Jacques Jayez

How hard are hard triggers? *

Keywords: experimental semantics, presupposition, accommodation, hard triggers

 distinction between hard and soft triggers from an experimental point of view. We show that there are apparent counterexamples to the distinction, discuss their status and describe future experiments aiming at clarifying the processing issues that form the core of the problem.

Introduction

The literature on presuppositions (PP) suggests that not all PP triggers are equal. Some of them seem to entail rather strictly their PP, whereas others are more tolerant. There are several versions of this basic intuition. In this paper, we study [START_REF] Abusch | Lexical alternatives as a source of pragmatic presuppositions[END_REF][START_REF] Abusch | Presupposition triggering from alternatives[END_REF] approach, which is based on an explicit suspension test, illustrated in (1), where the PP triggers are underlined.

(1) a. I don't know whether he participated but, if he won, . . . b. ?? I don't know whether he participated, but, if Mary participated too, . . .

For most speakers, introspection leads to reject (1b). Items that behave like too are called hard triggers (HT) by Abusch. Those which behave like win are soft triggers (ST). This paper is mainly an experimental contribution to the study of the distinction between HT and ST. In section 2, we present briefly a number of works where relevant or analogous distinctions are drawn, before summarizing Abusch's proposal in section 2.5. In section 3, we describe three pilot experiments that address directly the HT vs. ST distinction. In spite of their limits, they show that the notion of local accommodation, which provides a basis for the HT vs. ST distinction, remains unclear in judgment tasks, because it involves processing issues that are beyond introspection. In section 4, we explain what the possible options are and set an agenda for our future experimental work using eye-tracking.

Variation in strength

2.1. Hard and soft triggers: the sources of the distinction

The difference between hard and soft triggers (HT and ST) was first noticed by [START_REF] Karttunen | Some observations on factivity[END_REF]. Karttunen's general idea is that, in order for a PP to be projected, this PP must be satisfied by the context sentence. However, different triggers can have different projection properties, even when they are put in the same context. For example, consider the difference between (2a) and (2b).

(2) a. If I regret later that I have not told the truth, I will confess it to everyone. b. If I realize/discover later that I have not told the truth, I will confess it to everyone.

Factive and semifactive verbs behave in different ways with respect to local accommodation. In (2a), the PP projected by a full factive like regret (i.e. 'I have not told the truth') is resistant to suspension, whereas in (2b) semifactives like realize or discover project a PP that is more easily suspendable.

PP projection and local accommodation

Zeevat (1992) establishes a threefold distinction, between lexical triggers, resolution triggers and triggers like too and again, that do not belong either to the first or to the second group. Such a distinction is based on the different accommodation properties of triggers. First, lexical triggers (e.g. factives) involve concepts and concept applicability conditions: the concepts can be applied only if these conditions are present in the context. The conditions for the concept to be applied are the lexical PP of the concept. This means that the applicability of the concept depends on the PP being true. Notice that, in Zeevat's framework, lexical triggers follow Heim's notion of accommodation [START_REF] Heim | On the projection problem for presuppositions[END_REF].

Second, resolution triggers (e.g. definite descriptions, when and after clauses) are clearly anaphoric: like anaphora, they set up relations between different parts of a text. Thanks to their indexical nature, they refer to their antecedent and deliver a value to the current context in order to build a new concept. Although they attribute some properties to their referent, they do not demand these properties to be part of the agent's beliefs. This suggests that resolution triggers follow Van der Sandt's account of accommodation (Van der Sandt, 1989), as Van der Sandt's accommodation rule simply requires that the trigger have access to its antecedent or to the accommodation site.

The third category, which seems to intersect with Abusch's definition of HT, includes adverbs like too, another and again. Such triggers have relaxed accessibility constraints, in that they have the property of identifying antecedents in parts of the context that are not accessible to the other triggers. As showed by (3a,b), for example, too is able to look for its antecedent in both the consequent and the antecedent of a conditional.

(3) a. If John has time, he will visit us tonight. Mary will come too. b. If John will come tonight, we must warn Fred. Mary will come too.

However, this account seems to be incomplete in three respects. First, as claimed by Zeevat him-self, the accessibility constraints of too are not clear: the access to normally inaccessible parts does not arise in all cases. Further, it is not possible to account for such an irregular behavior on the basis of typical accommodation rules. Finally, it is unclear whether there is a principled reason that separates the third category of triggers from the resolution group. Two types of contrasts are taken into account. The first compares the answers addressing the PP with the answers addressing the main content, while the second compares the positive and the negative answer. The authors make two predictions with respect to trigger behavior: in the case of PP denying, endorsing the main content should be better for the anaphoric than for the lexical triggers, while refuting the main content should be better for the lexical ones.

Concerning the results, as it was predicted, refutation is significantly better than endorsement for lexical triggers. However, two unexpected results come up. First, still behaves like a lexical trigger. Second, there is a difference between too on one side and again and still on the other. The hypothesis predicts that they should behave in the same way, but the results show that, for too, endorsing is better than refuting. This suggests that the distinction between lexical and resolution triggers is not always clear. Amaral et al.'s results are quite difficult to interpret. They try to give an empirical account of trigger classification, but they do not completely succeed in providing clear experimental evidence for it. Anyway, their results confirm that the category of PP triggers is not uniform.

PP projection and contextual neutralization

Abbott (2006) explicitly formulates the question of why HT are so hard to be locally accommodated. In her account, the distinction between HT and ST is based on contextual neutralization, as it is easy to find contexts which suspend soft PP. Look, for instance, at (5a,b): when discover and know are put in the antecedent of a conditional or in a modal context, the PP they trigger is easily neutralized.

(5) a. If anyone discovers that the rumour was a hoax, it will be a scandal. b. Perhaps God knows that we will never reach the stars.

ST include the following structures: cognitive factive predicates (e.g. be aware, discover, know), change of state verbs (stop, start, continue) and achievement verbs with a preparatory phase (e.g. win). HT, on the other hand, include emotive factive predicates (e.g. forget, regret, be odd), definite descriptions, cleft constructions and manner adverbials (also, even, too, etc.). Abbott's framework is based on the notion of detachment. The idea is that a speaker who chooses to add optional information intends to convey it. In such a case, it is easy to detach optional information through rephrasing. Therefore detachment expresses the property of finding a form which expresses the main content without expressing the PP. As there is no other reason for that particular information to be included in the utterance, we expect it to be not easily neutralizable by context. This argument can be applied to the HT vs. ST distinction, as the PP of HT corresponds to pieces of information which are orthogonal to the main content. Since hard PP are detachable, they cannot be easily neutralized. Consider, for instance, the contrast between (6a) and (6b).

(6) a. Mary hit the target again. b. Mary hit the target.

What would be the point of using (6a) instead of (6b)? The only reason for the speaker to include again in the utterance is that she wants to convey that Mary hit the target previously. In that case, the sentence could be easily reformulated detaching the information communicated by again. Following Abbott's rule, we say that again is not easily neutralized by context, therefore it can be considered as a HT. On the contrary, the PP of a ST is hardly detachable, thus it can be easily neutralized by context.

However, this analysis has two main problems. First, as noticed by Abbott, non-cognitive factives like regret, be sorry etc., should be defined as HT: they are not easily detachable, hence they should be neutralizable. But we find exactly the contrary. Non-cognitive factives are resistant to local accommodation. Second, consider a verb like stop: in Abbott's account, it should be considered as a ST, hence it should be nondetachable. Nevertheless, consider the sentences in ( 7): (7b) is a part of the main content of (7a). Then, why is it not a viable, detached alternative to the sentence containing the PP? Finally, it is not clear whether Abbott neutralization and Abusch epistemic suspension are one and the same. In fact, Abbott claims that Abusch's examples are cases of contextual neutralization. However, when we look at Abusch's sentences, we see that they are better defined as cases of PP suspension, namely cases in which the truth of the PP is left hanging.

PP projection and at-issueness

Abbott's notion of detachment implies a distinction between the optional information and the information which is at-issue. The notion of at-issueness has been employed to provide an account of projection behavior [START_REF] Simons | What projects and why[END_REF]. At-issueness is defined with respect to Question Under Discussion à-la Roberts : a proposition p is at-issue if and only if the speaker intends to address the QUD through the question whether p. The idea is that only not-at-issue contents can project. PP are usually not-at-issue, so they show a projective behavior. However, PP can be at-issue (even if, usually, they are not). In that case, they fail to project. In the example below (taken from Simons et al. ( 2010)), the A sentence can be an answer to both question Q1 and question Q2. In the first case the PP triggered by know (i.e. 'Harry is dating Sally') is not-at-issue, hence it can project. In the case of Q2, on the contrary, the PP cannot project as it is at-issue.

(8) Q1 -What does Bill think about Harry dating Sally? Q2 -Is Harry dating Sally? A -Bill doesn't know that he is. [START_REF] Xue | Correlation between presupposition projection and at-issueness: an empirical study[END_REF] show experimentally the correlation between at-issueness and projection behavior. They construct two experimental tasks in order to test the difference between four PP triggers: know, find out, too, again. In the first task, sentence-question pairs are provided. Each pair includes one target conditional sentence and a question task. As showed by (9b), questions aim at rejecting the PP triggered in the target sentence (9a). Moreover, three possible answers are provided, cf. (10). If the subjects think that it is possible that Christine does not like tea, the target PP fails to project. On the contrary, if they think that it is not possible that Christine does not like tea, the PP triggered by know is projected.

(9) a. If Paul knows that Christine likes tea, he will give her a teapot as a present. b. Is it possible that Christine doesn't like tea?

(10) a. Yes, it's possible. b. No, it's not possible. c. I don't know.

Results show that the PP triggered by too and again can be more easily projected than the PP triggered by know and find out. However, there is a significant difference between know and find out that cannot be explained in Xue and Onea's framework, based on at-issueness.

In the second task, the same four triggers are tested with respect to at-issueness. As shown in (11), each stimulus consists of a target sentence and three answer options. All the three answers contradict the PP triggered: (11d) constitutes a direct denial, whereas (11c) and ( 11b) are more indirect. The prediction is that if the PP is at-issue, the subjects will deny it directly.

(11) a. Tina has just found out that Max is on vacation. b. Yes, and Max is not on vacation at all. c. Yes, but Max is not on vacation at all. d. No, Max is not on vacation at all.

Analyzing the results, Xue and Onea remark that the PP triggered by know are more often rejected than the PP triggered by find out, which entails that they are more likely to be at-issue. Moreover, the PP triggered by find out are more likely to be at-issue than those triggered by too and again. This suggests that each PP trigger is associated to a probability of reconstruction of a not-at-issue context. However, some problems remain unsolved. First (as noticed by Xue and Onea themselves), it is not clear whether the observed correlation between projection and not-at-issueness is a causal one. Second, it has been noted that triggers like too and again can hardly be at-issue. How come? Given that at-issueness is pragmatically determined, is the probability of not-at-issueness influenced by the lexical nature of triggers? Is there a link between the semantic content of triggers and their ability to appear in an at-issue context? Finally, the structures of the sentences used in the two tasks are quite different: in the first experiment, the trigger is embedded under a suspending operator, whereas in the second experiment the PP projects as usual. In order to test the suspension properties of different categories of PP, triggers should be embedded in target sentences with the same structure. This suggests that it would be useful to find a sort of suspension-test structure. Such a structure is provided by [START_REF] Abusch | Lexical alternatives as a source of pragmatic presuppositions[END_REF][START_REF] Abusch | Presupposition triggering from alternatives[END_REF].

Abusch's suspension test

Abusch's main idea (2002; 2010) is that HT are resistant to local accommodation, whereas ST can be more easily suspended and then locally accommodated. Abusch provides a test in order to make this property more explicit. The pattern is: I don't know whether p, but if p ′ . . . , where p ′ presupposes p. So, the test structure consists of a sequence: sentence expressing ignorance about the presupposed content + conditional sentence. The PP trigger always occurs in the antecedent of the conditional. The initial sentence suspends the presupposed content, which has then to be locally accommodated at the level of the antecedent. For instance, look at the difference between ( 12) and ( 13)-( 14). Abusch argues that the PP triggered by win passes the test, whereas in the case of too and clefts the sentence sounds "odd, if not completely inacceptable".

(12) I don't know whether John ended up participating in the Road Race yesterday. But if he won it, then he has more victories than anyone else in the history.

(13) ?? I don't know whether anyone read that letter. But if it is John who read it, let's ask him to be discreet about the content.

(14) ?? I don't know whether John read that proposal. But if Bill read it too, let's ask them to confer and simply give us a yes-no response.

Too and clefts are thus considered as cases of HT, whereas ST include the following categories: achievement verbs with preparatory phases (e.g. win), inchoatives (e.g. break, grow up, dry), contrastive statives (e.g. predicates such as newcomer or bachelor), affirmation-negation structures (e.g. John is in Boston and not in New York), verbs of reciprocal and accompanied action (e.g. accompany), questions and intonational focus.

Surprisingly, the status of too as a HT, which is apparently unobjectionable, proves less robust than currently believed. Consider (15). It seems that it makes perfect sense: I'll avoid the party because if I go and John goes to, there will be unpleasant consequences. ( 15) is difficult to interpret without assuming some local accommodation.

(15) I won't go to the party because, if John goes too, I'll have to endure the kind of stupid conversation he is fond of.

An experimental approach

In order to assess the robustness of Abusch's characterization of HT, we ran three experiments.

The first two are just fast pilot experiments whereas the last one is a little more ambitious.

3.1.

A first try at investigating the perception of HT and ST

First experiment

The first experiment aimed at determining whether subjects distinguished between HT and ST.

They were asked to rate sentences on a seven-point scale of naturalness. We considered the case of too and it-clefts vs. win, with two subcases for each category.

Material There were 15 stimuli, including 6 fillers, 6 targets and 3 controls. The experimental stimuli are given below in figure 1. The control for win (win.co) makes the PP that Peter participated in the race an explicit member of the speaker's information state. An analysis with the R nparcomp package [START_REF] Konietschke | Package 'nparcomp[END_REF] provided the following table, where we show only the confidence intervals of direct interest. The numerical results at the bottom indicate the estimated probability with its lower and upper bounds at 95% confidence [START_REF] Brunner | The nonparametric behrens-fisher problem: Asymptotic theory and a small-sample approximation[END_REF].

FIG. 3 Contrasts for experiment 1 Conclusion

The results support Abusch's claim that win is a weak trigger. There is no significant difference between the case where the PP is explicit (win.co) and the other cases (win.with.ana and win.wo.ana). Additionally, the two subcases (with and without anaphor) are not different. In contrast, too.co is significantly different from the other two subcases, which are mutually equivalent. The case of clefts, which are HT according to Abusch, is slightly different since cleft.with.ana is not different from the control. We conjecture that this is related to such seemingly natural examples as ( 16). However, this kind of example needs further investigation as their interpretation apparently uses local accommodation.

(16) I don't know whether Michel read the document, but if it's him, we'll ask him to remain discreet about its content.

These observations are in need of confirmation, since we had only one sentence per category per subject, a fact which leaves open the possibility that the effect (contrast) was due to individual features of the stimulus.

Experiment 2

Material We present only the stimuli of direct interest in the context of this paper, ignoring other, more exploratory, stimuli. We had two more target sentences with win and three sentences for too.

The control was different from the two targets in order to provide more diversity.

Category Text Context

The local newspaper started a short story contest with a very tight deadline. Competitors had three days to submit their manuscript. win.with.ana I don't know whether Mark participated in the contest but, if he won, this suggests that he is fairly talented. win.wo.ana I don't know whether someone participated in the contest but, if Mark won, this suggests that he is fairly talented.

Context

The text of a paper is to be read over, in order to minimize the risks of mistakes. too.co I know that Julia checked the paper and, if Andrea checked it too, we can send it.

Context

Paul and Mary had an argument and don't want to be together on any occasion too.ign.but I don't know whether Paul will go to the party, but, if Mary goes too, it will be embarrassing. too.ign.bec I don't know whether Paul will go to the party because, if Mary goes too, it will be embarrassing.

FIG. 4 Target material for experiment 2

Method and results There were 154 participants, divided into 6 groups, with 2 controls and 2 targets for each group. Again, no group saw two targets for the same trigger or a target and its control. The net results and the contrasts are as follows.

Sentence

Conclusion

The additional stimuli for win confirm Abusch's idea that win is a ST. More interestingly, the non-parametric test delivers a mixed result for the because vs. but comparison. Because is similar to the control whereas but is significantly different. However, the two items do not differ significantly between them. This is not problematic in itself since contrasts are not intrinsically transitive with respect to non-significant difference, that is, A ≈ B & B ≈ C does not entail A ≈ C, where x ≈ y denotes the fact that there is no significant difference between x and y. Here, too.co ≈ too.ign.bec and too.ign.bec ≈ too.ign.but, but too.co ≈ too.ign.but.

Focusing on aussi (too)

The goal of experiment 3 was (i) to provide more observations on the because vs. but contrast with too and (ii) to compare the because/but forms with and without too. The intuitive motivation behind the latter test is the idea that accommodating the proposition corresponding to the PP could perhaps be independent from the presence of too. The target stimuli can be found at http: //perso.ens-lyon.fr/jacques.jayez/stimuli/.

Method and results There were 82 participants divided into 6 groups. They had to evaluate 5 sentences in 5 contexts. Each sentence had the form: I don't know whether p because/but, if p ′ too/ø, q. where p ′ too, but not p ′ alone, presupposed p. The net results and the contrasts are shown below.

Sentence These results show that because and but give rise to markedly different judgments, thus confirming the introspective observation mentioned in section 2.5 . Moreover, the fact that bec.with.too and bec.wo.too are not significantly different suggests that the accommodated proposition is made accessible independently from the presence of the too trigger. However, when compared to the control of the second experiment, the impression is different since bec.wo.too is different from the control whereas bec.with.too is not. General conclusion It is very likely that gagner (win) is a ST. The situation is much less clear for the alleged HT that we have been considering. Clefts give rise to results that are difficult to interpret and deserve new systematic experiments. Aussi (too) seems to be perfectly compatible with local accommodation in certain contexts, which invite a counterfactual interpretation. Clearly, a more precise experimental investigation would be welcome.

Experimental follow-up

Back to theory

In this section, we discuss only the case of aussi and address three questions. First, would it be possible that the observed differences are due to differences in discourse structure? Some results from experiment 2 could be taken as an indication in this direction. In addition to ignorance initial clauses (I don't know whether . . . ), we had negative sentences such as Paul won't go to the party because/but, if Mary will go too, it will be embarrassing, in the too.bec and too.but categories respectively. Too.bec is significantly better than too.but. This makes sense if one assumes that the two discourse structures obtained by making the PP explicit are different, which seems to be the case since (17a) sounds more natural than (17b), which is improved by reading the initial clause as modal or echoic/evidential ('Paul probably won't go to the party' or 'People say that Paul won't go to the party').

(17) a. Paul won't go to the party because, if he goes, and Mary goes too, it will be embarrassing.

b. ?? Paul won't go to the party but, if he goes, and Mary goes too, it will be embarrassing.

However, if the explanation for the observed contrasts was to be found in discourse structure alone, the reason why contrasts extend to ignorance structures would remain mysterious. In the ignorance counterpart to ( 17), ( 18), the two subordinate clauses with because and but seem to be much more similar than the two parallel clauses in ( 17).

(18) a. I don't know whether Paul will go to the party because, if he goes, and Mary goes too, it will be embarrassing. b. I don't know whether Paul will go to the party but, if he goes, and Mary goes too, it will be embarrassing.

We conclude that, while discourse structure can play a role, it is not the main factor, and perhaps not even a factor, in the case of ignorance structures.

A second question is the role of counterfactuality. In experiment 2, the non-ignorance version (too.because), shown in ( 19), was rated very favorably by the subjects (mean = 6.12, variance = 2.03) when compared to the non-ignorance version for but, too.but (mean = 2.52, variance = 2.54).

(19) Paul won't go to the party because, if Mary goes too, it will be embarrassing.

Clearly the future situations considered in the antecedent of the conditional are counterfactual with respect to the initial assertion that Paul won't go to the meeting. This shows that local counterfactual accommodation is possible with a HT. The situation is apparently entirely parallel for (some) ST, see (20).

(20) a. Thomas won't participate in the contest because, if he wins, he will have to say a few words in front of the entire school and he is just too shy for that. b. ?? Thomas won't participate in the contest but, if he wins, he will be very happy.

The contrast between because and but under counterfactual interpretations is not surprising. Examples like (17b) and (20b) convey a contradiction. The speaker explicitly denies some proposition p before assuming that it might be true. In the because cases, the speaker explains why p cannot be true by implying that an agent entertains some plan containing counterfactual situations where p is true. The connection between counterfactuality and planning has probably a firm cognitive basis. Recent research on the brain regions recruited in counterfactual reasoning [START_REF] Barbey | Architecture of counterfactual thought in the prefrontal cortex[END_REF] suggest an interaction between various regions specialized in the treatment of different aspects of representational networks dubbed Structure Event Complexes (SEC). SEC contain information about features present in courses of events, such as agents and their mental states, objects, actions, and context settings. The various features and the strategies that help individuals to combine them correspond in part to functionally distinct regions. Of special relevance is the fact that counter-factual reasoning demonstrably involves anticipation of regret [START_REF] Coricelli | Regret and its avoidance: a neuroimaging study of choice behavior[END_REF] and, quite generally, is triggered by problem anticipation. So, one can expect that discourses describing reasons for avoiding a course of actions are intimately connected with counterfactual accommodation. However, the way in which linguistic cues are used to construct an avoidance interpretation in the first place remain to be investigated.

The last point to be addressed is the possibility of a diagnostic concerning HT and ST. There is at least one simple hypothetical scenario that would allow us to keep the distinction between ST and HT, essentially along the lines of Abusch. Assume that the linguistic cues trigger an avoidance interpretation, which is cognitively connected, as we just saw, to a counterfactual interpretation. Then, the question arises of what linguistic cues are sufficient to help construct the observed interpretation. If the linguistic sequence before the trigger contains enough resources for the counterfactual interpretation to emerge, the missing PP is accommodated as a standard proposition, that is, independently from the trigger and without any presuppositional status. In that case, the trigger finds the antecedent it needs at the moment it is perceived and does not cause any local accommodation. We have just a normal case, where a PP trigger finds an antecedent in the context. The interpretation sequence is represented in ( 21). Alternatively, if the set of linguistic cues available before the trigger occurs is not sufficient for the required interpretation (accommodation) to obtain, we have to admit that other pieces of linguistic information, including probably the trigger itself, play a role in the derivation of the PP. In that case, it seems that Abusch's claim about HT has to be at least qualified. Since the missing PP is recovered after the trigger is seen, it is not possible to say that the trigger finds something that has been previously derived. So, one has to admit that HT are not incompatible with local accommodation. More precisely, we would suggest the following characterization.

(22) A HT is a presuppositional item or construction that looks for an antecedent which (a) is already present in the context at the moment the trigger occurs or (b) has maximum likelihood given the context.

Condition (22b) does not require that the PP be already present at the moment the trigger occurs, nor that the context be limited to information available before the trigger occurs. In fact, it is possible that a likelihood estimation needs lexical material occurring after the trigger, in our case the consequent of the if -clause.

The observations we gathered up to now suggest the following conclusions.

1. HT are not compatible with local accommodation if there is no linguistic material, different from the trigger itself, that could make the accommodated PP salient/plausible. This is supported by the difference between the too.co vs. too.ign.bec and too.co vs. too.ign.but in experiment 2 and also by the but.with.too vs. bec.with.too contrast in experiment 3, see figures 6 and 8. 2. The idea that the missing proposition could be accommodated before the occurrence of the trigger seems to clash with the observations in figure 9. If the trigger played no role other than absorbing a proposition that has been made salient/plausible before, one would expect the version with too and the version without too to pattern similarly with respect to the control. Actually, the version with too is much nearer to the control than the version without too, even though they are not mutually significantly different.

If these observations were to be confirmed, a natural conclusion would be that HT differ from ST only by the degree of likelihood they expect to find in the context. Whereas ST accept local accommodation without any extra requirement (other than consistency), HT accept local accommodation when the accommodated proposition is strongly favored by the context.

Eye-tracking experiment

In order to study the processing of our stimuli, we have planned an eye-tracking experiment based on the same type of material as for experiment 3. It is well-known that the study of eye movements can shed light on co-reference processing, see [START_REF] Nair | The time course and neural basis of anaphor resolution[END_REF] for a recent reappraisal. It is impossible to discuss here the role of all the possible eye-tracking measures and we limit our remarks to the three traditional regions of interest that are mentioned in the literature on reference resolution, that is the trigger itself (too), the post-trigger region and the antecedent. The reader is referred to [START_REF] Rayner | Eye movements in reading and information processing: 20 years of research[END_REF] for a description of the main standard measures. In what follows the 'target' is the trigger (too).

The general idea is to compare 5 conditions: a control condition where the proposition corresponding to the PP is explicit and the target can find its antecedent without accommodation, a but-with-target condition, a because-with-target condition, a but-without-target condition and a because-without-target condition. The relevant measures are at least: (a) for the target, Gaze Duration (GD) and Go-Past Time (GPT), aka Regression Path Duration, i.e. the sum of all fixations from the first to the last on the target (i.e. before leaving the target on the right), including regressive fixations on the left of the target, (b) for the post-target region, spillover effect (SP), i.e. first fixation durations on the right of the target, and Regressions Out (RO), i.e. the frequency of regressions from the post-target region to earlier parts of the text, (c) for the pre-target region, Regressions In (RI), i.e. the frequency of regressions to the pre-target region from later points in the text, typically from the target to a part of its antecedent, and reprocessing time (RT), i.e. the sum of all fixation durations on the region after the first-pass.

If, following Abusch, the HT is entirely 'passive', meaning that it does not prompt any accommodation but just expects an antecedent to be around at the moment it (the trigger) occurs, we should not find strong differences between the control and the because-with-target condition in the posttarget region (SP and RO). Since the missing proposition becomes available before the occurrence of too, processing the consequent of the if -clause, that is, the post-target region, should be similar in both cases. Moreover, when comparing the because versions with and without the trigger, the expectation is that what corresponds to the post-target region (the consequent of the if -clause) should not be subject to significantly different explorations (SP and RO). The trigger is supposed to not contribute substantially to recovering its antecedent. So, in the version without the trigger, the 'antecedent' (e.g. the proposition that Paul goes to the party) is available after the explicit if -clause (if Mary goes) has been processed, exactly like in the version with the trigger. In contrast, significant differences should appear between the but-with-target and the because-with-target conditions (at least effects on GD, GPT, RI and RT).

Alternatively, if the trigger has its say in accommodation, the eye-tracking observations will be mixed and certainly more difficult to interpret. For instance, the versions with and without the target will probably be different in the post-trigger region. The control and the because-with-target conditions should also be markedly different.

Conclusion

Obviously, there are reasons to reexamine Abusch's distinction between HT and ST. Our preliminary results suggest that the distinction could be more fine-grained than what has been generally assumed. The idea that PP triggers have various strengths is not new, as noted in section 2. However it is striking that even a trigger like too, whose 'hardness' was taken to be unproblematic, raises problems. Further experimental research should help us to determine whether its status as a HT has to be retained or partially abandoned and, more generally, whether the question of HT must be rethought.

( 7

 7 ) a. Paul has stopped smoking. b. Paul does not smoke.

  .co , win.with.ana ) p( win.co , win.wo.ana ) p( win.with.ana , win.wo.ana )

FIG. 7

 7 FIG. 7Net results for experiment 3

(

  21) a. I don't know whether Paul will go to the party because if Mary goes [lexical material] b. I don't know whether Paul will go to the party because if he goes and Mary goes [interpretation] c. I don't know whether Paul will go to the party because if (he goes) i and Mary goes too i [resolution]

  [START_REF] Amaral | Experimental evidence on the distinction between foregrounded and backgrounded meaning[END_REF] test Zeevat's account from an experimental point of view. Their aim is to check whether resolution and lexical triggers differ in the way they bring about backgrounding information. They implicitly operate a modification in Zeevat's classification, as they put triggers like too into the anaphoric category (which corresponds to Zeevat's resolution group). In their experiment, subjects are presented with written question-answer pairs; the question always contains a PP trigger, and either a positive or a negative answer is provided. An example of the target question-answer pairs is given below.

(4) Q -Did Brian lose his wallet again? A1 -Yes, he did lose his wallet again. [Endorsing main content + endorsing PP] A2 -No, he didn't lose his wallet this time. [Refuting main content + endorsing PP]

  The first target (win.with.ana) replicates Abusch's structure for win. It is said to be 'anaphoric' because of the pronoun. There is another version (win.wo.ana), where the PP that Peter participated is replaced by a weaker PP that someone participated in the ignorance statement I don't know whether . . . . The control for too makes the PP explicit. Too.with.rel makes the conclusion of the conditional sentence relevant to the combination of the accommodated PP and the explicit antecedent. If Paul and John read the letter, they will be both angry with Mary. In too.wo.rel the conclusion does not convey any obvious link to the PP content. Cleft.co is analogous to the other controls. Cleft.with.ana and cleft.wo.ana reproduce the same distinction as for win. Peter participated in the race. If he won, he has got more victories than anybody else in history.win.with.ana I don't know whether Peter participated in the race but, if he won, he has got more victories than anybody else in history.ContextDuring an important athletics meeting the participants to the 5000 metres are coming by plane. The weather conditions are so bad that it's not certain that they will be able to reach their destination. It's particularly frustrating for Peter, who is a super champion of the 5000 metres. win.wo.ana I don't know whether someone could participate in the race, but, if it's Peter who won, he has got more victories than anyone else in history. Context Mary wrote a letter to her boss, to accuse her colleagues, Paul and John, to be inefficient at work. too.co I know that Paul read the letter. If John read it too, they will be both angry with Mary. too.with.rel I don't know whether Paul read the letter, but, if John read it too, they will be both angry with Mary. too.wo.rel I don't know whether Paul read the letter, but, if John read it too, we'll ask him to be discreet about the content. Context There exists a secret document containing embarrassing revelations for a major political party. Michel is a member of the party and has a reputation for being unable to hold his tongue. cleft.co I know that someone read the document. If it's Michel, we'll ask him to be discreet about its content. cleft.with.ana I don't know whether Michel or someone else read the document but, if it's him who read it, we'll ask him to be discreet about its content. cleft.wo.ana I don't know whether someone read the document but, if it's Michel who read it, we'll ask him to be discreet about its content.

	Category	Text
	Context	Peter is a specialist of the New York marathon, that he won four times
	win.co	I know that Sentence.Type	Nb.Subjects Mean	Variance
		1 too.with.rel	30	4.80	3.13
		2 cleft.co	51	6.29	0.89
		3 too.wo.rel	25	5.20	2.67
		4 win.co	42	6.02	0.95
		5 cleft.with.ana	28	6.07	1.40
		6 too.co	50	6.40	0.78
		7 cleft.wo.ana	27	5.44	2.56
		8 win.with.ana	26	5.92	1.67
		9 win.wo.ana	24	6.00	2.70
		FIG. 2 Net results for experiment 1

FIG. 1 Target material for experiment 1

Method and results 160 students participated. They were divided into 6 groups, where no group saw a target and its control or two targets for the same trigger. The following table contains the net results.


Modesto T Lopez-Lopez

Pavel Kuzhir

Andrey Zubarev
email: andrey.zubarev@usu.ru

Effect of drop-like aggregates on the viscous stress in magnetic suspensions

Keywords: magnetorheological suspensions, drop-like aggregates, magentovisous effects

Effect of drop-like aggregates on the viscous stress in magnetic suspensions

Modesto Lopez-Lopez, Pavel Kuzhir, Andrey

Introduction.

Suspensions of magnetizable particles in carrier liquids, so-called magnetorheological suspensions (MRS), attract considerable interest of investigators and engineers due to rich set of physical properties which find active applications in many modern and perspective high technologies. One of the most interesting and valuable, from the practical point of view, features of MRS is possibility to change, in a very broad range, their rheological properties and behavior under the action of quite moderate magnetic fields. The physical cause of the strong rheological effects is formation of heterogeneous structures (aggregates) composed of magnetic particles and aligned with the applied field. Helpful reviews of the works on physics and practical applications of the magnetic suspensions can be found in [1][START_REF]Colloidal Magnetic Fluids[END_REF][START_REF] Odenbach | Magnetoviscous Effects in Ferrofluids[END_REF][START_REF] Ginder | [END_REF][5].

In the quiescent suspensions, subjected to an external magnetic field, the aggregates can span the gap between the opposite walls of the flowing channel. In this state, MRS demonstrates elastic behavior with respect to the shear deformations. When the applied shear stress exceeds some threshold value (so-called static yield stress), the bonds between the aggregates and the walls are broken and the elastic regime changes to the viscous flow regime. In this regime, the measured macroscopical shear stress  can be presented as

a        0 (1)
Here  0 is the viscosity of the carrier liquid,  is the macroscopic shear rate,  a is the stress produced by the aggregates. This stress is determined by the concentration, shape, length and orientation distribution of the aggregates.

Two kinds of the aggregates are usually considered. The first one is linear chains; the second kind of the aggregates is the dense bulk drops [1]. Theoretically, the effect of the chains on the stationary viscous properties of MRS with magnetizable particles has been studied in refs. [6,7].

The effect of the bulk "drops", consisting of great number of particles, has been studied in refs. [8,9]. The model [8] is based on minimization of the magnetic (electrical) free energy of a magnetizable (polarizable) ellipsoidal drop tilted with respect to the applied field. Analysis [8] has been done for highly elongated drops and leads to the following scaling relation:

3 / 4 0 3 / 1 H a    
, where H 0 is the magnetic field inside the suspension. It should be noted that the approach of the ref. [8] does not take into account any mechanisms of the drop destruction by the hydrodynamic viscous forces. Analysis shows that consideration of these mechanisms is principally important for development of a physically correct theory of rheological properties of suspensions with the heterogeneous aggregates.

The rupture of particles from the aggregated surface by the viscous forces has been considered in [9]. This model leads to the relation,

2 0 H a  
; like in the chain model [6], the stress,  a , does not depend on the shear rate  . The model [9] is often used for the interpretation of rheological effects in the magnetic suspensions (see overview in ref. [1]). However, this model contains a parameter (the thickness of a gap between the particles in the aggregates) which is not determined theoretically and is considered as a fit parameter of the model. Strictly speaking, the interparticle gap thickness must depend both on the field H 0 and the shear rate  , however in [9] this thickness is considered as a constant. Analysis shows that dependence of the gap thickness on the shear rate leads to qualitative change of the dependence of a  on  . Therefore, the results of [9] require very cautious attitude.

Like in ref. [8], the model [9] deals with the limiting approximation of the highly elongated aggregates. However this approximation is not valid when the shear rate  is large enough and too long aggregates are destroyed by the viscous forces.

We present here results of theoretical study of effect of the bulk drops on the magnetoviscous effects in MRS with the linearly magnetizable particles. The model is based on the analysis of hydrodynamic destruction forces acting on the aggregate surface and does not contain any adjustable parameters. It should be noted that appearance of the bulk drops has been observed in many experiments and computer simulations of magnetic suspensions (see, for example, overview in [1]).

In the framework of this model we suppose that the drop size is significantly less than the width of the flow channel (the case of the developed flow) and effect of the channel walls on the drop behavior is negligible. The validity of this assumption will be proved at the end of the paper. Unlike refs [8,9] we do not restrict ourselves by the asymptote of the highly elongated drops. It allows us to reproduce the suspension rheograms in the wide range of the shear rates,  .

Main approximations.

Let us consider a dense aggregate consisting of the large number of magnetizable particles. We will model the aggregate by an ellipsoid of revolution with the major and minor axes a and b, respectively. These magnitudes will be estimated below. We suppose that the suspension is subjected to a macroscopic shear flow with the rate  . When 0 



, the aggregate major axis is aligned along the magnetic field H 0 . Under the shear hydrodynamic forces, the ellipsoid axis deviates from the field by the angle . We will suppose that the field H 0 is applied in the direction of gradient of the flow velocity. Next, we suppose that concentration of the drops in the suspension is small enough and any interactions between them can be ignored. The validity of this assumption will be reconsidered at the end of the paper. The problem geometry is illustrated in Fig. 1. Macroscopic stress  a is determined by the shape of the drops and the angle  of the drop inclination with respect to the field direction. On the other hand, the angle  is determined by the hydrodynamic and magnetic torques acting on the aggregate; while the size and shape of the drop is defined by the combination of the hydrodynamic and magnetic forces acting on the drop surface. The magnetic force consists of the elongating force of the demagnetizing field along with the force of the surface tension. Obviously, the surface tension force tends to contract the drop. Our aim is to estimate the angle  as well as the hydrodynamic and magnetic forces, and thenthe size and the shape of the steady stable drop in the suspension under applied shear flow. For the maximal simplification of calculations we will consider this aggregate as a rigid ellipsoid, impenetrable for the carrier liquid, and restrict our analysis to a linear law of the particles magnetization.

The orientation angle . The magnetic torque m  , acting on the ellipsoidal drop, can be found, for example, in the book [START_REF] Landau | Electrodynamics of Continuous Media[END_REF] (see, also, [8,9]) as:

          2 sin ) 1 ( 2 1 3 1 2 1 2 0 2 0 H N N N V m       (2)
Here

2 3 4 ab V  
is the aggregate volume,  0 is the magnetic permeability of vacuum,  is the aggregate magnetic susceptibility, N is the aggregate demagnetizing factor in the direction of the main axis a. The explicit form of this factor can be found, in [START_REF] Landau | Electrodynamics of Continuous Media[END_REF]. The hydrodynamic torque h  has been calculated in ref. [START_REF] Jefferyi | [END_REF] (see, also, [8]) as:

) sin cos ( 1 2 4 2 2 2 2 0          r N N r V h  (3)
Here r=a/b is the drop aspect ratio, which will be determined below.

Equating the torques h  and m  , we get:

1 2 2 4 tan 2 BMa B Ma AC A     , (4)
where 0 2 00

Ma H

   is the Mason number characterizing a ratio of the hydrodynamic-tomagnetic forces acting on aggregates, , 1 2

4 2 N N r A            ) 1 ( 2 1 3 1 2 N N N B      , N N r r C    1 2 4 2 2

Hydrodynamic destructing forces

We will estimate now a hydrodynamic force, which tends to elongate and, finally, to break the drop in the direction of the main axis a.

Let us introduce the Cartesian coordinate systems with the axes Oz' and Ox', aligned along the gradient of the suspension velocity (i.e. along the field H 0 ) and along the velocity respectively; we also introduce another reference frame with the axes Oz along the major axis of the drop and the axis Ox situated in the plane Ox'z'. Both these coordinate systems are shown in Fig. 1.

In the laboratory (Ox'z') frame the components of the flow velocity read:

, ' v ' z x   0 v v z' '   y (5)
By using the standard formulas for transformations of vector components from one coordinate system to another, one can easily find the velocity components in the reference frame Oxz. After that we can determine the components of the rate-of-strain tensor in this frame:

 , sin cos 2 1 x v z v 2 1 2 2 z x                    xz (6) zx xz                    2 1 x v z v 2 1 z x , cos sin v z          z zz     cos sin x v x       xx
All remaining components of this tensor are zero.

The viscous force, acting on the unit area of the drop surface, has been estimated in ref. [12]. The component of this force, acting in z direction (i.e. along the major axis a of the drop), can be presented in the form:

, 8 ) 4 8 ( 2 2 2 2 0          b x A ab a z W A ab S P xz zz z  (7) 2 / 1 4 2 4 2 2             a z b y x S   yy xx zz A A A W    0 0      '' ' ' 2 ' ' 6 ' ' ' ' 2 0 0 2 0 0 0           xx zz zz A        xz xz xz a b a a b b a A          0 2 0 2 2 0 2 0 2 0 0 2 2 0 2 2          '' ' ' 2 ' ' 6 ' ' ' ' 0 0 2 0 0 0            xx zz yy A
Here x,y,z are coordinates of a point on the drop surface. The following obvious relation describing the aggregate surface holds:

1 2 2 2 2 2    b y x a z (8) Parameters ' ' , ' ' , , 0 0 0 0    
depend on the aggregate aspect-ratio r; their explicit forms are given in the Appendix I.

Integral of P z over the whole surface of the drop means the total force acting on the drop in the shear flow. One can easily see that this integral is equal to zero, as it should be for force-free aggregates. The hydrodynamic force f h , stretching the drop in z direction, equals to the integral from P z over a half of the surface, say, corresponding to z>0.

After calculations (see Appendix II) we get:

                     1 ln 1 1 1 1 2 4 2 2 2 2 2 2 0 r r r r r r b W A ab f zz h   (9)

Magnetic forces.

The magnetic force, which determines the shape of the aggregate, can be determined as:

a F f m m     (10)
where F m is the magnetic free energy of the drop. This energy can be written in the following form:

m b s F F F  (11)
Here F b is the bulk free energy of the drop, determined by the effects of the drop demagnetizing field, F s is the surface tension free energy. The bulk free energy can be presented as (see, for example [13]):

  22 2 0 0 cos 2sin 2 1 2 1 b F V H NN              
The surface free energy is:

ds F s s   
Here  s is the coefficient of the surface tension, ds is an infinitesimal element of the drop surface. Strictly speaking,  s depends on the position of a point on this surface. This fact makes all calculations very complicated and cumbersome. For maximal simplification of the calculations, we will estimate F s as:

   s F (12)
Here  is the surface tension coefficient, averaged over the drop surface,  is the surface area.

For the prolate ellipsoid of revolution the area can be calculated as:

                     1 1 arcsin 1 4 3 2 2 2 2 3 / 2 3 / 2 r r r r V   (13)
The stretching force f b , corresponding to the free energy F b , is:

      1/ 3 22 2 1/ 3 2 0 , , 0 22 cos 2sin 3 4 | | | 2 2 3 1 21 bb b V V V FF rN f V r H a r a r V N N                              (14)
The average coefficient of the surface tension can be estimated as (see, Appendix III):

                                       2 2 2 0 0 1 2 sin 2 1 cos 4 N N Н ( 15
)
Here  is the thickness of the interface zone between the dense drop and the dilute environment.

In the order of magnitude, this thickness equals to the particle diameter (see, for example, [8]).

The force of the surface tension is:

3 / 1 3 / 1 , 3 4 2 3 | r V r F a F f s V s s                 (16)
The explicit form of f s is cumbersome and we omit it here for brevity. The shape of the steady stable drop is determined from the condition that the total deforming force f, acting on the drop surface, is zero. Substituting  from (4) into eqs. (9,[START_REF] Pokrovskii | Statistical Hydromechanics of Dilute Suspensions[END_REF][START_REF] López-López | Colloids and Surfaces A: Physicochem[END_REF], we get:

( , ) ( , ) ( , ) ( , ) 0 h b s f V r f V r f V r f V r     (17)
The second equation, necessary for calculation of two variations V and r, can be found from the following considerations. The plots of the force f, as a function of the aspect ratio r, for three magnitude of the volume V are shown in Fig. 2.

Fig.2. Illustration of dependence of the deformation force f vs. the drop aspect ratio r.

The positive magnitudes of f correspond to the drop elongation along the major axis a; the negative onesto the drop contraction. If V>V c , the force stretches the drop until it breaks; this happens at all magnitudes of the aspect ratio r. Therefore, the aspect ratio r c and the volume V c of the stable drop are determined as solutions of the systems of equation ( 17) and the equation 0

) , (    r r V f ( 18
)
The system ( 17),( 18) can be easily solved numerically.

Magnetoviscous stress  a.

In the first approximation the stress  a , produced by the magnetizable aggregates, can be estimated as (see, for example, [8,9] and references there):

m a a n   2 1 
where n a is the number of the aggregates in a unit volume of the system. By using here the relation ( 2), one can get

           2 sin )) ( 1 ( 2 ) ( 1 ) ( 3 1 4 1 2 0 2 0 H r N r N r N a       (19)
Here

V n a  
is the volume concentration of the aggregates. Estimates show that for a magnetic field strength H 0 as low as 1 kA/m, the energy of the magnetic interaction between the particles is much higher than the thermal energy kT. In this case, all the particles must be condensed into the domains (drops) of dense phase and we get:

a   0  
where  0 is the total volume concentration of the particles in the suspension,  a is the particle volume concentration in the drop.

In the dense aggregate this concentration can be estimated as  a 0.6 -0.7. We find the stress  a by substitution of Eq. ( 4) for  and the solution of Eqs. ( 17), (18) into the expression [START_REF] Christensen | Mechanics of Composite Materials[END_REF]. Predictions of the theoretical model for the total stress  are compared with experimental results in Fig. 3. Details of experimental methods are given in Appendix IV. Note that the stress  does not depend on the parameter  of the drop surface tension. This follows both from the general dimensional analysis, as well as from the solution of the system (17,18). Fig. 3 Total stress  vs. the shear rate  . Lines represent theoretical predictions and dots the experimental data.

Solid lines -calculations with (17)(18)[START_REF] Christensen | Mechanics of Composite Materials[END_REF], the dashed onesby using the asymptotic estimate [START_REF] Batchelor | [END_REF]. As observed in Figure 3 there is a quite good correspondence between theory and experiments. This agreement shows that the observed magnetorheological effects can be explained by appearance of the drop-like aggregates and that the suggested model is adequate, at least, in its main points.

Estimates show that, for small Mason numbers Ma<<1, the aspect ratio r>>1 and the general solution [START_REF] Christensen | Mechanics of Composite Materials[END_REF] shows the following asymptotic behavior:

    , 3 / 1 0 3 / 2 2 0       H a     3 / 1 4 2 22 7            (20)
It should be noted that the same scaling relation

3 / 1 3 / 4    H a 
has been obtained in [8] from the energetic considerations, discussed in Introduction of the present paper. However the relation [START_REF] Batchelor | [END_REF] corresponds to experimental situation only when the shear rate  are small enough. For large magnitudes of  , the asymptotic relation (20) overestimates the experimental results and the disagreement between theory and experiments increases with  . The relation (19) can be applied in much more wide region of  than (20).

Let us now analyze briefly the range of validity of our model. Firstly, our model is valid for the shear rates higher than some critical value corresponding to the maximum length of the aggregates when they become gap-spanning. This length is easily calculated under the asymptote of low shear rates, or equivalently, low Mason numbers giving the flowing expression for the critical Mason number: µm between the bulk aggregates and the surrounding medium, aggregate magnetic susceptibility, ≈85, and magnetic field intensity H 0 =5.7-8.6 kA/m), we obtain the following estimate for the critical Mason number and the critical shear rate above which our model is considered to be valid: Ma c ~10 -4 and 1  s -1 . Thus, in our experiments, focused on the developed flow regime at relatively high shear rates (1 500

  s -1
), the aggregates are not expected to span the gap, and the present model could be applied safely.

Secondly, it should be noted that we ignored hydrodynamic interactions between the drop-like aggregates.. Obviously, in suspensions with high enough concentrations of the particles and, therefore, high concentration of drop-like aggregates, , both hydrodynamic and magnetic interactions between the drops can, in principle, be significant. However analysis shows that in suspensions of elongated particles (drop-like aggregates in our case), the effect of the hydrodynamic interaction is weak as compared to the effect of the interaction between the flow and individual particles [START_REF] Batchelor | [END_REF]21]. It is commonly recognized that the stress in the semidiluted fiber suspensions differs only modestly from that in the diluted ones [START_REF] Larson | The Structure and Rheology of Complex Fluids[END_REF]. Furthermore, in concentrated suspensions of rod-like particles the short-range hydrodynamic interactions between particles become significant only at concentrations respecting the condition 1 sin 10     [START_REF] Férec | [END_REF], with  being the average angle between axes of neighboring particles. In the case of strongly oriented drop-like aggregates, the angle  appears to be much smaller than unity ( <<1 ), and the short-range hydrodynamics should not play any significant role on the stress level.

Thirdly, magnetic interaction between the drops can also affect the magnetic force and torque acting on each drop, as well as the macroscopic suspension stress. A simple estimate of the effect of the neighboring aggregates on the magnetic torque acting on a given aggregate can be obtained using the Maxwell-Garnett mean field theory [START_REF] Berthier | Optique des milieux composites[END_REF] applied to the limit of low Mason numbers, thus high aggregate aspect ratios r>>1. At this condition, the aggregate demagnetization factor vanishes, N≈0, and the fraction in Eq. 2 for the magnetic torque reduces to 2 ( 1) /(2 ( 1) )

      if the magnetic interactions between aggregates are taken into account, instead of 2 /(2 )

 

if the interactions are ignored. For the aggregates of high magnetic permeability, ≈85 (as the ones composed of iron particles -our experimental case), the difference between both estimates is only a few percent. Thus, inter-aggregate magnetic interactions are not expected to enhance considerably the magnetic torque and the suspension stress, and the relationships ( 2) and ( 19) ignoring these interactions may still be applied. In summary, we believe that the assumption of negligible inter-aggregate interactions is justified for the MR suspensions used in our experiments having a particle volume fraction up to 10%. The quantitative agreement between the theoretical and experimental results supports this assumption. Extension of the present theory to a broader concentration range, where interactions between the drops cannot be more ignored, could be a natural generalization of the present model.

Conclusion

Results of theoretical study of magnetoviscous effects in magnetorheological suspensions with the drop-like aggregates are presented. The analysis is done beyond the standard asymptotic simplification of extremely elongated drops. We suppose that in the shear flowing suspension the volume and shape of the stable drop is determined by the balance between the hydrodynamic and magnetic forces which tend, respectively, to elongate and contract the drop in the direction of its main axis. The theoretical results are in agreement with the experiments in a wide region of shear rate of the suspension flow, whereas the standard asymptotic estimates correspond to the experiments only when the shear rate is small enough.

Appendix I.

The kinetic coefficients  0 0 ,...  , determined in [12] (see, also, [START_REF] Pokrovskii | Statistical Hydromechanics of Dilute Suspensions[END_REF]), read:

                 1 2 1 2 ln 1 1 2 1 2 2 2 2 3 0 r r r r r r b  ,                 1 2 1 2 ln 1 2 1 1 2 2 2 2 3 0 r r r r r r b  ,                         1 2 1 2 ln 1 2 1 4 1 2 1 4 2 2 2 2 2 2 2 3 0 r r r r r r r r b  ,                       1 2 1 2 ln 1 2 1 2 3 1

Appendix II. Calculation of the hydrodynamic deformation force f h .

For calculation of the force f h we will introduce the cylindrical coordinate systems (z,,) according to the rule:

    sin , cos ,    y x z z
. The following relation applies for the ellipsoid surface:

                        0 2 / 1 4 2 4 2 2 2 0 0 2 0 ) ( ) ( ) 4 8 ( 2 ) (         (A.1)
The last integral can be presented as:

                                   1 1 ln 1 1 2 1 1 2 ) ( ) (

Appendix III. Estimate of the mean surface tension .

By using the definition of the surface tension [START_REF] Ono | Molecular theory of surface tension in liquids[END_REF], we can estimate the coefficient of the surface tension as

  m s    2 1 (A.3)
Here  is thickness of the transition zone between the phase of the dense droplet and the dilute environment, m  is the density of the free energy of magnetic interaction between particles in the dense drop. The last magnitude is:

2 0 2 H m      (A.4)
where H is magnetic field inside the drop. The Cartesian components of this field in the coordinate system Oxz, shown in Fig. 1, can be written down as (see, for example, [START_REF] Landau | Electrodynamics of Continuous Media[END_REF]):

, 1

1 0 H N H z    0 ) 1 ( 2 2 H N H x     (A.5) Obviously 2 2 2 z x H H H   .
The thickness  of the transition layer between the droplet and surrounding medium depends on the position of a point on the droplet surface. Its calculation presents very sophisticated problem of statistical physics of the interface zone. For dense drops with the concentration of particles near the concentration of the dense packing, the thickness  is of the order of magnitude of the particle diameter d. In the approximation that  is constant and does not depend on the position on the droplet surface, we replace in (A.3)  s to . Combining (A.3)-(A.5), we come to the estimate (12,[START_REF] Ono | Molecular theory of surface tension in liquids[END_REF].

Appendix IV. Experimental methods.

Iron powder (HQ quality; density 7.5 g•cm -3 ) supplied by BASF (Germany) was used as magnetic phase for the preparation of the MRS. SEM pictures revealed that this powder consisted of spherical particles with 930 nm of average diameter and 330 nm of standard deviation [START_REF] López-López | Colloids and Surfaces A: Physicochem[END_REF]. Kerosene (viscosity 2.1 mPa•s; density 0.79 g/cm3) supplied by Sigma-Aldrich (Germany) was used as carrier liquid. Clay particles (Claytone HY), supplied by Southern Clay Products, Inc. (Texas, USA) were used as stabilizing (thickening) agent in order to hinder the settling of the iron particles. In the developed shear flow regime, the viscosity of the claykerosene mixture was 5 mPa•s. Iron suspensions were prepared as described in Ref. [17] and had a final iron particle volume concentration of 10 %. Previous experiments showed that at low field, the relative magnetic susceptibility  p of the iron powder is approximately independent of the field and takes an approximate value  p =130 [18]. Thus, the susceptibility of the drop with the densely packed particles can be roughly estimated as ~ p  p [START_REF] Christensen | Mechanics of Composite Materials[END_REF]. By using  p ~0.65, we have the estimate ~85. Rheological measurements were performed in a controlled rate mode using a MCR 300 Physica-Anton Paar magnetorheometer at 25 °C. The measuring system geometry was a 20 mm diameter parallel-plate set for a gap width of 0.35 mm.

Fig. 1 .

 1 Fig.1. Sketch of the model of the drop-like aggregates. The horizontal arrows illustrate the suspension macroscopic flow.

  Line 1 and open squares correspond to H 0 =8.6 kA/m; line 2 and black squares -to H 0 =5.7 kA/m. Parameters of the systems:  0 =0.1;  a =0.65; =85; 0 5   mPa•s.

  the flow channel thickness corresponding to the rheometer gap in our experiments. For the typical set of the parameters appropriate to our experiments (gap thickness, g=0.35 mm, transition layer =0.5

  .1) into (A.2) we come to the relation(9).

Fig. 1 .Fig. 2 .

 12 Fig.1. Sketch of the model under consideration. Horizontal arrows illustrate the macroscopic velocity of suspension.

Fig. 3 . 5 

 35 Fig.3. Total stress  vs. the shear rate  . Lines represent theoretical predictions and dots the experimental data. Solid lines -calculations with(17)(18)[START_REF] Christensen | Mechanics of Composite Materials[END_REF], the dashed onesby using the asymptotic estimate[START_REF] Batchelor | [END_REF]. Line 1 and open squares correspond to H 0 =8.6 kA/m; line 2 and black squares -to H 0 =5.7 kA/m. Parameters of the systems:  0 =0.1;  a =0.65; =70; 0 5   mPa•s.

Acknowledgment

This work has been supported by the Russian Fund of Fundamental Investigations, grants 12-01-00132, 13-02-91052, 13-01-96047, 14-08-00283; by the Act 211 Government of the Russian Federation № 02.A03.21.0006; by the Junta de Andalucía (Spain), project P09-FQM-4787; and by the University of Granada (Acción Integrada con Russia; Plan Propio 2011); and CNRS PICS N° 6102 is also acknowledged.