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Papers by claire meyer

Research paper thumbnail of Focal Conic Stacking in Smectic A Liquid Crystals: Smectic Flower and Apollonius Tiling

Materials, Apr 22, 2009

We investigate two different textures of smectic A liquid crystals. These textures are particular... more We investigate two different textures of smectic A liquid crystals. These textures are particularly symmetric when they are observed at crossed polars optical microscopy. For both textures, a model has been made in order to examine the link between the defective macroscopic texture and the microscopic disposition of the layers. We present in particular in the case of some hexagonal tiling of circles (similar to the Apollonius tiling) some numeric simulation in order to visualize the smectic layers. We discuss of the nature of the smectic layers, which permit to assure their continuity from one focal conic domain to another adjacent one.

Research paper thumbnail of Periodic lattices of frustrated focal conic defect domains in smectic liquid crystal films

Soft Matter, 2012

We have created periodic lattices of close-packed non-toroidal focal conic domains (FCD) in smect... more We have created periodic lattices of close-packed non-toroidal focal conic domains (FCD) in smectic A liquid crystal films deposited on solid substrates that induce unidirectional planar anchoring, at the interface with air which induces homeotropic anchoring. Each cell of the ...

Research paper thumbnail of Double helices folding half parabolic focal conics in chiral smectics

Liquid Crystals, 2011

In this paper, we report the existence of a double helix folding a part of one of two cofocal par... more In this paper, we report the existence of a double helix folding a part of one of two cofocal parabolae. We observe the winding/unwinding of the double helix as temperature is changed and this mechanism is accompanied here by a change of the latus rectum p of the corresponding parabola. We propose a model of the layers inside and outside

Research paper thumbnail of Influence of the rheological properties on the electrical impedance of hydrogels

Journal of Applied Physics, 2012

We show that the anomalous frequency dependence of the real part of the electrical impedance of h... more We show that the anomalous frequency dependence of the real part of the electrical impedance of hydrogels can be interpreted by taking into account their non-Newtonian character, according to which the effective viscosity, η, depends on the frequency of the imposed deformation. Our experimental results are in good agreement with the Poisson–Nernst–Planck model if the ionic viscosity is taken proportional to the macroscopic one, measured by means of a viscositymeter, and the diffusion coefficient is assumed frequency dependent according to the formula of Stokes D = KBT/(κη), where κ is a shape coefficient. From this result it follows that the non-Newtonian character of complex liquid can be investigated by means of the impedance spectroscopy technique.

Research paper thumbnail of Optical Microscopy Observations and Construction of Dupin Cyclides at the Isotropic/Smectic A Phase Transition

Materials, Aug 12, 2021

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Research paper thumbnail of Biaxiality-driven twist-bend to splay-bend nematic phase transition induced by an electric field

Science Advances, 2020

An electric field–induced, symmetry-breaking, transition from N TB to N SB nematics reveals the i... more An electric field–induced, symmetry-breaking, transition from N TB to N SB nematics reveals the importance of local biaxiality.

Research paper thumbnail of Fréedericksz-Like Transition in a Biaxial Smectic- A Phase

Research paper thumbnail of Flexoelectrically Driven Electroclinic Effect in the Twist-Bend Nematic Phase of Achiral Molecules with Bent Shapes

Physical Review Letters, 2013

We extend the twist-bend nematic (N TB) model to describe the electro-optics of this novel phase.... more We extend the twist-bend nematic (N TB) model to describe the electro-optics of this novel phase. We predict an electroclinic effect (ECE) subject to a dc electric field E applied perpendicular to the helix axis or wave vector q, with rotation of the N TB optic axis around E. This linear effect, with its flexoelectric origin, is a close analog to the electro-optic effects observed for chiral liquid crystals. However, in nematics composed of achiral molecules having a bent shape, it is the electro-optic signature of the N TB phase. We test our model experimentally in the low-temperature nematic phase of the odd liquid crystal dimer, CB7CB, with its molecules having, on average, a bent shape. The ECE measurements confirm the previously proposed twist-bend nematic structure of this phase, with its broken chiral symmetry, extremely short (<10 nm) doubly degenerate pitch and ultrafast, submicrosecond response times.

Research paper thumbnail of The temperature dependence of the heliconical tilt angle in the twist-bend nematic phase of the odd dimer CB7CB

Journal of Materials Chemistry C, 2015

Precise birefringence measurements in large monodomains of the twist-bend nematic phase strongly ... more Precise birefringence measurements in large monodomains of the twist-bend nematic phase strongly support its heliconical structure and doubly degenerate handedness.

Research paper thumbnail of The Construction of the Dupin Cyclides in a Smectic A Polygonal Texture

Journal of Materials, 2014

We report experimental observations with optical microscopy of the usual so-called polygonal text... more We report experimental observations with optical microscopy of the usual so-called polygonal texture. We have made simulations of the Dupin cyclides in one small region of the sample.

Research paper thumbnail of Cholesteryl and diosgenyl glycosteroids: synthesis and characterization of new smectic liquid crystals

Carbohydrate research, Jan 2, 2015

While present in large numbers in nature, studies on the physical chemical aspects of glycosteroi... more While present in large numbers in nature, studies on the physical chemical aspects of glycosteroids are quite rare and focused on cholesterol, and all compounds studied thus far have shown liquid crystalline properties in a narrow temperature range. New glycosteroids composed by cholesterol or diosgenin and different glycosidic moieties have been synthesized here in order to analyze the influence of the structure on the formation of mesophases. These compounds have been studied by crossed polarized optical microscopy. These studies have revealed that these new glycosteroids form Smetic A liquid crystals in a broad temperature range.

Research paper thumbnail of Influence of alkyl chain length on the mesomorphism of 5-S-Alkyl-5-thiopentonolactones and 5-S-Alkyl-5-thiopentitols

Carbohydrate Research, 2014

Mesomophic properties of S-alkylthiopentonolactones (D-ribono, D-arabinono and D-xylono) and corr... more Mesomophic properties of S-alkylthiopentonolactones (D-ribono, D-arabinono and D-xylono) and corresponding alditol derivatives with the general formula Su-SR (R=C n H 2n+1; n=5-12) are studied. It was shown that the thermotropic and lyotropic phase transition temperatures are influenced by the following structural parameters: alkyl chain length, cyclic or acyclic Su structure and alditol conformation. Besides, it seems that n parity affects thermotropic phase transition temperatures.

Research paper thumbnail of Optical Microscopy Observations and Construction of Dupin Cyclides at the Isotropic/Smectic A Phase Transition

Materials, 2021

In this work, we are interested in the nucleation of bâtonnets at the Isotropic/Smectic A phase t... more In this work, we are interested in the nucleation of bâtonnets at the Isotropic/Smectic A phase transition of 10CB liquid crystal. Very often, these bâtonnets are decorated with a large number of focal conics. We present here an example of a bâtonnet obtained by optical crossed polarized microscopy in a frequently observed particular area of the sample. This bâtonnet presents bulges and one of them consists of a tessellation of ellipses. These ellipses are two by two tangent, one to each other, and their confocal hyperbolas merge at the apex of the bâtonnet. We propose a numerical simulation with Python software to reproduce this tiling of ellipses as well as the shape of the smectic layers taking the well-known shape of Dupin cyclides within this particular bâtonnet area.

Research paper thumbnail of Helical defects in smectic-Aand smectic-A∗phases

Physical Review E, 2010

There are two categories of helical line defects in Sm-A phases: screw dislocations of small Burg... more There are two categories of helical line defects in Sm-A phases: screw dislocations of small Burgers vectors and double helices ͑DHs͒, whose macroscopic configuration constitutes a mode of splitting of screw dislocations of giant Burgers vectors. Their counterparts in Sm-A ‫ء‬ 's ͑Sm-A's with chiral molecules͒ show a number of differences with the former and are investigated theoretically on the basis of recent observations ͓C. Meyer et al., Liq. Cryst. 37, 1047 ͑2010͔͒. The first part of the paper is a short review of the main features of helical defects in Sm-A's proper. In Sm-A ‫ء‬ 's, small Burgers vector screw dislocations with the same chirality as the high-temperature N ‫ء‬ phase are favored over the opposite ones, a result that is related to the defect core singularity. This is also true for the macroscopic DH ‫ء‬ s for a more subtle reason; we advance that the DH ‫ء‬ nucleation at the N ‫ء‬ → Sm-A ‫ء‬ transition stems from a peculiar texture of the cybotactic groups, akin in the ideal case to a set of two twisted disclinations in the N ‫ء‬ phase, linked by a stacking fault of continuous disclinations. This stacking fault vanishes in the Sm-A ‫ء‬ phase, and one recovers a DH ‫ء‬ much similar to a DH but with the appropriate chirality. Cases that differ from ideality are described: they involve small Burgers vector screw dislocations and can be evoked to explain the numerous observed distorted double helices ͑the Darboux condition is not obeyed͒ and twisted ribbons. The case when the N ‫ء‬ → Sm-A ‫ء‬ transition is type II ͑presence of a twist grain boundary phase in between͒ is briefly discussed.

Research paper thumbnail of Imperfections in focal conic domains: the role of dislocations

Philosophical Magazine, 2006

It is usual to think of Focal Conic Domains (FCD) as perfect geometric constructions in which the... more It is usual to think of Focal Conic Domains (FCD) as perfect geometric constructions in which the layers are folded into Dupin cyclides, about an ellipse and a hyperbola that are conjugate. This ideal picture is often far from reality. We have investigated in detail the FCDs in several materials which have a transition from a smectic A (SmA) to a nematic phase. The ellipse and the hyperbola are seldom perfect, and the FCD textures also suffer large transformations (in shape or/and in nature) when approaching the transition to the nematic phase, or appear imperfect on cooling from the nematic phase. We interpret these imperfections as due to the interaction of FCD's with dislocations. We analyze theoretically the general principles subtending the interaction mechanisms between FCD's and finite Burgers vector dislocations, namely the formation of kinks on disclinations, to which dislocations are attached, and we present models relating to some experimental results. Whereas the principles of the interactions are very general, their realizations can differ widely in function of the boundary conditions.

Research paper thumbnail of Rheological properties of chiral liquid crystals possessing a cholesteric–smectic A transition

Research paper thumbnail of Structural and Thermomechanical Investigation of Lyotropic Liquid Crystal Phases Doped with Monodisperse Microparticles

Applied Rheology, 2014

We present a study of the structural and thermomechanical properties of lyotropic phase in the qu... more We present a study of the structural and thermomechanical properties of lyotropic phase in the quasi ternary system made of Cetylpyridinium chloride (CPCl)/hexanol/salt water (0.9 % by mass) with and without cobalt microparticles. Phase transition temperatures of the structural sequence isotropic L 1/nematic calamitic Nc,/hexagonal H have been determined by differential scanning microcalorimetry. Temperature induced developable domains in hexagonal phase H and disclinations in calamitic nematic phase Nc were observed in crossed polar optical microscopy in confined geometry. A rheological study of calamitic nematic phase Nc highlighted structuring effect of cobalt microparticles from a concentration of 2 % to be demonstrated by an increase in viscosity and viscoelastic moduli. This could be explained by a stabilization of disclinations.

Research paper thumbnail of Rheology of lyotropic and thermotropic lamellar phases

Rheologica Acta, 2000

The existence of such a critical shear rate is supported by theoretical calculations (Zilman 1999).

Research paper thumbnail of Double helical defects in smectic A and smectic A* phases

Liquid Crystals, 2010

Double helical (DH and DH*) domains, defects of the smectic A (SmA) phase, have for the first tim... more Double helical (DH and DH*) domains, defects of the smectic A (SmA) phase, have for the first time been studied in the smectic A* (SmA*) phase, composed of chiral molecules. Both left- and right-handed DH*s are found in SmA*s, but not in equal numbers. The majority of the DH*s in the two left-handed cholesterics studied are left-handed, whereas in the

Research paper thumbnail of Effects of Shear on a Lyotropic Lamellar Phase

Molecular Crystals and Liquid Crystals Science and Technology. Section A. Molecular Crystals and Liquid Crystals, 1999

We have investigated the steady-state rheological behaviour of the lamellar phase of a dilute lyo... more We have investigated the steady-state rheological behaviour of the lamellar phase of a dilute lyotropic system (CPCI, hexanol, brine). In accordance with previous measurements in another lyotropic system, we obtain a power-law dependence of the viscosity as a function of the shear-rate (η∼γ). In our case. α does not depend on the brine volumic fraction φ in each of the

Research paper thumbnail of Focal Conic Stacking in Smectic A Liquid Crystals: Smectic Flower and Apollonius Tiling

Materials, Apr 22, 2009

We investigate two different textures of smectic A liquid crystals. These textures are particular... more We investigate two different textures of smectic A liquid crystals. These textures are particularly symmetric when they are observed at crossed polars optical microscopy. For both textures, a model has been made in order to examine the link between the defective macroscopic texture and the microscopic disposition of the layers. We present in particular in the case of some hexagonal tiling of circles (similar to the Apollonius tiling) some numeric simulation in order to visualize the smectic layers. We discuss of the nature of the smectic layers, which permit to assure their continuity from one focal conic domain to another adjacent one.

Research paper thumbnail of Periodic lattices of frustrated focal conic defect domains in smectic liquid crystal films

Soft Matter, 2012

We have created periodic lattices of close-packed non-toroidal focal conic domains (FCD) in smect... more We have created periodic lattices of close-packed non-toroidal focal conic domains (FCD) in smectic A liquid crystal films deposited on solid substrates that induce unidirectional planar anchoring, at the interface with air which induces homeotropic anchoring. Each cell of the ...

Research paper thumbnail of Double helices folding half parabolic focal conics in chiral smectics

Liquid Crystals, 2011

In this paper, we report the existence of a double helix folding a part of one of two cofocal par... more In this paper, we report the existence of a double helix folding a part of one of two cofocal parabolae. We observe the winding/unwinding of the double helix as temperature is changed and this mechanism is accompanied here by a change of the latus rectum p of the corresponding parabola. We propose a model of the layers inside and outside

Research paper thumbnail of Influence of the rheological properties on the electrical impedance of hydrogels

Journal of Applied Physics, 2012

We show that the anomalous frequency dependence of the real part of the electrical impedance of h... more We show that the anomalous frequency dependence of the real part of the electrical impedance of hydrogels can be interpreted by taking into account their non-Newtonian character, according to which the effective viscosity, η, depends on the frequency of the imposed deformation. Our experimental results are in good agreement with the Poisson–Nernst–Planck model if the ionic viscosity is taken proportional to the macroscopic one, measured by means of a viscositymeter, and the diffusion coefficient is assumed frequency dependent according to the formula of Stokes D = KBT/(κη), where κ is a shape coefficient. From this result it follows that the non-Newtonian character of complex liquid can be investigated by means of the impedance spectroscopy technique.

Research paper thumbnail of Optical Microscopy Observations and Construction of Dupin Cyclides at the Isotropic/Smectic A Phase Transition

Materials, Aug 12, 2021

This article is an open access article distributed under the terms and conditions of the Creative... more This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY

Research paper thumbnail of Biaxiality-driven twist-bend to splay-bend nematic phase transition induced by an electric field

Science Advances, 2020

An electric field–induced, symmetry-breaking, transition from N TB to N SB nematics reveals the i... more An electric field–induced, symmetry-breaking, transition from N TB to N SB nematics reveals the importance of local biaxiality.

Research paper thumbnail of Fréedericksz-Like Transition in a Biaxial Smectic- A Phase

Research paper thumbnail of Flexoelectrically Driven Electroclinic Effect in the Twist-Bend Nematic Phase of Achiral Molecules with Bent Shapes

Physical Review Letters, 2013

We extend the twist-bend nematic (N TB) model to describe the electro-optics of this novel phase.... more We extend the twist-bend nematic (N TB) model to describe the electro-optics of this novel phase. We predict an electroclinic effect (ECE) subject to a dc electric field E applied perpendicular to the helix axis or wave vector q, with rotation of the N TB optic axis around E. This linear effect, with its flexoelectric origin, is a close analog to the electro-optic effects observed for chiral liquid crystals. However, in nematics composed of achiral molecules having a bent shape, it is the electro-optic signature of the N TB phase. We test our model experimentally in the low-temperature nematic phase of the odd liquid crystal dimer, CB7CB, with its molecules having, on average, a bent shape. The ECE measurements confirm the previously proposed twist-bend nematic structure of this phase, with its broken chiral symmetry, extremely short (<10 nm) doubly degenerate pitch and ultrafast, submicrosecond response times.

Research paper thumbnail of The temperature dependence of the heliconical tilt angle in the twist-bend nematic phase of the odd dimer CB7CB

Journal of Materials Chemistry C, 2015

Precise birefringence measurements in large monodomains of the twist-bend nematic phase strongly ... more Precise birefringence measurements in large monodomains of the twist-bend nematic phase strongly support its heliconical structure and doubly degenerate handedness.

Research paper thumbnail of The Construction of the Dupin Cyclides in a Smectic A Polygonal Texture

Journal of Materials, 2014

We report experimental observations with optical microscopy of the usual so-called polygonal text... more We report experimental observations with optical microscopy of the usual so-called polygonal texture. We have made simulations of the Dupin cyclides in one small region of the sample.

Research paper thumbnail of Cholesteryl and diosgenyl glycosteroids: synthesis and characterization of new smectic liquid crystals

Carbohydrate research, Jan 2, 2015

While present in large numbers in nature, studies on the physical chemical aspects of glycosteroi... more While present in large numbers in nature, studies on the physical chemical aspects of glycosteroids are quite rare and focused on cholesterol, and all compounds studied thus far have shown liquid crystalline properties in a narrow temperature range. New glycosteroids composed by cholesterol or diosgenin and different glycosidic moieties have been synthesized here in order to analyze the influence of the structure on the formation of mesophases. These compounds have been studied by crossed polarized optical microscopy. These studies have revealed that these new glycosteroids form Smetic A liquid crystals in a broad temperature range.

Research paper thumbnail of Influence of alkyl chain length on the mesomorphism of 5-S-Alkyl-5-thiopentonolactones and 5-S-Alkyl-5-thiopentitols

Carbohydrate Research, 2014

Mesomophic properties of S-alkylthiopentonolactones (D-ribono, D-arabinono and D-xylono) and corr... more Mesomophic properties of S-alkylthiopentonolactones (D-ribono, D-arabinono and D-xylono) and corresponding alditol derivatives with the general formula Su-SR (R=C n H 2n+1; n=5-12) are studied. It was shown that the thermotropic and lyotropic phase transition temperatures are influenced by the following structural parameters: alkyl chain length, cyclic or acyclic Su structure and alditol conformation. Besides, it seems that n parity affects thermotropic phase transition temperatures.

Research paper thumbnail of Optical Microscopy Observations and Construction of Dupin Cyclides at the Isotropic/Smectic A Phase Transition

Materials, 2021

In this work, we are interested in the nucleation of bâtonnets at the Isotropic/Smectic A phase t... more In this work, we are interested in the nucleation of bâtonnets at the Isotropic/Smectic A phase transition of 10CB liquid crystal. Very often, these bâtonnets are decorated with a large number of focal conics. We present here an example of a bâtonnet obtained by optical crossed polarized microscopy in a frequently observed particular area of the sample. This bâtonnet presents bulges and one of them consists of a tessellation of ellipses. These ellipses are two by two tangent, one to each other, and their confocal hyperbolas merge at the apex of the bâtonnet. We propose a numerical simulation with Python software to reproduce this tiling of ellipses as well as the shape of the smectic layers taking the well-known shape of Dupin cyclides within this particular bâtonnet area.

Research paper thumbnail of Helical defects in smectic-Aand smectic-A∗phases

Physical Review E, 2010

There are two categories of helical line defects in Sm-A phases: screw dislocations of small Burg... more There are two categories of helical line defects in Sm-A phases: screw dislocations of small Burgers vectors and double helices ͑DHs͒, whose macroscopic configuration constitutes a mode of splitting of screw dislocations of giant Burgers vectors. Their counterparts in Sm-A ‫ء‬ 's ͑Sm-A's with chiral molecules͒ show a number of differences with the former and are investigated theoretically on the basis of recent observations ͓C. Meyer et al., Liq. Cryst. 37, 1047 ͑2010͔͒. The first part of the paper is a short review of the main features of helical defects in Sm-A's proper. In Sm-A ‫ء‬ 's, small Burgers vector screw dislocations with the same chirality as the high-temperature N ‫ء‬ phase are favored over the opposite ones, a result that is related to the defect core singularity. This is also true for the macroscopic DH ‫ء‬ s for a more subtle reason; we advance that the DH ‫ء‬ nucleation at the N ‫ء‬ → Sm-A ‫ء‬ transition stems from a peculiar texture of the cybotactic groups, akin in the ideal case to a set of two twisted disclinations in the N ‫ء‬ phase, linked by a stacking fault of continuous disclinations. This stacking fault vanishes in the Sm-A ‫ء‬ phase, and one recovers a DH ‫ء‬ much similar to a DH but with the appropriate chirality. Cases that differ from ideality are described: they involve small Burgers vector screw dislocations and can be evoked to explain the numerous observed distorted double helices ͑the Darboux condition is not obeyed͒ and twisted ribbons. The case when the N ‫ء‬ → Sm-A ‫ء‬ transition is type II ͑presence of a twist grain boundary phase in between͒ is briefly discussed.

Research paper thumbnail of Imperfections in focal conic domains: the role of dislocations

Philosophical Magazine, 2006

It is usual to think of Focal Conic Domains (FCD) as perfect geometric constructions in which the... more It is usual to think of Focal Conic Domains (FCD) as perfect geometric constructions in which the layers are folded into Dupin cyclides, about an ellipse and a hyperbola that are conjugate. This ideal picture is often far from reality. We have investigated in detail the FCDs in several materials which have a transition from a smectic A (SmA) to a nematic phase. The ellipse and the hyperbola are seldom perfect, and the FCD textures also suffer large transformations (in shape or/and in nature) when approaching the transition to the nematic phase, or appear imperfect on cooling from the nematic phase. We interpret these imperfections as due to the interaction of FCD's with dislocations. We analyze theoretically the general principles subtending the interaction mechanisms between FCD's and finite Burgers vector dislocations, namely the formation of kinks on disclinations, to which dislocations are attached, and we present models relating to some experimental results. Whereas the principles of the interactions are very general, their realizations can differ widely in function of the boundary conditions.

Research paper thumbnail of Rheological properties of chiral liquid crystals possessing a cholesteric–smectic A transition

Research paper thumbnail of Structural and Thermomechanical Investigation of Lyotropic Liquid Crystal Phases Doped with Monodisperse Microparticles

Applied Rheology, 2014

We present a study of the structural and thermomechanical properties of lyotropic phase in the qu... more We present a study of the structural and thermomechanical properties of lyotropic phase in the quasi ternary system made of Cetylpyridinium chloride (CPCl)/hexanol/salt water (0.9 % by mass) with and without cobalt microparticles. Phase transition temperatures of the structural sequence isotropic L 1/nematic calamitic Nc,/hexagonal H have been determined by differential scanning microcalorimetry. Temperature induced developable domains in hexagonal phase H and disclinations in calamitic nematic phase Nc were observed in crossed polar optical microscopy in confined geometry. A rheological study of calamitic nematic phase Nc highlighted structuring effect of cobalt microparticles from a concentration of 2 % to be demonstrated by an increase in viscosity and viscoelastic moduli. This could be explained by a stabilization of disclinations.

Research paper thumbnail of Rheology of lyotropic and thermotropic lamellar phases

Rheologica Acta, 2000

The existence of such a critical shear rate is supported by theoretical calculations (Zilman 1999).

Research paper thumbnail of Double helical defects in smectic A and smectic A* phases

Liquid Crystals, 2010

Double helical (DH and DH*) domains, defects of the smectic A (SmA) phase, have for the first tim... more Double helical (DH and DH*) domains, defects of the smectic A (SmA) phase, have for the first time been studied in the smectic A* (SmA*) phase, composed of chiral molecules. Both left- and right-handed DH*s are found in SmA*s, but not in equal numbers. The majority of the DH*s in the two left-handed cholesterics studied are left-handed, whereas in the

Research paper thumbnail of Effects of Shear on a Lyotropic Lamellar Phase

Molecular Crystals and Liquid Crystals Science and Technology. Section A. Molecular Crystals and Liquid Crystals, 1999

We have investigated the steady-state rheological behaviour of the lamellar phase of a dilute lyo... more We have investigated the steady-state rheological behaviour of the lamellar phase of a dilute lyotropic system (CPCI, hexanol, brine). In accordance with previous measurements in another lyotropic system, we obtain a power-law dependence of the viscosity as a function of the shear-rate (η∼γ). In our case. α does not depend on the brine volumic fraction φ in each of the