worthwhile and justifies enjoying 'satisfaction with oneself' (E 281/587). In a conflictual society, only the just order guaranteed by God can support the virtue that enjoins to set 'all personal interest aside' (E and to worry about the suffering of others. But it seems that 'the hope of the just' (E 313/635) is irremediably insufficient to make virtue effective in a social state where the general will has been silent. Divine order remains a projection that is of utmost importance to the conscience but is powerless to produce a true common identity (Ginevra Manuscript I 2; see Radica 2008:

135-143). The beneficent will of man cannot be expressed or guaranteed by any general will of the human species (See Litwin 2012).

In the 'common ego' moi commun (SC I,6), the individual self feels he is part of a whole to which he is ordained. The subject's morality depends on the representation of himself within an order where the individual is not at the centre. Thus, the identity of the citizen has meaning in his own eyes only through the place he occupies in the common unity. He cannot conceive of his own merit independently from the values of the fatherland.

But the ancient city is dead: Rousseau diagnoses the inevitable rise of individualism (E 40/250). For lack of forming a citizen in the full sense of the term, Rousseau's governor forms a man: a being who is aware of his place in humanity. However, human selfconsciousness cannot easily replace patriotic self-consciousness. Conflictual private interests constantly threaten the identification with one's fellow men. The belief in God ensures that everyone is accountable to his own conscience, but it fails in providing the affective conditions for an identification with a common good in the social order. In the divine order, everyone is brought back to the solitude of his own conscience. However, virtue requires a sense of belonging to a community: no one can be actively beneficent without being attached to a place on which his identity is dependent. In the absence of a political community, the common ego will be that of home.

According to Rousseau, not only does Locke fail in bringing his critique of aristocratic honour to completion, but he remains blind to the affective conditions of an effective virtue. Rousseau reads the end of Locke's Thoughts on Education in light of the Treatise of Civil Government. In the latter, Locke shows that law is not a limitation of liberty but its condition. Obedience to the law of nature, 'made known by reason only', protects all from subjection to 'the arbitrary will of another' (TCG VI, §57). Although Rousseau retains this idea, he addresses a profound criticism to modern jusnaturalism: natural law has in itself no power of obligation (see Bernardi 2007). Individual interest is not spontaneously reconciled with justice. Everyone wants to benefit from the beneficence of others, while avoiding mutual obligation. Rousseau's political answer is known to us: only is a people united by the general will likely to prescribe to individuals the reciprocity of their duties. The political community itself cannot ignore an affective base: the common ego rests on a sense of belonging.

In modern society, only 'love, properly so called' can 'take the place' of 'the love of humanity' and 'of the fatherland' (LDA 337/107). But this supplement is not without difficulties in the eyes of Rousseau himself. All feeling of love is exclusive, while the moral value of feeling lies in its generality. Insofar as 'the isolated man' who loves only himself is 'the most wicked of men', 'it is much better to love a mistress than to love oneself alone in all the world'. But if the love for a woman takes precedence over love of mankind, this 'dissolute attachment' will soon do 'damage to all the others' (LDA 338/107). How can a loving relationship support benevolence towards men instead of ending up excluding it?

Acknowledgment of debt

The danger lies in having formed a man who attributes his merit entirely to himself.

Unaware of whom his identity is indebted to, the individual's benevolence might weaken to the point of becoming complacency. Emile is bound to moral, if not political, commitments. By contrast, the cosmopolitan man has something in common with the free rider. The fact that Emile was raised always to be in his own place does not mean that he is exempt from the duty of taking a place in the world.

Emile is definitely liberated from aristocratic arrogance and the ruthless contempt of the rich.

The reason Emile can scour the countryside as a benefactor is because he knows where his place is, where to start and where to return. Only the love of a woman can still give the man without a fatherland a place. Since virtuous will weakens and loses itself in illusions by becoming individualized, the modern man must feel his attachments. Love provides the supplement to all other social bonds. This explains why, in Rousseau's eyes, the young woman must only love 'the peaceful and domestic life' (E 388/739). To the question 'who', Rousseau substitutes the question 'where': where will the woman really feel in her own place?

Modern woman's place

According to Rousseau, the answer to this question calls for a spatial definition:

against the depraved women who 'immediately feel they belong s'y sentent d'abord à leur place'

to 'wild company', the honest woman will fully enjoy the feeling of her existence in the 'refuge' of her home (E 388/739). The spatial determination of her place depends on a moral position of the female self. For Rousseau, the woman must feel the warmth and honesty of family relationships. The home as the asylum of the honest woman is the effect of 'our institutions' (E 389/740). The honest woman feels safe from mundanity in her domestic shelter, as opposed to the libertine who views family life only as a prison and an alienation. While the Roman woman exercised her power through certain public actions (E 390/742), the modern woman can only reconquer her empire by confining herself to her family relations. Woman's retreat is the necessary consequence of both social perversion and the death of fatherland.

Without sincere affection for one another, modern individuals live in a society of 'strangers' (E 739/388). Without a 'common self' resized to the boundaries of the household, the man will be at best 'a likable foreigner' among polite and selfish hypocrites (E 339/670). Without the woman finding refuge in her household, man will not know which 'natural judge of his merit' to devote himself to (E 398/752). Just as Emile's education is the necessary consequence of the absence of a fatherland, the woman's 'refuge' is a consequence of social perversion. But those consequences are symmetrically reversed. While Emile is educated to be everywhere in his place, Sophie must be maintained in her household. Or rather: in order to be an independent man and to take place in society without being perverted, Emile needs a woman whose feeling of existence is entirely attached to her family relationships.

Virtue is reconquered at the cost of a sexual definition of liberty: independence for man, empire for woman. For Rousseau, the concept of empire is always synonymous with a false freedom, an alienated liberty. Female freedom is under house arrest: the woman must move from the 'paternal home' to her 'own home' (E 388/739). The feminine feeling of existence is linked to the appropriation of a place. According to Rousseau, the woman needs a place that belongs to her, an exclusive place which escapes the eyes of others, a place of intimacy. Conversely, man can live outside, even wander, without any attachment, without a home. In many of Rousseau's descriptions, the woman 'stays put' 'la femme reste à sa place' while the man is in motion (E 383/732). The woman is the operator of the man's settling process.

For man to escape relations of domination, the woman must delimit her empire. In order for man to remove himself from relations of submission, the woman must establish herself in a relationship of dependence. Through a loving bond, she renews the social bond.

Without her, modern man would have no sense of belonging to a place. Sophie's empire attaches Emile to a place that he makes his own. Yet Emile's education has seemed to lead him to a different conclusion: 'I have found that dominion empire and liberty are two incompatible words; therefore, I could be master of a cottage only in ceasing to be master of myself' (E 472/856). Before being led to establish himself, Emile opposes self-appropriation and appropriation of a place, just as liberty is opposed to empire. The certainty of being in his own place everywhere can feed the illusion of not having to choose a location. Freedom seems contrary to any particular rooting. However, against the individual who believes he has no social debt, the final effort of Rousseau's pedagogical work is that of Emile's social inscription. In order for man to be both master of himself and at home in a particular place, for him to be everywhere in his place while occupying a particular place in social relations, for him to be positioned without losing his freedom, the woman must feel in her own place at home only. The love of a woman renders compatible what was not: independence and empire, liberty and dominion. Woman's freedom is sacrificed so that man can keep his.

  notorious chapter IV of his second Treatise, Locke claims and justifies a natural right to individual property, Rousseau makes the rich the mere usufructuary of a good which 'passes through his hands' because he inherits it and of which he is only transitorily and conditionally the master. Then, what is 'the condition attached to property'? Locke's famous definition of legitimate appropriation by labour in the state of nature is coupled with a double condition. On the one hand, a clause of abundance: the appropriation is legitimate insofar as it does not harm others, 'since there was still enough' for their subsistence(TCG V,33). This condition goes together with a non-waste clause (TCG V,31). On the other hand, a clause of individual appropriation: man extends his property to things only as an extension of his own body and of the 'work of his hands' (TCG V,27). As C. B. Macpherson shows in his distinguished work on possessive individualism, this last clause is invalidated by

  governor 4 must follow the development of the child's faculties and direct his natural interest (E 117/358). Just like Locke (Thoughts § 166), Rousseau prefers teaching through experience and the direct relation with things, rather than through lessons (E 166/427). Not only does the author of Emile borrow many medical precepts from Locke (E 126/371), he also criticizes the parental prejudices that hinder the child's autonomy. Yet, despite such a legacy, most references to Locke in Emile are criticisms (E 89-

). Locke's Thoughts on Education were written according to the hedonistic principles of his Essay on the Human Understanding (see

Morère 2005: 75-76; Tarcov 1984: 77)

. In contrast with an ordinary education, where study and grief go hand in hand (Essay II,33), Locke wishes to link learning to pleasure by arousing the interest of the child, an interest which will be all the more acute as the child begins to understand the usefulness of what he is learning. Self-love, the natural motive that presides over the development of reason, must not be repressed but, instead, guided in order for the future adult to govern himself.

In this sense, Rousseau pursues the educational revolution initiated by Locke, whose finality is the child's autonomy. This cannot be obtained by an arbitrary constraint that would only lead to the child's desire to take his master's place as a tyrant (E 92/321). On the contrary, the

  Did Locke not, before Rousseau, attach merit to the individual and not to his birth rank? In what way does Rousseau's subversive critique of aristocratic honour challenge the social order based on the individual's natural rights, established in the Treatise of Civil

	esteem wisely. The Lockean gentleman, independent but sociable, may inaugurate the era of
	bourgeois ideology. Would Rousseau have recognized in the features of Locke's gentleman
	the bourgeois he criticizes elsewhere?
	Permanency of inequalities
	In Rousseau's eyes, Locke's pupil remains a gentleman. Should the revolutionary
	impact of Locke's statement not be nuanced? Thoughts on Education does not so much
	inaugurate the bourgeois era as it rather plays one aristocracy against the other: merchant
	aristocracy against the nobility at court. Lockean education is guided by what is useful to the
	wealth of the English gentleman and the prosperity of his commerce (Thoughts §164). In
	reality, Locke plays it both ways: on the one hand, the tutor curbs the aristocratic morgue to
	form an honest man; on the other, he links each lesson to the management of the future
	nobleman's affairs. Through this pedagogical orientation, Locke contributes to the formation
	of a bourgeois individual if, by this, one means a being who no longer places his honour in
	his belonging to an inherited rank nor in a pedantic distinction from those who dedicate
	themselves to the doux commerce. The Lockean gentleman is neither a Cornelian hero nor an
	idle courtier. His success must be economic and social. While Locke extends the ambition of
	the merchant nobility to all men, Rousseau neutralizes social conditions to bring all men
	back to their human condition.	On the other hand, Lockean education
	may have appeared revolutionary in the democratic sense of the term. In the Preface to his
	French translation of Locke's Thoughts, Pierre Coste points out that, though the book is
	certainly intended for the English nobility, the word 'gentleman' has a broader meaning in
	English than in French. Under this term, he includes 'the people we, in France, call people
	from good homes, good bourgeois, etc.'. The gentleman is no longer characterized by a
	privilege of birth or a heroic sense of honour due to his rank (see Johnson 2012). Does
	Locke subvert the purpose of aristocratic education? In theory, Lockean pedagogy would
	apply to every individual as every man is defined by an equal freedom. According to Nathan
	Tarcov (Tarcov 1984: 209-211), Locke contributes decisively to taming aristocratic pride and
	making the noble ethos civil. Locke's education makes the gentleman a pragmatic and
	enterprising individual. The Lockean pupil then symbolises the bourgeois, one who is
	industrious by interest but is also civil and keen on social relations and who cultivates self-

Despite all the pedagogical transformations made by Locke, Rousseau persists in seeing a gentleman in his pupil, because, in his eyes, Locke did not carry the critique of aristocratic honour to completion. Aristocratic honour is based on a belonging to a distinctive and exclusive lineage of which the nobleman must be worthy. For Rousseau, the self-esteem it leads to is illegitimate because it is not based on the individual's real merit. He dissociates honour from the social condition inherited by the individual (see NH II,2). The author of Emile tells of having refused 'the honour' of being the tutor of the son of a nobleman. His educational principles would have inevitably come into conflict with those of the child's father. While the latter would have wanted his son's education to be worthy of his rank, Rousseau would have subverted the sense of honour of his pupil to the point of showing contempt for his status: 'His child would have repudiated his title; he would no longer have wished to be a prince'

(E 50/264)

. This is why Emile can only be an orphan.

  Lockean education may have formed an individual without a local anchoring -he can go and conquer America (TCG V, §41) -and without any awareness of his moral and social debt, the governor's departure seals the advent of the pupil's independence. Independence threatens virtue. This is what the strange aborted work that follows Emile tells us. In the first letter of Emile and Sophie or Les solitaires, Emile portrays himself as an independent man, close to the Stoic. His 'heart has been torn apart by all his attachments' (ES 685/881) because of his wife's adultery: 'I had to seek whether I was still that man who knows how to fill his place in his species when no individual takes an interest in it any longer. But where is that place for the one for whom all of his supports have been destroyed or changed?' (ES 705/905). Then begins Emile's wandering, like a Ulysses without any Ithaca. The incompleteness of the work seems to attest that man loses his beneficent humanity if he does not know to which particular place he is attached. The attachment to his place depends on the interest that a singular being takes in him, and that he takes in return.Modern man cannot fulfil his duties towards humanity if no one takes an interest in his own merit.Already in Book IV, the governor had made Emile feel that he could not remain under the illusion that the merit of what he is was his alone. Contrary to the pity that puts us in the place of others and develops into a justice which compensates for inequalities, amourpropre is the desire 'to be in the first position place' and to distinguish oneself 'among men' (E 235/523). But envy does not stifle Emile's pity, who judges men as slaves of their prejudices and their passions. 'If he judges them well, he will not want to be in the place of any of them' (E 244/536). Emile's happiness, however, could constitute an illegitimate source of 'pride'. 'Emile, in considering his rank in the human species and seeing himself so happily placed there', is tempted to believe that he owes his wisdom only to himself (E 245/536-537). It is therefore necessary to humiliate the pupil's amour-propre by making him Emile's demand for recognition is neither vain nor illegitimate. First, esteem must be granted, as we have seen, according to criteria of independent judgment, and must not be entirely dependent on public opinion. Emile knows what makes the real value of a human being; love does not change him but, on the contrary, strengthens the virtuous will that already defines him (E 433/801). Esteem, therefore, must be reciprocal: Emile wishes to be esteemed only by an estimable woman. By contrast, because he did not provide a criterion of independent judgment, Locke may have, in spite of himself, reiterated the prejudices linked to the rank of his gentleman. Secondly, Emile's request for esteem is not disproportionate: it is only addressed to those for whom he has particular affection. The gratitude of Emile for his governor founds the esteem he has for him and the desire to be valued in return. His search for a wife who 'sustains love by the means of esteem' (E 393/746) relies on this friendship. By contrast, the honest Lockean man is polite to all, but cannot choose by whom he really wants to be recognized. What difference does it make to me where I am? Wherever there are men, I am at home with my brothers; wherever there are no men, I am in my own home' (E 472/857).Again, the illusions of the Stoic cosmopolitan's speech are dismissed by the governor (see Bernardi 2013; on Rousseau's Stoic heritage, see Brooke 2012), who makes the young man aware of the debt he owes to his country, even if it no longer is a fatherland (E 473/858).

	However,
	feel all that he owes to his governor, a revelation that might seem brutal but that is founded
	on reciprocal affection. Originally thinking himself autonomous, Émile gradually becomes
	aware of his debt. Far from being under the illusion that he is a self-made man, he realizes
	that he owes his happiness to the governor's education.
	This indebted self-consciousness provides new pedagogical means. Emile's gratitude
	for his governor establishes the 'authority' of the latter when the young man needs a Mentor
	to prevent him from yielding to 'the Sirens' song' (E 326/652-653). The governor must lead
	Emile to choose a woman who deserves his esteem and who, reciprocally, wishes to please
	only a man of merit. The proper contentment of oneself must be sustained by the esteem of
	one's relatives: no man can fill his place within humanity (that is to say, as we have seen,
	being human in the sense of being beneficent) when no one is interested in his merit. The
	empathic expansion of amour de soi needs to be sustained by a just satisfaction of amour-propre:
	no one can remain virtuous for long without recognition of their own worth by others (see
	Bloom 1993; Neuhouser 2008). Rightful self-esteem needs to be confirmed by the esteem of
	others.

All of Book V is devoted to Emile's reappropriation of his affective ties thanks to his recognition of the merit of others and his desire for mutual esteem. Rousseau transposes the vocabulary of 'honour' into 'merit'. Merit is no longer associated with rank or social condition, but with man's actions. However, this merit is not purely individual. The indebtedness of merit makes it a moral force: Emile wishes to deserve the esteem of those to whom he is indebted. The governor takes the 'place of the father' when Emile assigns him to it, that is to say, when he becomes aware of what has constituted the governor's merit so far (E 407/765). In a similar way, Rousseau's pupil is at first tempted to believe that he is not attached to any particular country: 'What difference does it make to me what my position on earth is?

'There is only one science to teach to children. It is that of man's duties. (...) I call the master of this science governor rather than preceptor because his task is less to instruct than to lead. He ought to give no precepts at all; he ought to make them be discovered.'(E 266/52)

This does not mean, of course, that Rousseau only has Locke in his sights. On the idea of generosity, Rousseau also dialogues with the Christian conception of charity, Augustinism and its materialist reversal on the one hand (see Lafond 1996; Bernardi 2014: chapter 4) and with theories of obligation in modern natural law on the other (see Derathé 1995; Bernardi 2007).

See Voltaire, Dictionnaire philosophique, art. 'Gueux'.

Virtue's refuge

After Robinson, after the Paladin, Emile's hero becomes Telemachus (E 467/849).

Fénelon's Telemachus notably provides the model for a peasant society, where luxury does not exist (Fénelon 1994: Book 8). Just as Telemachus refuses to be the king of another kingdom than that of Ithaca, Emile returns to his country at the end of his travels. However, while the purpose of Fénelon's education is to make Telemachus a good king, Emile is not trained to be a chief, despite the authority he has over others. Rousseau does not content himself with civilizing aristocratic pride. He also takes his distance from the ancient heroism he has glorified elsewhere. To 'know how to keep in one's place' is also to become aware of the human's limits: man cannot be virtuous when he is above ground, without any love to reinforce his self-esteem, nor a sense of belonging to a place from which he can display his beneficence. The beneficence of man also depends on awareness of the measure of human capacities. The man who believes that he is not located in the world misunderstands who he is. Rousseau puts back in his place the one who, believing that he is able to do good everywhere, considers himself a superior being. Virtue is resized: 'Besides, since Emile is not a king and I am not a god, we do not fret about not being able to imitate Telemachus and Mentor in the good they did for men. No one knows better than we do how to keep in our place, and no one has less desire to leave it. We know that the same task is given to all, and whoever loves the good with all his heart and does it with all his power has fulfilled his task.' (E 467/849).

Ultimately, Book V is necessary for anchoring the honest man in a place. Modern man's freedom of choice cannot be emancipated from attachments and commitments.

Reciprocally, beneficence can only be lastingly active if one is attached to the place where he is situated. Certain to have found the woman that suits him, Émile can engage in his charitable activities around Sophie's house. The governor can recognize in his pupil the virtues which defined his moral identity (E 431/799). If Émile engages in beneficent activities in the surrounding countryside, it is not only to please Sophie: he knows that this is his duty. But Sophie's love gives him additional reasons to be virtuous. Contrary to the condescending alms of the nobleman or the rich, Emile commits himself entirely: he takes part in the work of the peasants. 'In becoming the benefactor of some and the friend of the others', Emile 'does not cease to be their equal' (E 436/805). The beneficent activity of In the end, Rousseau addresses a double criticism to the Lockean gentleman. On the one hand, without any independent criteria of evaluation of needs, possessions, and actions, Locke's pupil is destined to perpetuate the prejudices of his social condition. On the other hand, being unconscious of his debt, he will be doomed to believe that his merit is individual and will be unable to choose the place of his existence other than by an appropriation devoid of any true active beneficence. On the contrary, Rousseau wants his pupil to be all at once autonomous in his judgment, a master of criteria ensuring his true independence from social prejudices, and a benefactor aware of his social and affective debt. While Emile's selfsatisfaction is based on his knowledge of the human condition, the just appreciation of his own merit is sustained by the esteem of his beloved. Far from the gentleman merchant, Rousseau's modern man is truly beneficent. No man can claim to be free without being aware of his place in humanity: this is the first challenge that Rousseau addresses to modernity. No man can claim to be virtuous without acknowledging his debt and committing himself lastingly to his social relations: this is the second challenge that Rousseau addresses to modernity. But the author's answer does not fail to make women orphans, since they pay the price for it. Rousseau, in having formed a man who is freed from his social prejudices, has nonetheless formed a man who is imprisoned in his male prejudices.


Tristan Fournaise

Jérémy Petit

Claire Gaiani
email: claire.gaiani@univ-lorraine.fr

Main powder physicochemical characteristics influencing their reconstitution behavior

Keywords: powder reconstitution, food powder, wettability, particle size, chemical composition

Thirty-six food powders corresponding to a wide range of physicochemical characteristics (bulk and surface chemical composition, median particle size, span, water activity) and manufacturing processes (grinding, freeze-drying, spray-drying, crystallization) were investigated for their reconstitutability. Their reconstitution profiles were acquired by conductivity measurements and fitted with Hill model. Physicochemical characteristics of investigated powders were correlated to their wetting and reconstitution times by principal component analysis. Four powder categories were identified on the basis of wetting and reconstitution times; i.e. green group (good reconstitutability); yellow and orange groups (intermediate reconstitutability); red group (poor reconstitutability). Long wetting times were associated to high particle surface hydrophobicity, small median particle size, as well as high protein and lipid contents in the powder bulk. Long reconstitution times were linked to the powder manufacturing process (i.e. grinding), as well as to low sugar content in the powder bulk.

Introduction

Biologically-derived powdered materials are involved in the manufacturing of many industrial products (such as cosmetics, foods, and pharmaceutics). In the food field (but not only), various raw materials and ingredients, such as flours, spices, and processed products like instant coffee powder or powdered milk are traded in powder form. They originate either from liquid conversion into powder by various techniques such as spray-drying, freeze-drying, drumdrying, belt-drying, or crystallization, or from size reduction of solid materials [START_REF] Karam | Effects of drying and grinding in production of fruit and vegetable powders: A review[END_REF][START_REF] Mitchell | Mapping the rate-limiting regimes of food powder reconstitution in a standard mixing vessel[END_REF]. Because of the various powder origins, their particle size and shape distributions, bulk and surface chemical compositions, and physical properties are highly variable. Therefore, more than one analytical technique is often required to obtain a full set of information about a given scientific question [START_REF] Burgain | Surface chemistry and microscopy of food powders[END_REF].

The reconstitution of powders is of upmost relevance for industrial applications, considering that most powdered ingredients are reconstituted or extracted before use. Literature put in evidence the existence of four main reconstitution steps: wetting and swelling (which may occur simultaneously depending on powder composition); sinking; dispersion (including breaking of lumps and agglomerates and fragmentation of individual particles); and solubilization. The main scientific obstacle is that these steps can hardly be isolated. Indeed, several reconstitution steps overlap at different time scales [START_REF] Schubert | Instantization of powdered food products[END_REF] and the entire reconstitution mechanism is still complicated to state [START_REF] Mitchell | Mapping the rate-limiting regimes of food powder reconstitution in a standard mixing vessel[END_REF][START_REF] Forny | Wetting, disintegration and dissolution of agglomerated water soluble powders[END_REF][START_REF] Gaiani | Surface composition of dairy powders observed by X-ray photoelectron spectroscopy and effects on their rehydration properties[END_REF].

Powder wetting is the phenomenon defined by the replacement of the gaseous phase by water at the powder surface. It can be experimentally determined by using standard methods of the International Dairy Federation [START_REF] Idf | Détermination de la dispersibilité et de la mouillabilité[END_REF] developed for milk powders. Previous studies evidenced that powder wetting is more efficient for large particles (at least over 90 µm) or agglomerated powders [START_REF] Fournaise | Impact of formulation on reconstitution and flowability of spray-dried milk powders[END_REF][START_REF] Hla | Wetting behaviour of instantized cocoa beverage powders[END_REF][START_REF] Hogekamp | Rehydration of Food Powders[END_REF][START_REF] Schuck | Analytical Methods for Food and Dairy Powders[END_REF]. High particle size induces small particle-solvent contact angle, thus facilitating wetting. High porosity and spherical particles also have a good wetting behavior [START_REF] Hla | Wetting behaviour of instantized cocoa beverage powders[END_REF][START_REF] Ji | Effects of fluid bed agglomeration on the structure modification and reconstitution behaviour of milk protein isolate powders[END_REF]. In addition to physical properties, chemical composition can also influence powder wettability.

For instance, high lipid or protein contents makes powder surface hydrophobic, leading to poor wettability [START_REF] Schuck | Analytical Methods for Food and Dairy Powders[END_REF][START_REF] Nijdam | The effect of surface composition on the functional properties of milk powders[END_REF][START_REF] Wu | Effects of spraying surfactants in a fluidised bed on the rehydration behaviour of milk protein isolate powder[END_REF]. On the contrary, hydrophilic components located at powder surface like carbohydrates or surfactants enhance its wettability [START_REF] Ji | Effects of fluid bed agglomeration on the structure modification and reconstitution behaviour of milk protein isolate powders[END_REF][START_REF] Wu | Effects of spraying surfactants in a fluidised bed on the rehydration behaviour of milk protein isolate powder[END_REF][START_REF] Hammes | Study of the influence of soy lecithin addition on the wettability of buffalo milk powder obtained by spray drying[END_REF][START_REF] Ji | Enhanced wetting behaviours of whey protein isolate powder: The different effects of lecithin addition by fluidised bed agglomeration and coating processes[END_REF].

Sinkability is defined as the ability of particles or particle agglomerates to sink below the water surface [START_REF] Jiang | 21 -Fruit and vegetable powders[END_REF]. Sinking mainly depends on particle size distribution, porosity, and density: as a general rule, large and/or high-density particles enhance sinking. However, large particles of high porosity (low density) exhibit higher sinking rate than small and low porosity (high density) particles, as sinking is favored by water capillary diffusion into inter-and intraparticular pores [START_REF] Ji | Enhanced wetting behaviours of whey protein isolate powder: The different effects of lecithin addition by fluidised bed agglomeration and coating processes[END_REF][START_REF] Caric | Milk powders, Physical and Functional Properties of Milk Powders[END_REF][START_REF] Mitchell | Surface tension-driven effects in the reconstitution of food powders[END_REF]. Cohesive powders often sink in the form of lumps [START_REF] Mitchell | Mapping the rate-limiting regimes of food powder reconstitution in a standard mixing vessel[END_REF].

Dispersibility is defined as the ability of a powder to disperse into water. Powder dispersion consists in two simultaneous mechanisms [START_REF] Mimouni | Investigation of the microstructure of milk protein concentrate powders during rehydration: Alterations during storage[END_REF][START_REF] Fang | On quantifying the dissolution behaviour of milk protein concentrate[END_REF]: lumps and agglomerates breaking into individual particles and individual particles fragmentation, both leading to size reduction and specific surface area increase, further facilitating interactions of the solid matrix with water.

Dispersion occurs when the forces exerted by the solvent to separate particles overcome particle cohesion [START_REF] Schuck | Analytical Methods for Food and Dairy Powders[END_REF][START_REF] Freudig | Dispersion of powders in liquids in a stirred vessel[END_REF][START_REF] O'mahony | B: Proteins: Applied aspects[END_REF]. The dispersion rate is enhanced for high porosity, low density, or lowly cohesive particles [START_REF] Fournaise | Impact of formulation on reconstitution and flowability of spray-dried milk powders[END_REF][START_REF] O'mahony | B: Proteins: Applied aspects[END_REF][START_REF] Goalard | Characterization of the Dispersion Behavior of Powders in Liquids[END_REF].

Solubilization is often considered as the determinant reconstitution step as it is the final one [START_REF] O'mahony | B: Proteins: Applied aspects[END_REF]. It results in the complete disappearance of soluble granular structures and the release of all soluble components (e.g. proteins, minerals, etc.) [START_REF] Gaiani | Dairy Powder Rehydration: Influence of Protein State, Incorporation Mode, and Agglomeration[END_REF][START_REF] Marabi | Assessing dissolution kinetics of powders by a single particle approach[END_REF]. Complete powder solubilization leads to a homogeneous solution without insoluble particles, which is an important criterion for the consumer. The chemical composition is crucial for powder solubility. For example, powder solubilization is generally delayed by the presence of hydrophobic molecules at the particle surface [START_REF] Lee | Functional Properties of High Hydrostatic Pressure-Treated Whey Protein[END_REF]. Also, it has been observed that intermicellar interactions of caseins significantly decrease the solubilization rate [START_REF] Fang | On quantifying the dissolution behaviour of milk protein concentrate[END_REF].

Countless techniques have been used to describe and characterize the successive powder reconstitution steps and interesting advancements have been achieved [START_REF] Mitchell | Mapping the rate-limiting regimes of food powder reconstitution in a standard mixing vessel[END_REF][START_REF] Forny | Wetting, disintegration and dissolution of agglomerated water soluble powders[END_REF][START_REF] Mitchell | Surface tension-driven effects in the reconstitution of food powders[END_REF][START_REF] Goalard | Characterization of the Dispersion Behavior of Powders in Liquids[END_REF][START_REF] Galet | The Wetting Behaviour and Dispersion Rate of Cocoa Powder in Water[END_REF].

Nevertheless, previous studies have mainly been focused on a limited number of powders similar in origin and composition (i.e. often milk powders). Therefore, owing to the great variety of industrially available powders, a larger investigation is still needed in order to identify the main physicochemical characteristics controlling powder reconstitution. For this purpose, the wettability and reconstitutability of thirty-six powders of various origins and natures were determined and linked to manufacturing process, chemical compositions (bulk and surface), and physical characteristics (median particle size) by principal component analysis.

Material and methods

Investigated powders

Thirty-six powders, varying in chemical composition (water, lipids, proteins, carbohydrates and minerals contents), physical properties (particle size distribution) and manufacturing process (spray-drying, drum-drying, freeze-drying, crystallization), were investigated (Supplementary Material Table S1). In order to change the particle size distribution while keeping the same powder bulk composition, polenta and instant coffee powder were ground (to reach 1.0 mm and 0.08 mm, respectively) with a ZM 200 (Retsch, France) ultra-centrifugal mill at 8 000 rpm using small powder amounts in order to limit the heating of the grinding system and thus of produced powder [START_REF] Waiss | Effect of milling and sieving processes on the physicochemical properties of okra seed powders[END_REF]. This approach allowed obtaining a wide range of reconstitution profiles.

Physicochemical characterization

Particle size distribution

Laser diffraction (Mastersizer S, Malvern Instruments Ltd, Malvern, UK) was used to evaluate particle size distribution with a 5 mW He-Ne laser operating at 632.8 nm wavelength and a 300 RF lens. Dry dispersion was carried out with an Aero S air disperser module (Malvern Instruments Ltd). The analytical conditions were adapted for each powder: air pressure was fixed at 2 bar, feed rate between 30 and 60 %, and hopper length between 2 and 3 mm. The volume-equivalent sphere diameter was chosen as size estimator. Classical granulometric parameters D10, D50, and D90 were used to characterize powders, where Dx designates the diameter for which x % of the particles have a smaller size. The width of particle size distribution was estimated by the span, calculated with Equation 1 [START_REF] Fournaise | Impact of formulation on reconstitution and flowability of spray-dried milk powders[END_REF][START_REF] Guerin | Lactobacillus rhamnosus GG encapsulation by spray-drying: Milk proteins clotting control to produce innovative matrices[END_REF][START_REF] Salameh | Physico-chemical and rheological properties of Lebanese kishk powder, a dried fermented milk-cereal mixture[END_REF].

𝑠𝑝𝑎𝑛 =

𝐷 90 -𝐷 10 𝐷 50

(Equation 1)

Water content

The water content was determined by the mass loss of 2.5 g powder after drying at 103 °C during at least 3 h following ISO 5537:2004 [START_REF] Afnor | Dried milk -Determination of moisture content (Reference method)[END_REF].

Water activity

Water activity (aw) was determined with a HygroPalm23-AW portable water activity-meter (Rotronic, France) in a temperature-controlled room at 20 °C using a 3 cm powder layer following ISO 21807:2004 [START_REF] Afnor | Microbiology of food and animal feeding stuffs -Determination of water activity[END_REF].

Chemical composition of powder bulk

The bulk composition (i.e. contents in carbohydrates, lipids, proteins, minerals, water) was determined only for whole and skim milk powders. For all other powders, data about powder chemical composition were extracted from supplier technical sheets (Table S1,

Supplementary material).

The total nitrogen content and the non-proteic nitrogen content corresponding to the soluble fraction remaining after precipitation with trichloroacetic acid were determined by the Kjeldahl method. Nitrogen contents were converted into protein contents using a 6.38 conversion factor.

Total lipids were quantified with a method adapted from [START_REF] Folch | A Simple Method for the Isolation and Purification of Total Lipides from Animal Tissues[END_REF]. 5 g powder was dissolved into a 2:1 (v/v) mixture of chloroform/methanol for lipid extraction. The mixture was stirred at 700 rpm during 15 min. Then, the soluble phase containing sample lipids was separated by filtration on a sintered glass filter of 10 -16 μm porosity and recovered in a round-bottom boiling flask that was previously dried and weighted. The solvent of the soluble phase was removed with a rotary vacuum evaporator (Heidolph Laboratora 4000) at low stirring and 40 °C. The flask empty from residual solvent was dried at 103 °C for 15 min to ensure complete solvent evaporation and finally weighted.

Minerals content was determined by calcining 2 g sample at 550 °C during 12 h.

Lactose content was obtained by difference with other components (Equation 2):

% lactose = 100 -(% water + % proteins + % minerals + % lipids) (Equation 2)

Powder surface composition characterization by X-ray photoelectron spectroscopy

XPS measurements are performed in ultra-high vacuum (10 -8 Pa). The surface of the powder is irradiated, which causes a complete transfer of X-ray photon energy to atomic electrons of the sample. When the electron binding energy Eb is lower than the photon energy hʋ, with h the Planck constant (6.63 × 10 -34 m 2 .kg.s -1 ) and ʋ the radiation frequency (s -1 ), an electron is emitted from the atom with a typical kinetic energy Ek related to Eb (Equation 3):

𝐸 𝑏 = ℎ𝜐 -𝐸 𝑘 (Equation 3)
Analyses were realized with a Kratos Axis Ultra (Kratos Analytical, Manchester, UK) X-ray photoelectron spectrometer with a monochromatic Al X-ray source at 150 W. The analytical area was about 700 µm x 300 µm and the analytical depth 10 nm. Powder samples were attached to a sample holder with double-sided conductive tape. XPS spectra were then recorded and treated using the Kratos Vision software. Quantification was performed using the photoemission cross-sections and transmission coefficients given in the Kratos Vision package.

The main elements (C, O, N, P, Ca) detected at powder surface were identified by means of their respective binding energy. Also, the carbon peak was deconvoluted into its main chemical For milk powders, it was assumed that nitrogen was present in proteins only; therefore, the surface composition can be calculated using the matrix method based on theoretical atomic composition of main components [START_REF] Fournaise | Impact of formulation on reconstitution and flowability of spray-dried milk powders[END_REF][START_REF] Nijdam | The effect of surface composition on the functional properties of milk powders[END_REF][START_REF] Gaiani | Étude des mécanismes de réhydratation des poudres laitières[END_REF][START_REF] Nikolova | Impact of Spray-Drying Process Parameters on Dairy Powder Surface Composition and Properties[END_REF]. Briefly, the atomic proportions of carbon, oxygen, and nitrogen were used in a matrix formula (Equations 4.1-4.3) in order to deduce the surface proportions in the different sample compounds: αLa for lactose (La), αP for proteins (P), and αLi for lipids (Li).

𝐼 𝐶 = α P × 𝐼 𝐶.𝑃 + α La × 𝐼 𝐶.𝐿𝑎 + α 𝐿𝑖 × 𝐼 𝐶.𝐿𝑖 (Equation 4.1)

𝐼 𝑂 = α P × 𝐼 𝑂.𝑃 + α La × 𝐼 𝑂.𝐿𝑎 + α 𝐿𝑖 × 𝐼 𝑂.𝐿𝑖 (Equation 4.2)

𝐼

Powder reconstitution behavior

Wettability

Wettability measurement was adapted from the IDF (1987) method: in this work, the wettability was defined as the time in seconds taken by 1.00 ± 0.01 g of powder to become wet when deposited at the surface of 10.0 g ± 0.1 g distilled water at 25 °C in a 20 mL beaker under magnetic stirring at 600 rpm.

Reconstitutability followed by conductimetry

Experimental setup. An experimental setup (Figure 1 Where:

-c(t) designates normalized conductivity (-); -κ(t) stands for conductivity at time t (µS.cm -1 );

κini represents the initial conductivity, i.e. distilled water conductivity (close to 0 µS.cm -1 );

κfin corresponds to the final conductivity (µS.cm -1 ).

Consequently, all normalized conductivity curves started at 0 and ended at 1. These curves had a sigmoidal shape (Figure 2 -right) which can be related to the different steps of powder reconstitution:

 first, upon powder wetting/swelling and sinking, very few powder components were solubilized and conductivity slightly increased very slightly over a rather long time;

 then, powder dispersion and solubilization occurred, leading to a marked conductivity increase;

 finally, as the amount of powder to reconstitute became low, conductivity still increased but evolved more slowly, until reaching the final conductivity once all soluble powder material was solubilized.

Curve fitting. The normalized conductivity curves were fitted with the OriginPro 2019 software (OriginLab Corporation) using the least squares method solved by the Levenberg Marquardt iteration algorithm. It was found that the Hill model (Equation 6) was the most suitable and simple model to fit normalized conductivity curves of all powders [START_REF] Hill | The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves[END_REF]:

𝑐(𝑡) = 𝑐 0 + (𝑐 ∞ -𝑐 𝑜 ) 𝑡 𝑛
𝑘 𝑛 +𝑡 𝑛 (Equation 6)

With:

-𝑐 0 , initial normalized conductivity (%);

-𝑐 ∞ , final normalized conductivity (%); -t, time (s); -k (s) and n (-), Hill model time constant and power, respectively.

For all powders, initial and final normalized conductivity being equal to 0 % and 100 %, respectively, the Hill model could simply be rewritten as (Equation 7):

𝑐(𝑡) = 𝑡 𝑛
𝑘 𝑛 +𝑡 𝑛 (Equation 7)

Model parameter k corresponds to the time needed to reach 50 % normalized conductivity. The slope of normalized conductivity curve at t = k was found equal to 𝑛 4𝑘

, then it can be considered that the model parameter n gives an indication of the powder reconstitution rate once wetted, swelled, and sinked, i.e. in the dispersion and solubilization steps of powder reconstitution.

Last, powder reconstitution time was deduced from obtained Hill model by taking the time needed to reach 95 % normalized conductivity, it was then noted t95% and expressed in seconds.

Statistical analysis

All analyzes were carried out on the thirty-six powders and performed in triplicate.

Principal Component Analysis (PCA) was used to link powder physicochemistry and manufacturing process to reconstitution behavior using Unscrambler (CAMO software AS, Norway). Due to the huge number of powders analyzed, the objective of PCA was to determine which main underlying factors could explain the observed differences in reconstitutability.

Results and discussion

Impact of particle size distribution and lipids content on powder reconstitution

To highlight the impact of particle size distribution and lipids content on powder reconstitution behavior, a focus is carried out here on instant coffee and milk powders.

Powders physicochemical characterization

Raw and ground instant coffee powders presented similar chemical composition and differed in median particle size D50 (around 1 630 µm and 31 µm, respectively) (Tables S1 &S2, Supplementary Material). Raw instant coffee powder had a monomodal particle size distribution with a span around 1, whereas the particle size distribution of ground instant coffee powder was bimodal with a span around 13, which was consistent for an agglomerated powder.

On the opposite, skim and whole milk powders differed in chemical composition and presented similar median particle sizes D50 (around 80 µm) and monomodal particle size distributions (Tables S1 &S2, Supplementary Material). Skim milk powder presented a low lipid content (1.5 % on dry basis), whereas whole milk powder was rich in lipids (26 % on dry basis).

The water contents of coffee and milk powders were comprised between 1.6 and 2 % on wet basis and their water activity ranged between 0.16 and 0.34 (Table S3, Supplementary Material), which is favorable to their preservation [START_REF]FAO (Food and agriculture organization of the united nations)[END_REF][START_REF] Hill | The possible effects of the aggregation of the molecules of haemoglobin on its dissociation curves[END_REF].

Particle surface characterization

The surface atomic proportions of instant coffee and milk powders are displayed in Figure 3 left. Carbon, oxygen, and nitrogen surface proportions were similar for all powders except for whole milk powder that had more surface carbon and less surface oxygen and nitrogen. Surface and bulk compositions of milk powders were compared in Figure 4. The bulk composition was measured by classical chemical analysis techniques whereas the surface composition was calculated with the matrix (Equations 4). It appears that whole milk powder was mainly covered by lipids, whereas skim milk powder presented a surface overrepresentation mostly in lipids but also in proteins in a lesser extent [START_REF] Murrieta-Pazos | Composition gradient from surface to core in dairy powders: Agglomeration effect[END_REF]. These differences between bulk and surface compositions are known to strongly influence powder reconstitution behavior [START_REF] Kim | Surface characterization of four industrial spray-dried dairy powders in relation to chemical composition, structure and wetting property[END_REF]. For coffee powders, it was not possible to use the matrix method as nitrogen is also present in non-proteic compounds like caffeine (and not only proteins as for milk powders). Nevertheless, the surface atomic composition was still informative. It was very close to that of skim milk powder for carbon and oxygen, but nitrogen contents were slightly lower (Figure 3 -left). Carbon bond ratios of the four powders are presented in Figure 3 -right. Again, only whole milk powder had a clearly more hydrophobic surface than the three other powders.

Powder reconstitution kinetics

Impact of particle size on reconstitution. The reconstitution behavior of raw and ground instant coffee powders, differing in median particle size, is detailed in Table 1 and Figure 5A. The wetting step is known to be highly linked to the median particle size, as well as bulk and surface compositions. As previously shown, the bulk and surface composition of instant coffee powders were identical (Figure 3 and Supplementary Material Table S1). It appeared that wettability was better for the raw instant coffee powder composed of larger particles (23 s wetting time)

than for the ground instant coffee powder (52 s wetting time). Indeed, a high proportion of large and/or agglomerated particles is known to improve powder wettability [START_REF] Hogekamp | Rehydration of Food Powders[END_REF][START_REF] Schuck | Analytical Methods for Food and Dairy Powders[END_REF]. The reconstitution time was also shorter for raw instant coffee powder probably owing to its shorter wetting step. Hill model parameters, time constant k and power n, were also informative about the reconstitution kinetics. k, corresponding to the time needed to reach half of the final conductivity, was doubled for the ground instant coffee powder, denoting slower reconstitution kinetics. Moreover, the slope of the normalized conductivity curve at half maximal normalized conductivity, equal to n 4k

, could be viewed as an indicator of reconstitution rate; for instant coffee powders, n 4k equaled 0.050 and 0.020 s -1 for raw and ground samples, respectively. This confirms the slower reconstitution rate of ground instant coffee powder, likely due to its lower median particle size preventing its correct wetting and dispersibility [START_REF] Freudig | Dispersion of powders in liquids in a stirred vessel[END_REF][START_REF] O'mahony | B: Proteins: Applied aspects[END_REF]; indeed, interparticular cohesive forces are expected to be stronger between small particles owing to their higher contact surface [START_REF] Fu | Effect of particle shape and size on flow properties of lactose powders[END_REF][START_REF] Zhou | Effect of host particle size on the modification of powder flow behaviours for lactose monohydrate following dry coating[END_REF].

Impact of lipids content on reconstitution.

Whole and skim milk powders presented similar median particle sizes but differed in chemical composition through their lipids content. Their reconstitution behavior is presented in Table 1 and Figure 5B. The bulk and surface compositions of these powders markedly differed. Whole milk powder, having a well higher surface lipid content, had a well higher surface hydrophobicity [START_REF] Hogekamp | Rehydration of Food Powders[END_REF][START_REF] Murrieta-Pazos | Composition gradient from surface to core in dairy powders: Agglomeration effect[END_REF]. This surely caused that whole milk powder had a wetting time (68 s) longer than skim milk powder (35 s), the latter having a more hydrophilic surface which is known to improve wettability. These results met literature regarding the negative influence of surface hydrophobicity on powder wetting [START_REF] Wu | Effects of spraying surfactants in a fluidised bed on the rehydration behaviour of milk protein isolate powder[END_REF][START_REF] Ji | Enhanced wetting behaviours of whey protein isolate powder: The different effects of lecithin addition by fluidised bed agglomeration and coating processes[END_REF][START_REF] Kim | Surface characterization of four industrial spray-dried dairy powders in relation to chemical composition, structure and wetting property[END_REF][START_REF] Gaiani | Surface composition of dairy powders observed by X-ray photoelectron spectroscopy and effects on their rehydration properties[END_REF]. The reconstitution time (t95%) was shorter for the skim milk powder, confirming the deleterious effect of surface lipids on reconstitution. This may be related to wettability that is well impaired at higher surface lipid content. Hill model parameters (time constant k and power n) were greater for skim milk powder, indicating a higher reconstitution rate and a shorter reconstitution time. This was confirmed by the calculation of the slope of the normalized conductivity curve at half-height (which is an indicator of reconstitution rate as previously mentioned):

𝑛 4𝑘 equaled 0.029 and 0.018 s -1 for skim and whole milk powders, respectively.

This confirms the slower reconstitution rate of whole milk powder.

Surface composition of the thirty-six food powders

On the best knowledge of the authors, food powder surface analysis by XPS has been performed only on few powders (i.e. dairy or wheat powders) [START_REF] Kim | Surface characterization of four industrial spray-dried dairy powders in relation to chemical composition, structure and wetting property[END_REF][START_REF] Saad | Impact of regrinding on hydration properties and surface composition of wheat flour[END_REF]. For the first time, a large investigation was performed on thirty-six food powders in order to collect surface atomic proportions (in carbon, oxygen, and nitrogen), as well as C/O and C-C/(other carbon bonds) ratios as indicators of surface hydrophobicity (Table S2, Supplementary Material). It appears that surface chemical composition was highly variable for investigated powders. Three hypothesized powder groups were constituted on the basis of surface hydrophilicity/hydrophobicity (Figure 6). The most hydrophilic surface powders were The loading plot shows how strongly each powder physicochemical characteristic influences the variability amongst powders, represented according to the two principal components PC1 and PC2 (Figure 7). PC1, corresponding to the horizontal axis and representing 34 % of powder characteristics variability, was linked to reconstitution times (t95%, k, n) and manufacturing process. PC2, associated with the vertical axis and corresponding to 27 % powder variability, was correlated to median particle size (D50), wetting time, and surface chemical composition.

Hence, a long wetting time was related to a small median particle size and an elevated surface hydrophobicity [START_REF] Kim | Surface characterization of four industrial spray-dried dairy powders in relation to chemical composition, structure and wetting property[END_REF][START_REF] Szulc | Surface modification of dairy powders: Effects of fluid-bed agglomeration and coating[END_REF]. The relationship between median particle size and wettability had already been demonstrated on milk powders [START_REF] Chever | Agglomeration during spray drying: Physical and rehydration properties of whole milk/sugar mixture powders[END_REF], the current work thus makes it possible to generalize this relationship to food powders whatever their composition and manufacturing process. Hill model parameters logically appeared to be correlated with the reconstitution time: The reconstitution behavior of milk powders has been extensively described in the literature contrarily to other food powders [START_REF] Gaiani | Surface composition of dairy powders observed by X-ray photoelectron spectroscopy and effects on their rehydration properties[END_REF][START_REF] Caric | Milk powders, Physical and Functional Properties of Milk Powders[END_REF][START_REF] Fang | On quantifying the dissolution behaviour of milk protein concentrate[END_REF]. For the first time, the main factors influencing the reconstitution are identified for a large variety of powders. Manufacturing processes, mainly grinding and spray-drying, were associated to long and short reconstitution times, respectively.

Indeed, cereal powders (couscous powders, flour, semolina, wheat powders), obtained by grinding, had slow reconstitution kinetics. Besides, small particle and hydrophobic surface powders were correlated to long wetting times, whereas large particle and hydrophilic powders were associated with short wetting times. Finally, powder within each of red and green groups were also similar in terms of bulk composition (high lipids and high sugar contents, respectively).

Conclusion

For the first time, the main factors influencing powder reconstitution behavior (median particle size, chemical composition, surface composition, and manufacturing process) have been identified for a large number of food powders. The current study permitted to confirm and generalize the knowledge developed so far on a limited number of powders and identify four reconstitution behaviors. The industrial interest of the proposed classification resides in the fact that powder reconstitution properties can be modulated by changing powder formulation (particle size distribution, surface composition, bulk composition, etc.) without modifying the reconstitution conditions (stirring speed, temperature, etc.). It would be interesting to go one step further by linking powder physicochemical characteristics and manufacturing process to the different reconstitution steps.

  bonds (C-(C, H); C-(O, N); C=O; O-C=O).

  𝑁 = α P × 𝐼 𝑁.𝑃 + α La × 𝐼 𝑁.𝐿𝑎 + α 𝐿𝑖 × 𝐼 𝑁.𝐿𝑖 (Equation 4.3) I C , I O , and I N are the mole fractions of carbon, oxygen, and nitrogen at the sample surface (these values were directly obtained by XPS from the C1s, O1s, and N1s peak areas ); I C.P , I C.La , and I C.Li are the mole fractions of carbon in proteins, lactose , and lipids, respectively; I O.P , I O.La , and I O.Li are the mole fractions of oxygen in proteins, lactose, and lipids, respectively; I N.P , I N.La , and I N.Li are the mole fractions of nitrogen in proteins, lactose, and lipids.

  Conductivity normalization. Upon powder reconstitution, conductivity evolved from an initial value of 0 µS/cm (the real value was inferior to the conductimeter sensitivity) to a final value that depended from powder nature (Figure2-left). Therefore, to be able to fit conductivity curves and determine reconstitution times, conductivity values averaged from the three experimental replicates were normalized following Equation 5:

3 . 3 .

 33 associated with the lowest ranges of C/O and C-C/other C bonds ratios of 0 -2 and 0 -1, respectively. Intermediate (slightly hydrophobic) powders corresponded to ranges of C/O and C-C/other C bonds ratios of 2 -4 and 1 -2, respectively. The most hydrophobic surface powders were defined for the highest ranges of C/O and C-C/other C bonds ratios of 4 -7 and 2 -4, respectively. Sugars, acerola juice, lactose, agar, xanthan, pectin and baking soda were then sorted as the most hydrophilic surface powders of the study. On the opposite, hazelnut, cocoas, milk protein concentrate, whole milk and whey proteins powders were classified as the most hydrophobic surface powders of the study. Many investigated food powders (cereal powders, flours, coffee powders, couscous powders, instant mash potatoes, etc.) fell into the intermediate category of slightly hydrophobic surface. Principal component analysis linking physicochemical properties, manufacturing process, and reconstitution behavior of the thirty-six food powders A principal component analysis was performed to link powder physicochemical properties and their reconstitution behavior. The main objective was to capture the variability of data in a few principal components, which encompass the most variation of the dataset. The data taken into consideration in the principal component analysis are related to powder bulk and surface composition, manufacturing process, median particle size, and reconstitution properties (wetting time and reconstitution time) (Tables S1, S2, and S3, Supplementary Material).

a

  high k value or a low n value (both inducing a low slope of the normalized conductivity curve at half maximal normalized conductivity n 4k value) were related to a high reconstitution time, i.e. slow reconstitution kinetics. The score plot locates investigated powder samples on the PC1 × PC2 plot (Figure8). Powders situated on the bottom side (negative PC2) had longer wetting times, whereas powders found in the right side (positive PC1) were linked to long reconstitution times. Therefore, four groups of powders were defined on the basis of their reconstitution behavior: short wetting and reconstitution times (green); long wetting time and short reconstitution time (yellow); short wetting time and long reconstitution time (orange); long wetting and reconstitution times (red). The sorting of investigated powders into these four groups were in great accordance with the literature.

Figure 1 .

 1 Figure 1. Experimental setup with a focus on the geometrical characteristics of the A200 Impeller

Figure 2 .

 2 Figure 2. Temporal evolution of conductivity upon reconstitution before (left) and after (right)

Figure 3 .

 3 Figure 3. Surface atomic compositions (left) and carbon bond ratios (right) of instant coffee, ground

Figure 4 .

 4 Figure 4. Bulk and surface compositions of skim and whole milk powders.

Figure 5 .

 5 Figure 5. Effect of median particle size (A -left) and fat content (B -right) on powder reconstitution

Figure 6 .

 6 Figure 6. Hypothesized classification of investigated powders into three groups (more hydrophobic,

Figure 7 .

 7 Figure 7. Correlation scores obtained from PCA for the physicochemical and reconstitution

Figure 8 .

 8 Figure 8. Classification of the thirty-six investigated powders according to their wettability and

Figure( s ) 2 Figure 1 .

 s21 Figure(s) Click here to access/download;Figure(s);Figure_Table_PT_corrected.docx

Figure 2 .

 2 Figure 2. Temporal evolution of conductivity upon reconstitution before (left) and after (right)

Figure 3 .

 3 Figure 3. Surface atomic compositions (left) and carbon bond ratios (right) of instant coffee, ground

Figure 4 .

 4 Figure 4. Bulk and surface compositions of skim and whole milk powders.

Figure 5 .

 5 Figure 5. Effect of median particle size (A -left) and fat content (B -right) on powder reconstitution kinetics.

Figure 6 .

 6 Figure 6. Hypothesized classification of investigated powders into three groups (more hydrophobic,

Figure 7 . 6 Figure 8 .

 768 Figure 7. Correlation scores obtained from PCA for the physicochemical and reconstitution characteristics

  ) was developed to follow powder reconstitution kinetics by conductimetry. It was constituted of a jacketed glass reactor (GL18,

	Grosseron) thermostated by a heated water bath (Eco Gold, Lauda), a mechanical stirrer (ZR
	2102 control, Heidolph), and a 5.08 cm diameter impeller (Pitch blade turbine 2" 32Ra, Fusion
	fluid equipment). Powder reconstitution kinetics were followed by conductimetry
	(SevenCompact S230, Mettler Toledo) with a conductivity probe (InLab 731-ISM, Mettler
	Toledo) ranging from 0.01 to 1 000 mS.cm -1 . Powder was fed by a vibratory feeder (DR 100

Model, Retsch, France). Vessel design and reconstitution conditions were based on the literature (Figure

1

)

[START_REF] Mitchell | Mapping the rate-limiting regimes of food powder reconstitution in a standard mixing vessel[END_REF][START_REF] Mitchell | Surface tension-driven effects in the reconstitution of food powders[END_REF][START_REF] Goalard | Characterization of the Dispersion Behavior of Powders in Liquids[END_REF][START_REF] Galet | The Wetting Behaviour and Dispersion Rate of Cocoa Powder in Water[END_REF][START_REF] Schober | Effect of vortex formation on powder sinkability for reconstituting milk powders in water to high solids content in a stirred-tank[END_REF]

. Powder reconstitution experiments were performed with distilled water at 25.0 ± 0.2 °C in the following conditions: 10.0 % (w/w) powder/water mass ratios with a total mass (powder + water) fixed at 2.650 kg, 800 rpm stirring rate, and 3.6 g/s feeding rate. Experiment duration was adapted for each powder between 15 min and 2 h.

Table 1 .

 1 Wetting and reconstitution times, as well as Hill model parameters (time constant k and power n) and coefficient of determination (R²) of normalized conductivity curve fitting by Hill model of investigated milk and coffee powders.

	Tables
		Wetting time (s)	Reconstitution time t95% (s)	Hill model time constant k (s)	Hill model power n (-)	Hill model coefficient of determination R²
	Skim milk powder 35 ± 4	86.0 ± 10.0	27.2 ± 2.92 2.76 ± 0.13	0.95
	Whole milk powder	68 ± 8 105.0 ± 10.4	133.6 ± 9.18 0.96 ± 0.01	0.98
	Instant coffee powder	22 ± 2	34.7 ± 1.1	8.9 ± 0.2	2.16 ± 0.08	0.98
	Ground instant coffee powder	51 ± 4	106.5 ± 6.8	26.7 ± 3.7	2.15 ± 0.31	0.98

Acknowledgements

This research was partially supported by a grant from the International Fine Particle Research Institute (IFPRI). We thank Martine MALLET and Aurélien RENARD from the Spectroscopy and Microscopy of Interfaces platform of the LCPME (UMR 7564 CNRS-UL, University of Lorraine) for performing XPS analysis and data treatment. The authors acknowledge support of the LIBio by the "Impact Biomolecules" project of the "Lorraine Université d'Excellence"(Investissements d'avenir -ANR 15-004).

Highlights

 Food powders were sorted according to their reconstitution behavior