Bianca Cristine Marques

Artemio Plana-Fattori
email: artemio.planafattori@agroparistech.fr

Carmen Cecilia Tadini

Denis Flick

MODELING CONVECTIVE DRYING OF FOOD PRODUCTS: THE CASE STUDY OF YACON (Smallanthus sonchifolius)

Keywords: convective drying, shrinkage, yacón, diffusivity coefficient

The convective drying of a food product whose dehydration occurs under large deformation is studied. A numerical model is proposed for solving the heat and water mass transfer phenomena for cylindrical samples while including shrinkage. It is assumed that no porosity appears during drying. The finite volume method is applied, and mesh boundaries move with the dry matter. No information about the product's mechanical properties is required; shrinkage is predicted from geometrical considerations only. The approach is illustrated for the case of yacón samples, whose reduction in volume can reach 90 % after a few hours of drying. Previous work with a convective dryer pilot unit under controlled air temperature and relative humidity is considered, firstly in identifying key parameters related to the volume reduction and to the water diffusivity in the product, secondly in assessing the drying kinetics as predicted by the model.

INTRODUCTION

The shrinkage of fruits and vegetables strongly depends on their mechanical properties. The development of shrinkage models has assumed fruits and vegetables as elastic, hyperelastic, elasto-plastic or visco-elastic. Their heterogeneous structure turns very complex the actual shrinkage behavior. For instance, most of the available literature considered the modulus of elasticity of potato tissue as a function of water content, based on data from experiments conducted at room temperature (e.g. [START_REF] Yang | Drying model with non-isotropic shrinkage deformation undergoing simultaneous heat and mass transfer[END_REF]; however, the modulus of elasticity depends on the temperature and the material structure. The correlation developed for potato may not be applicable for other food materials due to their diverse nature and properties. For a realistic understanding, an accurate relationship of modulus of elasticity could be based on data generated while drying is in progress [START_REF] Mahiuddin | Shrinkage of food materials during drying: Current status and challenges[END_REF]. The assessment of thermo-physical and mechanical properties of food materials as a function of temperature and water content along the drying process certainly constitutes an interesting research topic. Looking for model development and given the wide variety of food materials, it would be desirable if alternatives exist to such a challenge.

Here we pursue the development of an approach for studying the evolution of food products that can experience significant shrinkage under convective drying. The original contribution lies in the experimental-based geometrical considerations for estimating how shrinkage is distributed in different directions. The detailed mechanical behavior of the food material is not required. The approach is implemented in a flexible numerical model which includes i) the coupling between heat and water mass transfer, and ii) the variation of water diffusivity in the food matrix with the moisture itself. These features have been quoted as mandatory in modeling moisture profiles during the drying process [START_REF] Perré | The proper use of mass diffusion equations in drying modeling: Introducing the drying intensity number[END_REF].

The approach is illustrated for cylindrical slices of yacón (Smallantus sonchifolius), a plant cultivated originally in the Andean region for its tuberous, mildly sweet roots. The interest in yacón has increased [START_REF] Caetano | Yacón (Smallanthus sonchifolius) as a food supplement: Healthpromoting benefits of frutooligosaccharides[END_REF]: it constitutes a good option for low-carbohydrate diets because of its low amounts of sucrose and glucose, and its high amount of non-digestible carbohydrates. The industrial utilization of yacón is quite broad [START_REF] Lebeda | Yacón (Asteraceae; Smallanthus sonchifolius)[END_REF]. More than 70 % of the fresh tuberous root biomass of yacón is composed of water [START_REF] Lachman | Yacón [Smallanthus sonchifolia (Poepp. et Endl.) H. Robinson] chemical composition and use: A review[END_REF]. Water activity is high, leading to a short shelf-life; partial hydrolysis of oligo-fructans can start a few days after harvest [START_REF] Graefe | Effects of post-harvest treatments on the carbohydrate composition of yacón roots in the Peruvian Andes[END_REF]. Drying is a convenient way to prepare yacón for storage, and the influence of drying conditions on its composition has been investigated [START_REF] Scher | Hot air drying of yacón (Smallanthus sonchifolius) and its effect on sugar concentrations[END_REF][START_REF] Campos | Stability of fructooligosaccharides, sugars and colour of yacón (Smallanthus sonchifolius) roots during blanching and drying[END_REF]Khajehei et al., 2018a;[START_REF] Salinas | The influence of convection drying on the physico-chemical properties of yacón (Smallanthus sonchifolius)[END_REF]. Shrinkage cannot be neglected in studying the evolution of yacón submitted to convective drying: the sample shape can be completely changed and the reduction in volume can reach 90 % [START_REF] Bernstein | Study of thermodynamic, structural, and quality properties of yacón (Smallanthus sonchifolius) during drying[END_REF]. The evolution of yacón slices under convective drying constitutes an interesting case study for discussing the possibilities and the limitations of an approach for estimating shrinkage without information about the product's mechanical properties.

The numerical model proposed in the pioneering work of Marques et al. (2020a) is here improved, mainly by expressing the diffusivity of water in yacón as a function of local temperature and water content values in the food matrix. Attention is focused on one of the air convective drying conditions studied experimentally by [START_REF] Marques | Data acquisition for modelling convective drying of yacón (Smallanthus sonchifolius) slices[END_REF].

PHYSICAL MODEL

The convective drying of a slice of food matrix is hereafter studied by taking into account the following assumptions:

• evaporation occurs at the surface only;

• energy transfer occurs due to heat conduction inside the food matrix and water convection at its surface;

• liquid water migrates inside the product relatively to dry matter following moisture gradient; and

• no porosity appears during drying.

The last assumption means that, locally, the total volume occupied by the food matrix containing 1 kg of dry matter can be expressed as the sum of volumes that are occupied by dry matter and water:

1

ρ dm = 1 ρ # dm + X w ρ # w (1)
wherein ρ dm is expressed in kg of dry matter [kg-dm] by cubic meter of food product; X w is the water content in the food product, dry basis [kg-w/kg-dm]; and ρ # dm and ρ # w are the dry matter and water mass densities [kg/m 3 ] (see Table ).

The conservation equation for the water content can be expressed, in its convective form, as:

∂ X w ∂t + ⃗ v dm • ⃗ ∇X w = 1 ρ dm ⃗ ∇ • ⃗ j w/dm (2)
wherein ⃗ v dm is the dry matter velocity in the food slice. The water flux relative to the dry matter is given by:

⃗ j w/dm = -D w ⃗ ∇ (ρ dm X w ) (3)
wherein D w is the water diffusivity [m 2 /s] in the food product. Equation 2 is solved by taking into account the following boundary condition at the food matrix surfaces:

⃗ j w/dm •⃗ n = k (a w {X w } C sat {T } -RH air C sat {T air }) (4)
wherein k is the mass transfer coefficient [m/s], a w {X w } is the water activity in the product at the water content X w , and C sat {T } is the saturated water vapor concentration at the temperature T [kg-w/m 3 ].

The internal energy of the food product (by kg of dry matter) is the sum of the internal energies of dry matter and water:

u = u dm + X w u w = C # dm + X w C # w T (5)
wherein C # dm and C # w are the dry matter and water heat capacities [J/kg-dm/K]. The conservation equation for the internal energy can be expressed as:

∂ u ∂t + ⃗ v dm • ⃗ ∇u = 1 ρ dm ⃗ ∇ • ⃗ j w/dm u w + ⃗ ∇ • ⃗ j q (6)
wherein the energy flux is given by:

⃗ j q = -λ ⃗ ∇T (7)
wherein λ is the bulk thermal conductivity, obtained as λ = (λ # dm ) α (λ # w ) (1-α) ; λ # dm and λ # w are the dry matter and water thermal conductivities [W/m/K], and α is the volume fraction occupied by dry matter in the food matrix. Equation 6 is solved by taking into account the following boundary condition at the food matrix surfaces:

⃗ j q •⃗ n = h (T -T air ) + L v ⃗ j w/dm •⃗ n (8)
wherein h is the heat transfer coefficient [W/m 2 /K] and L v is latent heat of water vaporization [J/kg].

Water diffusivity in the product is required for evaluating water migration inside the food matrix (equation 3). The two phase model proposed by [START_REF] Maroulis | Moisture diffusivity data compilation for foodstuffs: Effect of material moisture content and temperature[END_REF] is used:

D w {X w , T } = 1 1 + X w D w,dry {T } + X w 1 + X w D w,wet {T } (9) D w,dry {T } = D dry exp - E dry R 1 T - 1 T re f (10) D w,wet {T } = D wet exp - E wet R 1 T - 1 T re f . (11)
Activation energy values for diffusion in dry (E dry ) and wet material (E wet ) were both assumed to be 30 kJ/mol, from experimental convective drying of yacón [START_REF] Shi | Mathematical modeling on thin-layer heat pump drying of yacón (Smallanthus sonchifolius) slices[END_REF]. Reference temperature T re f was chosen 60 • C. Diffusivity values in dry material (D dry ) and in wet material (D wet ) were identified by comparing observations and model predictions of dimensionless water content (X ⋆ w = X w /X w,0 ). Water activity in the product is required for evaluating surface evaporation. The Guggenheim-Anderson-deBoer isotherm equation was applied, and the parameters were estimated from desorption measurements of yacón samples at the reference temperature of 60 • C [START_REF] Marques | Data acquisition for modelling convective drying of yacón (Smallanthus sonchifolius) slices[END_REF].

The crux of our approach is the representation of shrinkage, as a consequence of evaporation at the surface and water migration within the food matrix. Let us subdivide the food matrix before drying into a regular grid constituted by a large number of small volumes (cells). The development of porosity is neglected; hence moisture reduction is translated into water volume reduction and hence into total volume reduction at a local scale. Because the mass of dry matter contained in each cell remains constant, there is a displacement of dry matter along the drying. The velocity of this displacement corresponds to the vector ⃗ v dm in equations 2 and 6.

The blue line in Fig. 1 evidences that the diameter reduction of yacón slices under drying does not follow an isotropic shrinkage behavior, which corresponds to β = 1/3. Looking for a better match with experimental results, we focused the attention on the values of slice diameter and volume under vanishing water content. On one hand, Fig. 1 suggests D ⋆ ∼ 0.6 for the fully dried matrix. On the other hand, the application of equation 1 to X w → 0 and then to X w = X w,0 provides V ⋆ ∼ 0.05. Combining these results we reach a value close to β = 1/6, which is considered in the calculation of diameter reduction in the numerical model.

NUMERICAL MODEL

In the beginning, the food matrix is assumed to have a cylindrical shape with radius R 0 and height H 0 . The matrix is assumed to be steadily exposed to a uniform transfer of heat and mass across all its surfaces, suggesting the adoption of the same value for the heat transfer coefficients at the upper, lower and lateral surfaces.

The food matrix is represented by a two-dimensional (2D) axis-symmetrical computational domain with radius R 0 and height Z 0 = H 0 /2. The lower boundary of the domain corresponds to the plane of symmetry which divides the matrix into two identical halves. The finite volume method is applied, and the domain is subdivided into a number of control volumes (cells).

When drying starts (t = 0) all the cells are rectangular. In the present study, the mesh is built considering I and J cells along the radial and the axial directions; coordinates have the origin at the slice center. The computational domain has an initial aspect ratio R 0 /Z 0 ∼ 6; meshes are chosen in taking I = 6 * J. The (i, j)-th cell is characterized by:

• a bulk position [r(i, j), z(i, j)], required in the evaluation of energy and water mass rates; the position of inner cells is defined as their center, the position of the outer cells is defined at the surface of the domain;

• four vertices; [R(i, j), Z(i, j)] at its left-bottom corner;

• the surface ∆S(i, j) = π(R(i+1, j) 2 -R(i, j) 2 ) between two successive radial distances; • the height ∆Z(i, j) = Z(i, j + 1) -Z(i, j); and • the width ∆R(i, j) = R(i + 1, j) -R(i, j).
During the drying period (t > 0), the food matrix is submitted to convective heating and evaporation at its surface and to heat conduction and water migration inside. Independently on the drying state of the food matrix, all the cells are assumed to be trapezoids, the vertical sides of which are imposed to be parallel to the axis of symmetry. Their shape can be distorted as a consequence of distinct heat and mass transfer phenomena along with the axial and radial directions.

Each cell is associated with a single value for the product temperature and for the water content. In the beginning, initial values T 0 and X w,0 are assigned to all the cells. Once the initial volume V 0 of each cell is known, it is possible to calculate the mass of dry matter m dm contained therein:

m dm = ρ dm,0 V 0 (12)
wherein the initial density of dry matter in the food matrix can be expressed from equation 1. The mass of dry matter contained in each cell remains constant along with drying.

Convective conditions are assumed to be steady and defined by the air temperature (T air ) and relative humidity (RH air ). Such a situation causes heat and water mass exchanges between the product and the ambient air along the drying. After a time step (∆t), the total variation in the water content in the (i, j)-th cell and that in the temperature associated with this cell are calculated as :

∆X w (i, j) = ( ( (φ Z (i, j) -φ Z (i, j+1)) + + (φ R (i, j) -φ R (i+1, j) ) ) ∆t/m dm (i, j) (13)
∆T (i, j) = ( ( (Φ Z (i, j) -Φ Z (i, j+1)) + + (Φ R (i, j) -Φ R (i+1, j) ) ) ∆t/(m dm (i, j) C P (i, j)) (14)
wherein C P = C # dm + X w C # w . These equations employ rates of change (i.e. variations per unit of time) of the water mass (φ [kg-w/s]) and of the internal energy (Φ [J/s]) along the axial Zand radial Rdirections. In the case of inner cells, the water and energy rates are calculated as:

φ Z (i, j) = ∆S(i, j) D w (i, j) ρ dm (i, j) × ( X w (i, j-1) -X w (i, j) )/( z(i, j) -z(i, j-1) ) (15) φ R (i, j) = 2 π ∆Z(i, j) D w (i, j) ρ dm (i, j) × ( X w (i-1, j) -X w (i, j) )/( ln( r(i, j)/r(i-1, j) ) ) (16)
Φ Z (i, j) = ∆S(i, j) λ (i, j) × ( T (i, j-1) -T (i, j) )/( z(i, j) -z(i, j-1) ) (17) Φ R (i, j) = 2 π ∆Z(i, j) λ (i, j) × ( T (i-1, j) -T (i, j) )/( ln( r(i, j)/r(i-1, j) ) ) . ( 18
)
Water and energy rates are calculated at surface cells while respecting the boundary conditions of the problem (equations 4 and 8). For instance, in the case of the lateral surface:

φ R (I+1, j) = 2 π r(I, j) ∆Z(I+1, j) × k × ( a w (I, j) C w,sat {T (I, j)} -RH air C w,sat {T air } ) (19) Φ R (I+1, j) = 2 π r(I, j) ∆Z(I+1, j) × h × ( T (I, j) -T air ) + L v φ R (I+1, j) . (20)
Thus, energy rates at the surface are computed by adding two contributions: the first is proportional to the difference between the temperature in the product and in the ambient air, the second is proportional to the water mass rate.

After updating temperature and moisture values (equations 13-14), the cell volume can be obtained (equation 1). Basic geometrical considerations are successively applied for recomputing the radial and vertical coordinates of cells' corners. Radial coordinates decreased with moisture reduction, following the D ⋆ = (V ⋆ ) β relationship which was justified above; vertical coordinates are updated in a way to restore the cell volume.

During the drying, the cells at the axis of symmetry remained rectangular. The cell located at the axis of symmetry and at the plane of symmetry is the one associated with the slowest drying rate; its radial and vertical coordinates are the first to be updated. The shape of the remaining cells is nearly unconstrained during the drying period: the only assumption is that their vertical sides remain parallel to the axis of symmetry. The cells at the plane of symmetry are the longest in the slice; evaporation takes place only at the outer one only. Cells that are located at the upper and lateral surfaces are strongly affected by evaporation and they quickly became very thin; such a finding seems realistic, because the moisture gradients therein are the highest. The representation of these phenomena guided us in building a mesh with a relatively narrower surface cells, comparatively with the inner cells (see Figure 4).

The algorithm was written in Python language, and there is no reason why it cannot be done with other computational means. No attempts were conducted in optimizing the algorithm. (iii) Data provided by [START_REF] Hermann | Compositional diversity of the yacón storage root[END_REF] about nine accessions of fresh yacón allowed us to estimate the averaged composition: 0.37g/100g for proteins, 0.024g/100g for fat, 11g/100g for carbohydrates, 0.36g/100g for fibers, and 0.51g/100g for ash. These values were considered in applying Choi and Oikos' (1986) approach for estimating yacón thermal properties at the temperature of 40 • C. (iv) Value at 60 • C (air temperature).

(v) Value estimated after assuming that all the incoming heating is consumed into surface evaporation at the wet-bulb temperature. Such an estimation required the drying rate dX ⋆ w /dt, whose value 1.4 10 -4 s -1 at t = 0 was obtained by fitting experimental measurements of water content X ⋆ w during the drying. (vi) According to the mass-heat transfer analogy, the ratio of mass to heat transfer coefficients can be expressed by using the Lewis number, as Le -2/3 /(ρ C P ). Lewis number ∼ 0.90 assuming air thermophysical properties at T air . (vii) Compromise between the reliability of model predictions and the computational cost (typically, 3 hours on a 11 Gen Intel Core i7-1165G7 at 2.8 GHz, 16 Gb-RAM laptop). Figure 2A displays measurements of water content conducted under these conditions, as described by [START_REF] Marques | Data acquisition for modelling convective drying of yacón (Smallanthus sonchifolius) slices[END_REF]. The black line indicates model predictions reached after assuming, in equation 10, the values D dry = 4.4 10 -12 m 2 /s and D wet = 1.7 10 -10 m 2 /s for water diffusivity in dry and wet material, respectively. The root-mean-square error was about 0.023 in X ⋆ w units. The vanishing value of water diffusivity under dry conditions is consistent with the product structure, nearly crumbly / brittle, after six hours of drying. Figure 2C presents the total surface reduction along the drying. A first decreasing tendency can be recognized from the beginning down to X ⋆ w ∼ 0.4 when the diameter reduction becomes progressively more significant (Figure 3C); later on, the total surface decreases to 30-35 % of its initial value. Figures 2B and2D show the dimensionless drying kinetics dX ⋆ w /dt and dX ⋆ w /dt.S ⋆ . Both derivatives should be directly proportional to X ⋆ w according to Lewis' (1921) drying approach. That classical model assumes no shrinkage along the drying, which is unsuitable for yacón samples. Model predictions indicate a more complex behavior for dX ⋆ w /dt; actually, this derivative includes the decreasing tendencies at the surface and the core, which can be different and unsteady along the process (see below). Figures 2E and2F compare model predictions with the measurements of dimensions of yacón slices as obtained by [START_REF] Marques | Data acquisition for modelling convective drying of yacón (Smallanthus sonchifolius) slices[END_REF] under the same drying conditions. Model results and observations of the slice height are hard to compare: on one hand, predictions of height correspond to the axis of symmetry; on the other hand, the upper and lower surfaces of the samples become rough along the drying, reducing the accuracy of the thickness measurement. The general decreasing tendencies of slice height and diameter are captured by model predictions.

In addition to bulk results about the food matrix under drying, the approach allows studying the evolution of elementary volumes therein. Figure 3 presents selected properties at two opposite positions along the axis of symmetry of the food slice: at the surface (1) and the core (2). Position 1 moves along with the shrinkage history, being always located at the slice surface; it is exposed to moisture gradients that are stronger than that at position 2. Figure 3A reveals that these positions follow almost the same temperature history; such a finding comes from a combination of the small distance separating these positions and high thermal conductivity in the product (see below). Beginning at T 0 = 20 • C, the temperature quickly reaches the wet-bulb temperature (about 34 • C), allowing favorable conditions to evaporation at the surface. Figure 3B presents the water content history at these positions. Convective drying is effective: after 1.5 h, it remains about 2 % of the initial water content at the surface. At this time, drying really starts at the core, following a slow-fastslow decreasing tendency. After six hours of drying there remains about 4 % of the initial water content at the core. Water diffusivity in the product is assumed to depend on both temperature and moisture, whose relative importance evolves as heating and drying progress with time. The influence of temperature decreases as the product reaches T re f = 60 • C (equations 10 and 11). The influence of moisture is more complicated: our results indicate that the water diffusivity value in wet material is more than 30 times superior in dry material (see above) and, as expected, their relative importance depends on the water mass fraction. Figure 3C shows that, at the surface, water diffusivity decreases from 6 10 -11 to 10 -11 m 2 /s along the drying. In other words, even after six hours of drying, the 'wet material' component of equation 9 still plays a non-negligible role. At the core, the water diffusivity follows an increasing tendency until drying effectively starts therein (after about three hours of drying); later on, the influence of moisture reduction becomes dominant. The evolution of water activity (Figure 3D) is delayed with respect to that of water activity and that of water content (Figure 3B). This result comes from high activity values even under moderate moisture values (e.g. a w ∼ 0.99 at X w ∼ 4.5 kg-w/kg-dm). Figure 3D highlights that the water activity is not homogeneous across the product slice, even after six hours of convective drying.

Previous figures have shown properties of the food matrix, both for the entire slice (Figure 2) and at positions that seem opposite (Figure 3), during whole the drying. Figure 4 provides a third perspective, displaying the temperature, water content, water diffusivity and water activity fields throughout the food slice at selected times. I. . . A remarkable result is the thermal homogeneity of the product slice, during the whole drying period. An explanation is provided by the low values of Biot number h(H/2)/λ ; its decreasing tendency (0.2 down to 0.06) is due to a stronger decrease in height (0.007 down to 0.001 m) than in thermal conductivity (0.6 down to 0.3 W/m/K). II. . . As expected, evaporation at the surface drives the water migration across the food slice. The lateral surface of the slice experiences faster drying than its upper and lower surfaces. After six hours under the convective drying conditions here considered, the slice volume decreased to about 7 % of its initial value. III... Water diffusivity varies with time and space following a complex pattern. At the slice surface, its decreasing tendency is driven by the moisture reduction; such a tendency is also verified in the whole slice after about three hours when drying effectively starts at the core (see Figure 4C). The influence of temperature decreases along the drying period, as the slice achieves the reference temperature 60 • C. IV. . . Water activity remained high after four hours, over 0.90 throughout large portions of the product slice, suggesting favorable conditions to selected pathogens. Results indicate the importance of latest hours of drying in effectively reducing the water activity at the slice core.

All these remarks apply after employing finer and coarser meshes in solving the same problem (results not shown). The time and spatial distributions displayed in Figure 4 put in evidence the strong coupling between heat and water mass transfer phenomena during the convective drying of a food slice.

Lastly, to the authors' knowledge, these results represent the first efforts in displaying how the water diffusivity and water activity evolve throughout a food matrix exposed to convective drying.

CONCLUSIONS AND RECOMMENDATIONS

We demonstrate that selected properties of a food slice under convective drying can be studied with a simple model including shrinkage. Our approach assumes that the volume reduction is primarily driven by the diameter reduction, i.e., by decreasing moisture at the plane of symmetry of the product slice. The assessment of such a tendency was possible from measurements of slice diameter. In this study, the water diffusivity in yacón samples was approximated through the two-phase structural model proposed by [START_REF] Maroulis | Moisture diffusivity data compilation for foodstuffs: Effect of material moisture content and temperature[END_REF]. Water diffusivity values under dry and wet conditions were identified after comparing the evolution of moisture from the experiment and model. These values are about 100 and 10 times smaller than similar associated with potato in the literature. Future work should assess the reliability of this approach under other convective drying conditions, while conducting additional efforts in identifying the parameters required by the two phase model. Testing this approach should consider wider ranges of ambient conditions (air flow, temperature and relative humidity) and including different varieties of yacón and later other raw food products. Much work remains to be done in order to clarify the relationship between shrinkage and moisture loss.

BIOGRAPHIES

BIANCA CRISTINE MARQUES is a Brazilian Ph.D. student at the Univ. de São Paulo, being advised by Carmen. As a part of her research, she met Artemio and Denis during one year at AgroParisTech. ARTEMIO PLANA-FATTORI studied Atmospheric Sciences at the Univ. de São Paulo and later in the Univ. Lille (Ph.D. in 1994). After 20 years teaching and doing research in Brazil, he joined AgroParisTech in 2010, where he works with numerical modeling applied to food engineering.

CARMEN CECILIA TADINI conducts research on food science and engineering, with applications in pasteurization, bakery, drying and biodegradable films by extrusion. She is Full Professor at the Univ. de São Paulo and author of one of the few textbooks about Food Engineering in Portuguese.

DENIS FLICK is Full Professor at AgroParisTech. He conducts research in modeling and numerical simulation of coupled phenomena in food processes (heat and mass transfer, fluid flow and product deformation, product transformation), with applications in food cold chain equipment, heat exchangers, cooking and baking, dairy products, bread, and ice cream. His teaching area includes transport phenomena, thermodynamics, and numerical modeling.

Figure 1 :

 1 Figure 1: Dimensionless diameter of yacón slices, as a function of dimensionless water content: observations under selected convective drying conditions reported by Marques et al. (2020b) and predictions based upon isotropic shrinkage.

  k/h = 1.02 10 -3 (vi) mesh J = 5 (vii) I = 6 × J = 30 (vii) time step ∆t = 0.01 s (vii) (i) Drying convective conditions (Marques et al., 2020b). (ii) Values at 40 • C (average between the slice initial temperature and the air temperature).

  RESULTS AND DISCUSSIONAt this step of development of the model, only the drying conditions [air flow 4 m/s, T air = 60 • C, RH air = 20 %] are taken into account. These were the most reproducible among the experimental tests conducted by[START_REF] Marques | Data acquisition for modelling convective drying of yacón (Smallanthus sonchifolius) slices[END_REF] in drying yacón samples with a pilot unit convective dryer.

Figure 2 :

 2 Figure 2: State of the food slice according to model predictions (black lines) and to observations of mass loss (colored lines) and of slice dimensions (squares), under drying conditions [air flow 4 m/s, T air = 60 • C, RH air = 20 %]. Arrows recall that water content decreases along the drying.

Figure 3 :

 3 Figure 3: Selected properties in two positions along the axis of symmetry of the food slice: at the surface (1) and at the core (2).

Figure 4 :

 4 Figure 4: Temperature, water content, water diffusivity and water activity fields in the food slice at selected times. Dimensions of the food slice are expressed in meters. Positions 1 and 2 considered in Figure 3 are also displayed.

Table :

 : Key parameters considered in simulations.

	air temperature	T air = 60 • C (i)
	air relative humidity	RH air = 20 % (i)
	slice initial temperature	T 0 = 20 • C (i)
	slice initial water content	X w,0 = 11 kg-w/kg-dm (i)
	slice initial height	Z 0 = 0.007 m (i)
	slice initial radius	R 0 = 0.02 m (i)
	water density water heat capacity water thermal conductivity λ # ρ # w = 991 kg/m 3 (ii) C # w = 4180 J/kg/K (ii) w = 0.631 W/m/K (ii)
	dry matter density dry matter heat capacity dry matter th. conductivity λ # ρ # dm = 1590 kg/m 3 (iii) C # dm = 1620 J/kg/K (iii) dm = 0.250 W/m/K (iii)
	latent heat of vaporization L v = 2.36 10 6 J/kg (iv)
	heat transfer coefficient	h = 32 W/m 2 /K (v)
	mass / heat transfer coeff.

ACKNOWLEDGEMENTS

Authors B.C.M. and C.C.T. received grants from Brazilian agencies: grants 2018 / 21327-1, 2019 / 21832-0, and 2013 / 07914-8 from the São Paulo Research Foundation (FAPESP); finance code 001 from the Coordination for the Improvement of Higher Education Personnel (CAPES); and grant 306414 / 2017-1 from the National Council for Scientific and Technological Development (CNPq). We warmly acknowledge AgroParistech and UMR SayFood for kindly receiving the first named author for a one-year research internship.


Alexandra Midal
email: alexandra.midal@hesge.ch

Death of Women: The Dark Side of Modern Design History

Keywords: design history, serial killer, female gaze, dis-anonymisation, historiography

In the 1880's, Herman Webster Mudgett, better known as Henry Howard Holmes built a lethal, practical, and convenient building containing nearly one hundred rooms, apartments, and retail storefronts in Chicago. Holmes's design achievement is a functionalist paradigm that fits in perfectly with the perspective of modern mechanization and its implementation. As a manifestation of seriality, Holmes murders are the product of a convergence of rationales through which two seemingly antagonistic practices were united by one common denominator: the new industrial modes of production, of which design and serial murder are but two different manifestations. This dark side masterfully embodied by the anonymous designer enables us to rethink the history of design as written by Nikolaus Pevsner and Siegfried Giedion. A critique of the conventions of the discipline archetypically embodied by Holmes, whose attention to innovation and industrialization never subsided is all the more powerful as it deconstructs the original misconception of virtuous design. It is therefore around the edges of the epic narrative of its "pioneers," as Pevsner calls them, that the history of design-a history at once more complex and dark-unfolds. But there is more, most victims killed by Holmes were women. Not only women disappeared in the house, but this functionalist apparatus reflects and reveals a dreadful disappearance of women. They are absent from modern narrativized constructions that tends to present a single history of ideas and white ontological, moral, and social forms. If both women and evil are glaringly absent, these contributions are instrumental to the revision of the discipline

Introduction

Taken together, Nikolaus Pevsner's Pioneers of the Modern Movement and Siegfried Giedion's Mechanization Takes Command could be considered the founding texts of the history of design. In his 1936 book, Pevsner retraces the history of the Modern Movement, whose origins he locates in the European industrial revolution. Pevsner seeks to establish a singular, unitary lineage for the Modern Movement with a genealogy of heroic figure made explicit by the subtitle of his book, From William Morris to Walter Gropius. In a very different manner, Giedion's Mechanization Takes Command published twelve years later, after WWII, in 1948, encompasses a vast range of inanimate and sentient subjects: from bolts to the butchering of animal carcasses in the famous Chicago's slaughterhouses. Giedion's approach put together an encyclopedic history of innovation-intertwined with the history of art. Giedion's narrative displays the evolution of the techniques that unite the aesthetic and the mechanical becomes a triumphant story of progress. What, then, can be achieved by looking at these two texts together? What do they have in common, aside from offering two versions of the history of design and its origins written almost contemporaneously by two white European men?

Both claims an objective approach, and both offer a scheme of reference points from which it is possible to analyze design from its very beginnings. Both texts produced by male authors considered to be major critics associated with the Modern Movement in architecture, set up a biased design history for whom design was far from core concern. And as I have demonstrated in my counter-historiography of design: Design by Accident [START_REF] Midal | Design by Accident, For a New History of Design[END_REF], neither Pevsner nor Giedion set out to establish a history of design as such. For them, design was a functionalist anchor to a wider line of thought.

-A Woman Lineage Interestingly, for a couple of pages, in Mechanization Takes Command, Giedion succinctly evokes the work of American educator Catharine Beecher and explains how her 1841 bestseller A Treatise on Domestic Economy quite literally transformed the American domestic landscape. For Giedion, Beecher's embodies a kind of enclave in the history of design in which women establish the domestic sphere as a space of social and political form intertwined with national ramifications. Model figure, Catharine Esther Beecher, not only coined the "domestic economy." (Beecher 1846, 5) but she also elevated the organization of the home to the political sphere. Beecher pioneered the notions of domestic economy, rationality, and hygiene. Her contribution ranged from practical inventions, such as devices for ventilation and air circulation, or the continuous work surface (1869) that we still use today, to broader principles such as the rational design and use of rooms, the regulation of temperature, practical storage, and even body posture and care. Illustrated with diagrams showing optimum storage strategies for everything from shoes to spices to fabric, as well as anatomical charts and plumbing models, her books mark a change in the status of the housewife, recognizing the homemaker as a profession. She calls for housewives to be considered as "house physicians who would be as liberally educated and paid as men for curing diseases" (Sklar,1973;1981, 268) In amongst the recipes and advice on maintaining good health, one finds a redefinition of women's place in nineteenth-century industrial society. She equates the emancipation of women with the rational organization of their home. just as men begin their careers only after many years of study, it is only through some form of instruction that women can fully assume their professional responsibilities as mothers, wives, and homemakers. Such adaptation of the industrial model to the home brings an unexpected corollary: Beecher demands for women who had trained and been educated in the upkeep of the home to be granted financial independence. Beecher's notion of the rational home is complex, she problematizes the conception of functionalism as the efficient, impersonal servant of capitalism, and she considers that women should always obey the dominant patriarchy.

In extolling the value of domesticity and seeking to influence the education of an elite class of young women, Beecher aimed not so much to raise the status of American women as to make them aware of their grave responsibilities in the context of a nation in peril. The ambiguous nature of her revolution reflected the contradictions in her own life philosophy: while she was uninterested in altering the balance of power within the home, as the historian Janice Williams Rutherford observes, "Beecher espoused the doctrine of separate spheres, yet she sought the power and influence available only to men under the terms of that doctrine." (Rutherford 2003, xix) Beyond her promotion of rationality, and behind her functionalist discourse, Beecher's functionalism ultimately anticipates the outcomes of a parallel ideology that aimed not only to lessen the burden of women but also to lend weight to abolitionist arguments. Beecher expounded an ideology that aimed not only to ease the labor of women and more importantly to lend weight to her abolitionist convictions: Through rationalization, she demonstrated that slaves were no longer necessary for the upkeep of the home. Also, Beecher's position counters misconceptions that all discussion of design by women should reductively replay the tensions between industrial and craft production, and in turn between men and women. Returning to Beecher, the legacy of her educational mission, and the many theories it subsequently informed, dispels the notion of design as an exclusively design masculine phenomenon as it was said to be. Beecher's conclusions were but the starting point for an ongoing feminine reflection lineage on the mechanization of domestic tasks, such as the domestic Taylorism by feminist Paulette Bernege, which would continue throughout the twentieth century, but that was also easily put aside, and frequently forgotten. And Despite the social and political ramifications of their work, however, none of these women set out to reform the relationship between the sexes. Although she has often been relegated to the sidelines, much is owed to Lillian Moller Gilbreth, referred to during her lifetime as the "First Lady of Industrial Engineering," who, in addition to raising her twelve children, founded a school for time and motion studies that won the confidence of industrialists. She introduced principles of psychology to scientific management with her publication in 1914 of The Psychology of Management, with its explicit subtitle, The Function of the Mind in Determining, Teaching and Installing Methods of Least Waste. Gilbreth was far more than a mere spouse, assistant or collaborator: she earned a doctorate from Brown University and was the first woman to become a member of the prestigious American Society of Mechanical Engineers. She went on to teach mechanical engineering at Purdue University, emphasizing the importance of motivation, satisfaction and stress as important factors that needed to be integrated into rational organization, standardization, and ergonomics. In 1912, she had begun visual research on body movement and set up her first studio with her husband Frank. The dynamics of market-driven media worked to abstract the worker experience, increasingly alienated by commodification. In 1924, Frank was struck down by a heart attack in a phone booth, while he was on the line with his wife.

-A Female Gaze From that point on, Lillian took over the helm of the enterprise Gilbreth, Inc. on her own that the couple had created twelve years earlier. In order to better manage the raising of her eleven children, she relocated her laboratory and installed her office at her home. In turn, her family gradually became subjects for her research. She observed them to gauge whether she could apply the same principles of scientific labor management that were being implemented in factories to her household. Without stooping to caricature, it was understood that the couple divided tasks among themselves: Frank dealt with travel, the publicizing of their experiments and any artistic direction behind the camera, while Lillian handled the writing. Of course, his death changed the situation: Lillian continued to pursue their research projects, and oversaw the filming. One might surmise in a sense that she was the first woman who transferred cinematographic shooting techniques from the factory to the home. This shift in no way diminished the ambition and scope of her research, but in thus taking control of her film production, she instigated a revolution that redefined the housewife of the early 20th century. She was not the factory worker, mother and spouse who indefatigably dedicated herself to her household, but rather an operatorin-chief who assumed a double role of object and subject, as she explains in one of her works: If a film were taken… of you washing dishes, you could see yourself doing the work at the actual speed at which you did it and thus notice what rhythm and ease you had developed, or you could see yourself making the same motions very slowly, detect your slightest awkwardness, and find out just why you succeeded or failed at the work. (Gilbreth 1928, 114-116).

As numerous scholars analyzed it, Lillian Gilbreth inverted the dominant male gaze, replacing it with a 'female gaze: by encouraging women (as housewives) to conceive of themselves as both camera and subject, seeing and seen, repositioning the female gaze within the constraints of an explicitly masculine scientific objectivity. In his brilliant evaluation of L. D. Graham's recent analyses, Nicholas Sammond describes this characteristic evolution in cinema which developed in parallel with the rationalized observation of the home: "Gilbreth's fantasy of a domestic time-and-motion cinema placed a woman-already fragmented as woman, wife, and mother-in two subject positions simultaneously: as the producer of the spectacle of her filmed labour and as its spectator (Sammond 2006,105). The incorporation of scientific management considered an androcentric prerogative," shifted to the domestic sphere, a territory generically associated with the feminine. Even if this did not change the status of women, nor the preponderance of the dominant male gaze, as we know it, the contribution of Lillian Gilbreth made her as much a pioneer in the realm of cinema as she was in the history of design. Nevertheless, Lillian's contribution was limited to her status as wife and mother. Often relegated to being her husband's 'little woman', she often remained in his shadow, adopting a submissive position that was in no way commensurate with the importance of her work. Even after Frank's death, the works concerning the couple's research almost never treat Lillian's work as an individual effort. However, the patriarchal context, what is more, amidst a family that advocated eugenics, was not conducive to Lillian's assuming a position as a defender of equal rights for women, much as she might have desired it. Still, she does make a forceful argument for gender equality: So many things [that] have been accepted time without end as sex differences have proved to be only type differences that it is necessary to proceed slowly and carefully in any investigation if insufficiently grounded hypotheses are to be avoided. It may be that the findings of the ancients as to sex differences, mental and emotional, were wrong. (Sammond 2006,115-116).

It was necessary to wait for the publication of Graham's analyses to begin to balance this injustice. This fate is a constant that comes from the inherently patriarchal origins of the history of design, in which the contributions of women are often passed over, or merely subsumed with those of their husbands. This spectral element in some of Gilbreth's images captured the eye of graphic designer Rick Poynor who comments as follows: "What appealed to me then, and this hasn't changed nearly three decades later, is (…) the spectral figure of the woman (…)" [START_REF] Poynor | Exposure: Motion Efficiency Study by Frank Gilbreth[END_REF]. In his examination of a famous photogram by the Gilbreth visual Taylorism, dated 1912, of a woman factory worker busying herself at her work before a camera, Poynor perceives a triple negation: the spectral of gender, that of women, the spectral of activity, that of the labor and individuality of the author, and finally, the spectral of class struggle, with the physical disappearance of the factory worker. these proto-designer carried out research into the organization of the home raises something of a paradox. Their projects reinforce a marked separation between the public and private spheres, yet at the same time promote a reform of domestic organization and the education of women with a view to their emancipation. They strive for domestic chores to be recognized, not as the socially inexistent activity of the subaltern, but as a profession in its own right. However, while they succeeded in maintaining society's stability by reconciling division of roles along gender lines with the modernization of the private sphere that threatened to destabilize them, they also allowed men to retain their power and the spaces associated with it. This is why the advent of a female conception of design actually preserved divisions along gender lines rather than challenging them.

-Rewriting History: Women are Serial Victims To begin the history of design with Pioneers of the Modern Movement is to begin with a paradox. To suggest that this work, which declines to confer upon design the status of a discipline, and whose subject is not design but the prehistory of modern architecture, is clearly problematic. Nor does Mechanization Takes Command simplify the issue. Giedion was barely more interested in design itself than Pevsner. But the weaving together of these two histories sets out the basis for a critical awareness necessary for the construction of an autonomous history of design. Morris is no longer design's heroic figure, but is preceded by a heroine-or rather, non-heroine-in the form of Beecher, and her followers. In reintroducing into the history of design and its origins women, I am trying to participate in the urge for redefining the discipline's scope and stakes. But I am concerned that it is only one among many other revisions that needs to be made. Therefore, I would like to invite H. H. Holmes [START_REF] Midal | La Manufacture du meurtre[END_REF]2022), the so-called first serial killer of the US into the debate.

Why a serial killer? If the dismantling of the modern movement narration of design history needs to be done beyond the usual androcentrism, as well as the western unitarian vision, the questioning of the moral standing point defined as a pinnacle by Pevsner, that was never questioned as such, and he is still effective behind the pristine ethic vocabulary that prevail in design today, can find with the case study of H. H. Holmes an interesting counter point, but also as we will see at the end, in a male dominated debate, Holmes expresses and personifies the violence against women.

It will be remembered that the remains of a large kiln made of fire brick was found in the Castle basement. It had been built under Mr. Warner's supervision for the purpose of exhibiting his patents. [. . .] It was into this kiln that I induced Mr. Warner to go with me, under pretense of wishing certain minute explanations of the process, and then stepping outside, as he believed to get some tools. I closed the door and turned on both the oil and steam to their full extent. In a short time not even the bones of my victim remained. (H. H. Holmes 1896;2005, 347) It was in these terms that America's serial killer, Herman Webster Mudgett, better known as Henry Howard Holmes, confessed to one of the countless crimes he had committed by strangulation, asphyxiation, cremation, and various other means in the house he had designed for this very purpose. While the newspapers attributed several hundred murders and disappearances to him, the exact number of his victims cannot be established with certainty. Indeed, some of the people Holmes himself claimed to have killed, such as his janitor Robert Latimer, appeared in flesh during his trial (their identity could be established beyond doubt thanks to their birth certificates). There is no doubt, however, that Holmes was a serial killer, as well as a patent liar and a con man whose career in crime betrays a sound understanding of the technologies of his time-the era of late nineteenthcentury industrial capitalism. In 1896, aged thirty-five, Holmes, the man with multiple identities, was sentenced to death and hanged, taking his secrets, inventions, and lies with him to his grave. Just ten years earlier, Holmes had acquired a patch of land he had been coveting for a while. Although not a professional architect, he drew up the plans for his future home and supervised its construction down to the smallest detail. His construction was so vast that neighbors called it "the Castle." Few would have guessed, though, that behind its stylish facade, the house boasted some of the most advanced domestic furnishings of its day, including a dumb waiter, a humansized furnace, and a wall-to-wall remote-controlled gas and electricity system. The ultimate rational-mechanical setting for homely murder mysteries, Holmes's building partakes in the literal realization of the modernistfunctionalist project as formalized by Pevsner in Pioneers of the Modern Movement and by Giedion in Mechanization Takes Command. The figure of Holmes, it appears, occupies a counter-position to Pevsner's homogeneous, linear succession of virtuous and heroic "pioneers." But is Holmes any closer to Giedion's Mechanization, which adopts a radically different perspective? Remember Giedion's encyclopedic project maps the relationships between technological achievements on the one hand, and social and cultural evolutions on the other. This approach leads him to argue in favor of a history of aesthetic and mechanical innovation in the triumphant perspective of progress. It is in this perspective that Holmes's activities should be seen. At once lethal, practical, and convenient, his Castle contained nearly one hundred rooms, apartments, and shops. Holmes's architectural feat is firmly rooted in the historic functionalist project, questioning both this very project and its limits. It would be naïve to consider the inception of the American industrial revolution and the almost simultaneous emergence of the serial killer as a mere coincidence. Dark Designer: A Career? For this presentation, I decided to reach beyond society's morbid fascination with lurid crime stories, and to examine instead Holmes's architectural achievement not only as a functionalist paradigm that fits in perfectly with the perspective of modern mechanization and its implementation, but also as a manifestation of seriality at the crossroads of the assembly line and the invention of the concept of the "serial killer." My hypothesis is that, far from being a coincidental appearance, Holmes was the product of a convergence of rationales through which two seemingly antagonistic practices were united by one common denominator: the new industrial modes of production, of which design and serial murder are but two different manifestations. The joint emergence of these concepts suggests a triangular relationship between the conception of human life, seriality (and its corollaries), and the human psyche challenged by modernity. This shift in perspective is not without consequences. This shift was described by Holmes's contemporary, the engineer Thomas Alva Edison, in the following terms: "Problems in human engineering will receive during the coming years the same genius and attention which the nineteenth century gave to the more material forms of engineering." (Edison 1917, 301) "It has to be recognized that, in his ghoulish way, Holmes was as much the exponent of the American dream as Henry Ford or Horatio Alger." (Wilson 1969, 206) As Colin Wilson's assessment suggests, the practice of serial killing conflates with the history of industrialization. The proliferation of appliances designed to improve the household economy follows the rise of industry at large, echoing the modernization of factory assembly lines and the specialization of tasks. The unprecedented confluence of efficiency and mechanization was made possible by the latter spreading beyond the production of consumer goods to serve as a model for the slaughtering and dismembering of livestock on the world's first assembly lines in Chicago's mechanized meat factories. Against the backdrop of these simultaneous and massive developments, this disturbing coincidence appears as an incarnation of a world where the relationships between the inanimate and the living culminate in a situation where neither animal nor human life is spared by the machine and the lure of profit. The serial pattern characteristic of industrial production finds its most extreme manifestation in Holmes because, "in the story of Holmes and his crimes, there is nothing more interesting than the description of his Castle, where he is accused of having provided all sorts of devices for disposing of his victims [. . .] It was built with the sole idea of convenience for the commission of crimes (Anon. 1896, 3)," as a contemporary newspaper noted. At the dawn of the nineteenth century, by revisiting and adapting the principles of industrialization to the home, and by combining them with the convenience of efficiency and functionality, the first serial killer in American history exposed the uncontrollable consequences of mechanization and revealed its dark side.

The nineteenth century in the United States was marked by the invention of devices, tools, and systems derived from industrial manufacturing that became indispensable instruments in the smooth running of the modern house. Catharine Beecher was a conceptual pioneer in this field, as she conceived the equipment of the house according to hygienist and functionalist principles inferred from her observations of assembly-line work in the Lowell model plant. She invented domestic rationalization, applying the scientific principles of standardization to the household. Beecher conceived the house as a functional entity; mirroring the organization of the factory, she advocated a rationalization of the housewife's tasks with a view to saving time and alleviating fatigue. By appropriating the organizational principles of assembly lines and the specialization of tasks in the country's factories for her own purposes, she initiated a revolution. These transformations influenced the experiments of researchers and anonymous users alike, to which Giedion pays tribute in the subtitle of his book. Holmes's "anonymous contribution" can be situated between these two poles-in what Seltzer describes as a profession: "Serial killing, by all accounts, became a career option at the turn of the century" (Seltzer 1998,1). Holmes plays an important role in the origins and foundations of modern design, which since Pevsner had been interpreted as the galvanization of democratic morality adapted to the industrial changes introduced by manufacturers. By highlighting the extent to which the house had turned into a stage-and if we admit that "the scene of the crime is also the scene of invention" (Seltzer 1998, 217) -Holmes's story forms part of a history that reaches beyond a summary distinction between good and bad. Holmes's victims were mainly women. Newspapers estimated that he had employed more than one hundred women-and as sources vary widely and many are based on speculation, victim counting is a nearly impossible task. In one of his confessions, he admitted to having assassinated fourteen women: Julia L. Connor and her daughter Pearl, a woman named Lizzie, Sara Cook (who was pregnant), Mary Haracamp (a tenant), Emeline Cigrand Rosine van Jassand, Anna Betts, Gertrude Conner, someone he named "Miss Kate," Minnie and Nannie Williams, and Alice and Nellie Pitezel. As Frank Geyer, the Philadelphia police inspector who eventually tracked Holmes down in Boston, noted, all the women with whom Holmes had been romantically involved were blonde. His victims were almost exclusively women, whether his mistresses, employees, and/or accomplices. And the truly remarkable fact is that they all met their tragic fate in the mechanized lair of the Castle. Holmes's standardized murder practice negated both the individuation of the subject and the singularity of his victims, while engaging with techno-capitalist rationalization.

Androcentric Neurosis

Historically, design was founded on a rational homology between manufactured production and household organization, and between economics and functionalism. But a relationship also exists between the treatment of the products of capitalism, whether consumer goods or (mainly female) workers' bodies, and technical rationality pushed to its extremes. Preempting the laws of "good design," Holmes conceived a hyper-functional space in which he could perform all of his activities rationally, conveniently, and quietly. He was so attached to his house and its furnishings that, even as he was fleeing from the police, he was making projects to build a complex of houses based on the model of his Chicago Castle. His case therefore shakes the foundations of the naive Pevsner and Giedon's history of modern design.

The critique of the conventions of the discipline is more powerful as it deconstructs the original misconception of virtuous design. It is therefore around the edges of the epic narrative of its "pioneers," as Pevsner calls them, that our story-at once more complex and more daring-ties in with the origins of design. It is here embodied archetypically by Holmes, whose attention to innovations and industrialization never subsided. Examining the malevolent potential of design through the figure of Holmes and adopting the idea that crime produces an "increase in wealth"-to use Karl Marx's terminology in Theories of Surplus Value [START_REF] Marx | Apologist Conception of the Productivity of All Professions[END_REF])-allows us to highlight the ambiguities of a formidably complex yet often simplified discipline. As we know, William Morris was wary of the consequences of the industrial revolution on working and living conditions in urban behemoths such as London; Holmes, on the contrary, embraced its achievements wholeheartedly. The juxtaposition of these two antagonistic figures-Morris as Doctor Jekyll and Holmes as Mister Hyde-brings into focus the crucial point of our story: the relationship between morality and progress. Each in their own way, these two contemporaries (who, incidentally, died the same year) put this relationship to the test, the former by exalting it, the latter by exploiting it. Holmes's criminal career questions the foundations of mechanization as profoundly as the virtuous practices of Morris and the Arts & Crafts movement. Highlighting the innate polarity of design, their respective trajectories therefore raise similar issues. This approach takes inspiration from the work of historian Reyner Banham who, in "History and Psychiatry," (Banham 1960, 325-332) pointed out the blind spots and denials of the history of modern architecture and accused his predecessors of "amnesia." By appropriating the vocabulary of psychoanalysis to characterize historians' intentional and unintentional omissions, Banham took a distanced view that paved the way for a more nuanced reconstruction of the history of modern movement. His concept of a "zone of silence" -a grey area masterfully embodied by the anonymous Holmes-further enables us to rethink another history of design. By evoking its horror, we question the virtuousness with which technology was originally associated, if not confused. But more importantly, highlighting its intrinsic toxic potential enables us to shift the central status of functionalism in favor of a new perspective. It remains to be seen if design is strong enough-and nothing is less certain -to finally allow for the integration of these "missing masses," this accursed share, or to balance Pevsner perspective and to comply to Giedion's mechanization dedicated to the anonymous, even if absolutely different by nature, the role of women such as Beecher or Gilbreth by instance as well as the role of evil figure such as Holmes, are all alike forgotten invisible figure of a bias history of modern design that calls for revision. In combining woman designers on the one side and a serial killer of women on the other side, and to claim for the reintegration of these two grey forgotten zones of design history, even if entirely different, unveils simultaneously this two perspectives, one that try to restore the woman legacy for a design discipline, showing important milestones, anonymous as heroine, open to a necessary lineage up to today's, and the other, amoral, capitalist, murderer, show that beyond the usual binary design debates, it is important to dismantle the conventional design mythology narrative, moral on one side and patriarchal on the other without substituting it by one or other narratives. To integrate a series of parallel histories forgotten by the first western design histories, to incorporate numerous missing strata exposes the necessity to rethink in a bigger scope the diversity of design origins and perspectives. Still, the fact that the common thread here is that women are always the victims, may they be killed, their flesh destroy by quicklimes in Holmes Castle basement and their skeleton rearticulated to be sold to medicine school for 25 to 45 dollars each, or may they be the litter women of their husband, father or son and have disappeared in the closets of history, maybe it is time to stop using the usual metaphor of ghost or erasure and invisibility, and adjust H. H. Holmes as the embodiment of the immoral, androcentric, lethal design history, and instead reclaim a fair trial for the literal murder of the women -women historians as well as women designers.

About the Author:

Dr Alexandra Midal combines a curating and research activity in design and visual culture. Professor in the Master Spaces & Communication at HEAD -Genève, she teaches theoretical and practical workshops around the films by designers.

Former Director of the Regional Founds of Contemporary Art of Haute-Normandie (FRAC), and former assistant of Dan Graham, she has curated numerous shows in international museums. Her next show "Top Secret » investigates the image and espionage" La Cinématheque française, La Caixa, Madrid ; Barcelona. Midal realizes theoretical films touring in museums worldwide. Since 2016, Midal is curating the Design Film Festival, an education program of experimental films focused on exploring post-media design language and the narratives Her most recent publication is Design by Accident, For a New History of Design (Sternberg Press).