Simulations of liquid crystals in Poiseuille flow

Lattice Boltzmann simulations are used to explore the behavior of liquid crystals subject to Poiseuille flow. In the nematic regime at low shear rates we find two possible steady-state configurations of the director field. The selected state depends on both the shear rate and the history of the sample. For both director configurations there is clear evidence of shear thinning, a decrease in the viscosity with increasing shear rate. Moreover, at very high shear rates or when the order parameter is large, the system transforms to a ‘log-rolling state’ with boundary layers that may exhibit oscillatory behavior.     

Influence of weak anchoring on flow instabilities in nematic liquid crystals

We analyse the homogeneous instabilities in a nematic liquid crystal subjected to plane steady Couette or Poiseuille flow in the case when the director is prealigned perpendicular to the flow plane taking into account weak anchoring at the confining surfaces. The critical shear rate decreases for decreasing anchoring strength and goes to zero in the limit of torque-free boundary conditions. For Poiseuille flow two types of instability arise depending on the values of the azimuthal (W_a) and polar (W_p) surface anchoring strengths. The critical line in (W_a,W_p) space which separates the two instabilities regimes is obtained.     

Nonequilibrium molecular dynamics of the rheological and structural properties of linear and branched molecules. Simple shear and poiseuille flows; instabilities and slip

Nonequilibrium molecular-dynamics simulations are performed for linear and branched chain molecules to study their rheological and structural properties under simple shear and Poiseuille flows. Molecules are described by a spring-monomer model with a given intermolecular potential. The equations of motion are solved for shear and Poiseuille flows with Lees and Edward's [A. W. Lees and S. F. Edwards, J. Phys. C 5, 1921 (1972)] periodic boundary conditions. A multiple time-scale algorithm extended to nonequilibrium situations is used as the integration method, and the simulations are performed at constant temperature using Nose-Hoover [S. Nose, J. Chem. Phys. 81, 511 (1984)] dynamics. In simple shear, molecules with flow-induced ellipsoidal shape, having significant segment concentrations along the gradient and neutral directions, exhibit substantial flow resistance. Linear molecules have larger zero-shear-rate viscosity than that of branched molecules, however, this behavior reverses as the shear rate is increased. The relaxation time of the molecules is associated with segment concentrations directed along the gradient and neutral directions, and hence it depends on structure and molecular weight. The results of this study are in qualitative agreement with other simulation studies and with experimental data. The pressure (Poiseuille) flow is induced by an external force F(e) simulated by confining the molecules in the region between surfaces which have attractive forces. Conditions at the boundary strongly influence the type of the slip flow predicted. A parabolic velocity profile with apparent slip on the wall is predicted under weakly attractive wall conditions, independent of molecular structure. In the case of strongly attractive walls, a layer of adhered molecules to the wall produces an abrupt distortion of the velocity profile which leads to slip between fluid layers with magnitude that depends on the molecular structure. Finally, the molecular deformation under flow depends on the attractive force of the wall, in such a way that molecules are highly deformed in the case of strong attracting walls.     

Influence of weak anchoring on flow instabilities in nematic liquid crystals

We analyse the homogeneous instabilities in a nematic liquid crystal subjected to plane steady Couette or Poiseuille flow in the case when the director is prealigned perpendicular to the flow plane taking into account weak anchoring at the confining surfaces. The critical shear rate decreases for decreasing anchoring strength and goes to zero in the limit of torque-free boundary conditions. For Poiseuille flow two types of instability arise depending on the values of the azimuthal (W _a) and polar (W _p) surface anchoring strengths. The critical line in (W _a,W _p) space which separates the two instabilities regimes is obtained.     

Reentrant solitons

Abstract

Reentrant solitons are predicted to exist in homeotropic nematic liquid crystals under simple shear or in Poiseuille flow. The director equation of motion with the boundary effects due to the cell walls fully incorporated is given, which is then approximated and reduced to an effective equation of one spatial dimension with only two dimensionless parameters β and γ. For β fixed within a narrow range, as γ is varied a sequence of soliton-no soliton-soliton is obtained. This new reentrant soliton phenomenon is accessible to experimental verification.     

Stress-induced polymer deformation in shear flows

By means of dynamic Monte Carlo simulation of bulk lattice polymers in Couette shear flow, it was demonstrated that in addition to velocity gradient the constant driving forces acting as the activation aspect of shear stresses can also raise polymer deformation. Moreover, enhancing driving forces in a flow without any velocity gradient can reproduce nonNewtonian fluid behaviors of long-chain polymers. The simulations of Poiseuille shear flow with a gradient of shear stresses show that, the velocity gradient dominates small deformation in the flow layers of low shear stresses, while the shear stress dominates large deformation in the flow layers of high shear stresses. This result implies that the stress-induced deformation could be mainly responsible for the occurrence of non-Newtonian fluid behaviors of real polymers at high shear rates.     

Twist viscosities and flow alignment of biaxial nematic liquid crystal phases of a soft ellipsoid-string fluid studied by molecular dynamics simulation

We have calculated the twist viscosity and the alignment angle between the director and the stream lines in shear flow of a liquid crystal model system, which forms biaxial nematic liquid crystals, as functions of the density, from the Green-Kubo relations by equilibrium molecular dynamics simulation and by a nonequilibrium molecular dynamics algorithm, where a torque conjugate to the director angular velocity is applied to rotate the director. The model system consists of a soft ellipsoid-string fluid where the ellipsoids interact according a repulsive version of the Gay-Berne potential. Four different length-to-width-to-breadth ratios have been studied. On compression, this system forms discotic or calamitic uniaxial nematic phases depending on the dimensions of the molecules, and on further compression a biaxial nematic phase is formed. In the uniaxial nematic phase there is one twist viscosity and one alignment angle. In the biaxial nematic phase there are three twist viscosities and three alignment angles corresponding to the rotation around the various directors and the different alignments of the directors relative to the stream lines, respectively. It is found that the smallest twist viscosity arises by rotation around the director formed by the long axes, the second smallest one arises by rotation around the director formed by the normals of the broadsides, and the largest one by rotation around the remaining director. The first twist viscosity is rather independent of the density whereas the last two ones increase strongly with density. One finds that there is one stable director alignment relative to the streamlines, namely where the director formed by the long axes is almost parallel to the stream lines and where the director formed by the normals of the broadsides is almost parallel to the shear plane. The relative magnitudes of the components of the twist viscosities span a fairly wide interval so this model should be useful for parameterisation experimental data.     

Synergistic effects in flows of mixtures of wormlike micelles and hydroxyethyl celluloses with or without hydrophobic modifications

This work presents experimental results on simple shear and porous media flow of aqueous solutions of two hydroxyethyl celluloses (HEC) and two hydrophobically modified hydroxyethyl celluloses (HMHEC) with different molecular weights. Mixtures of these polymers with a cationic surfactant, cetyltrimethylammonium p-toluenesulfonate (CTAT) were also studied. Emphasis was given to the range of surfactant concentrations in which wormlike micelles are formed. The presence of hydrophobic groups, the effect of the molecular weight of the polymers, the surfactant and polymer concentrations, and the effect of the flow field type (simple shear versus porous media flow) were the most important variables studied. The results show that the shear viscosity of HEC/CTAT solutions is higher than the viscosities of surfactant and polymer solutions at the same concentrations, but surface tension measurements indicate that no complex formation occurs between CTAT and HEC. On the other hand, a complex driven by hydrophobic interactions was detected by surface tension measurements between CTAT and HMHEC. In this case, the viscosity of the mixture increases significantly more (up to four orders of magnitude at high CTAT concentrations) in comparison with HEC/CTAT aqueous solutions. Increments in the molecular weight of the polymers increase the interaction with CTAT and the shear viscosity of the solution, but make phase separation more feasible. In porous media flow, the polymer/CTAT mixtures exhibited higher apparent viscosities than in simple shear flows. This result suggests that the extensional component of the flow field in porous media flows leads to a stronger interaction between the polymer and the wormlike micelles, probably as a consequence of change of conformation and growth of the micelles.     

Microfluidic flows of wormlike micellar solutions

The widespread use of wormlike micellar solutions is commonly found in household items such as cosmetic products, industrial fluids used in enhanced oil recovery and as drag reducing agents, and in biological applications such as drug delivery and biosensors. Despite their extensive use, there are still many details about the microscopic micellar structure and the mechanisms by which wormlike micelles form under flow that are not clearly understood. Microfluidic devices provide a versatile platform to study wormlike micellar solutions under various flow conditions and confined geometries. A review of recent investigations using microfluidics to study the flow of wormlike micelles is presented here with an emphasis on three different flow types: shear, elongation, and complex flow fields. In particular, we focus on the use of shear flows to study shear banding, elastic instabilities of wormlike micellar solutions in extensional flow (including stagnation and contraction flow field), and the use of contraction geometries to measure the elongational viscosity of wormlike micellar solutions. Finally, we showcase the use of complex flow fields in microfluidics to generate a stable and nanoporous flow-induced structured phase (FISP) from wormlike micellar solutions. This review shows that the influence of spatial confinement and moderate hydrodynamic forces present in the microfluidic device can give rise to a host of possibilities of microstructural rearrangements and interesting flow phenomena.     

Interfacial interactions and colloid retention under steady flows in a capillary channel

Colloidal interfacial interactions in a capillary channel under different chemical and flow conditions were studied using confocal microscopy. Fluorescent latex microspheres (1.1 microm) were employed as model colloids and the effects of ionic strength and flow conditions on colloidal retention at air-water interface (AWI) and contact line were examined in static and dynamic (flow) experiments. Colloids were preferentially attached to and accumulated at AWI, but their transport with bulk solution was non-negligible. Changing solution ionic strength in the range 1-100 mM had a marginal effect on colloidal accumulation, indicating forces other than electrostatic are involved. Flow through the open channel resembled Poiseuille flow with AWI acting as a non-stress-free boundary, which resulted in near stagnation of AWI and consequently promoted colloid accumulation. Retention on contact line was likely dominated by film-straining and was more significant in flow relative to static experiments due to hydrodynamic driving force. Modeling and dimensionless analysis of the flow behavior in the capillary channel clearly indicate the important role of apparent surface viscosity and surface tension in colloidal interfacial retention at the pore scale, providing insight that could improve understanding of colloid fate and transport in natural unsaturated porous media.     

Determination of the distance-dependent viscosity of mixtures in parallel slabs using non-equilibrium molecular dynamics

We generalize a technique for determination of the shear viscosity of mixtures in planar slabs using non-equilibrium computer simulations by applying an external force parallel to the surface generating Poiseuille flow. The distance-dependent viscosity of the mixture, given as a function of the distance from the surface, is determined by analysis of the resulting velocity profiles of all species. We present results for a highly non-ideal water + methanol mixture in the whole concentration range between rutile (TiO(2)) walls. The bulk results are compared to the existing equilibrium molecular dynamics and experimental data while the inhomogeneous viscosity profiles at the interface are interpreted using the structural data and information on hydrogen bonding.     

Mesoscale constitutive modeling of magnetic dispersions: material functions for shear flows

We recently developed a constitutive model for magnetic dispersions by modeling the magnetic particles as rigid dumbbells dispersed in a solvent. The theory yielded a constitutive equation in which the stress tensor could be expressed as a function of the velocity gradient, an orientational order tensor, S, an average alignment vector, J, and any imposed external magnetic field, H. The constitutive equation is used here to predict material functions for steady shear flow (shear-rate dependent viscosity and first normal stress coefficient) as well as those for unsteady shear flows (stress growth upon inception of steady shear and small-amplitude oscillatory shear). The importance of effects of concentration, equilibrium nematic ordering in the dispersion, and anisotropy in the hydrodynamic drag are emphasized. Comparisons with available experimental data on viscosity for magnetic inks under steady shear flow and inception of steady shear flow show reasonably good agreement.     

Viscosity of confined inhomogeneous nonequilibrium fluids

We use the nonlocal linear hydrodynamic constitutive model, proposed by Evans and Morriss [Statistical Mechanics of Nonequilibrium Liquids (Academic, London, 1990)], for computing an effective spatially dependent shear viscosity of inhomogeneous nonequilibrium fluids. The model is applied to a simple atomic fluid undergoing planar Poiseuille flow in a confined channel of several atomic diameters width. We compare the spatially dependent viscosity with a local generalization of Newton's law of viscosity and the Navier-Stokes viscosity, both of which are known to suffer extreme inaccuracies for highly inhomogeneous systems. The nonlocal constitutive model calculates effective position dependent viscosities that are free from the notorious singularities experienced by applying the commonly used local constitutive model. It is simple, general, and has widespread applicability in nanofluidics where experimental measurement of position dependent transport coefficients is currently inaccessible. In principle the method can be used to predict approximate flow profiles of any arbitrary inhomogeneous system. We demonstrate this by predicting the flow profile for a simple fluid undergoing planar Couette flow in a confined channel of several atomic diameters width.     

Effect of confinement on droplet breakup in sheared emulsions

The breakup of Newtonian droplets in a Newtonian matrix during shear flow is investigated in a counterrotating parallel plate device. For bulk conditions, the critical capillary number for breakup is known to be only determined by the viscosity ratio. Here, we show that the critical capillary number is also affected by the degree of confinement: for low viscosity ratios, confinement suppresses breakup, whereas for high viscosity ratios, confinement promotes breakup. This way, above a critical value for the degree of confinement, even droplets with a viscosity ratio larger than 4, which are unbreakable by shear in a bulk situation, can be broken in a simple shear flow field.     

Interplay between shear flow and elastic deformations in liquid crystals

We study shear flow in liquid crystal cells with elastic deformations using a lattice Boltzmann scheme that solves the full, three-dimensional Beris-Edwards equations of hydrodynamics. We consider first twisted and hybrid aligned nematic cells, in which the deformation is imposed by conflicting anchoring at the boundaries. We find that backflow renders the velocity profile non Newtonian, and that the director profile divides into two regions characterized by different director orientations. We next consider a cholesteric liquid crystal, in which a twist deformation is naturally present. We confirm the presence of secondary flow for small shear rates, and are able to follow the dynamical pathway of shear-induced unwinding, for higher shear rates. Finally, we analyze how the coupling between shear and elastic deformation can affect shear banding in an initially isotropic phase. We find that for a nematic liquid crystal, elastic distortions may cause an asymmetry in the dynamics of band formation, whereas for a cholesteric, shear can induce twist in an initially isotropic sample.     

Effects of polymer adsorption on the effective viscosity in microchannel flows: phenomenological slip layer model from molecular simulations

Molecular simulations (Dissipative Particle Dynamics - DPD) were used to quantify the effect of polymer adsorption on the effective shear viscosity of a semi-dilute polymer solution in microchannel Poseuille flow. It is well known that polymer depletion layers develop adjacent to solid walls due to hydrodynamic forces, causing an apparent wall slip and reduced effective viscosity (increased total flow rate). We found that depletion layers also developed in the presence of hydrodynamically rough adsorbed layers on the wall. Polymer-polymer (steric) repulsion between flowing and adsorbed polymer expanded the depletion layer compared to no-adsorption cases, and the effective viscosity was reduced further. Desorption occurred for higher shear rates, reducing the repulsion effect and shrinking the depletion layers. A phenomenological algebraic model for the depletion layer thickness, including a shear modified adsorption isotherm, was developed based on the simulation data. The depletion layer model can be used together with the effective viscosity model we developed earlier.     

Shear thinning in dilute polymer solutions

We use bead-spring models for a polymer coupled to a solvent described by multiparticle collision dynamics to investigate shear thinning effects in dilute polymer solutions. First, we consider the polymer motion and configuration in a shear flow. For flexible polymer models we find a sharp increase in the polymer radius of gyration and the fluctuations in the radius of gyration at a Weissenberg number approximately 1. We then consider the polymer viscosity and the effect of solvent quality, excluded volume, hydrodynamic coupling between the beads, and finite extensibility of the polymer bonds. We conclude that the excluded volume effect is the major cause of shear thinning in polymer solutions. Comparing the behavior of semiflexible chains, we find that the fluctuations in the radius of gyration are suppressed when compared to the flexible case. The shear thinning is greater and, as the rigidity is increased, the viscosity measurements tend to those for a multibead rod.     

A comparative study between dissipative particle dynamics and molecular dynamics for simple- and complex-geometry flows

The purpose of this study is to compare the results from molecular-dynamics and dissipative particle dynamics (DPD) simulations of Lennard-Jones (LJ) fluid and determine the quantitative effects of DPD coarse graining on flow parameters. We illustrate how to select the conservative force coefficient, the cut-off radius, and the DPD time scale in order to simulate a LJ fluid. To show the effects of coarse graining and establish accuracy in the DPD simulations, we conduct equilibrium simulations, Couette flow simulations, Poiseuille flow simulations, and simulations of flow around a periodic array of square cylinders. For the last flow problem, additional comparisons are performed against continuum simulations based on the spectral/hp element method.     

Microstructure and Viscosity of Aggregating Colloids under Strong Shearing Force

Disaggregation under strong shearing force is simulated for an aggregating colloid based on a sticky particle model which can describe the disaggregating and aggregating kinetics, the deformation, and the rupture of clusters with a minimum number of parameters. For a 2-dimensional system, the viscosity and coordination number of the model colloid are calculated at each time step, and the changes of microstructure with shear flow are observed directly by displaying the configuration of particles onto a monitor. The viscosity depends on both area fraction and shear rate, but coordination number depends only on shear rate. Furthermore, the viscosity and coordination number at steady state are independent of the initial state of particles, which indicates that the disaggregation and aggregation are mutually reversible. Copyright 1999 Academic Press.     

Modelling of the simple shear flow of a flow-aligning nematic

The shear flow induced deformations of a nematic liquid crystal layer have been modelled numerically for the case of flow-aligning nematics. The director deviation from the plane of shear, which was predicted earlier for special surface orientation angles, has been confirmed. This deformation takes a form of director rotation about the axis perpendicular to the layer plane. As a result, transverse flow of the nematic arises. The rotation angle is close to pi at sufficiently strong shear stress, and the director is oriented at the usual flow alignment angle in a significant part of the layer. The director coming out of the shear plane should not be treated as a separate effect taking place during the flow, but rather as a way in which the usual flow-aligned structure is achieved.