Imposed Shear Flow Research Articles

Shear-induced mesostructures in biaxial liquid crystals

We study nematodynamics of a mesoscopic system consisting of sheared biaxial liquid crystalline polymers using a hydrodynamical kinetic theory. We solve the governing Smoluchowski equation using the Galerkin method in selected regions of the material parameter space and a range of accessible shear rates to investigate stable mesoscopic states and robust structures. The imposed shear flow breaks the rotational symmetry in the quiescent state to induce truly biaxial flow-aligning steady states, logrolling states, out-of-plane steady states, exotic time-periodic motions, and chaotic motions in different regimes of material parameters and shear rates.

Sheared nematic liquid crystal polymer monolayers

We provide a comprehensive study on the planar (2D) orienta- tional distributions of nematic polymers under an imposed shear flow of ar- bitrary strength. We extend previous analysis for persistence of equilibria in steady shear and for transitions to unsteady limit cycles, from closure models (21) to the Doi-Hess 2D kinetic equation. A variation on the Boltzmann distri- bution analysis of Constantin et al. (3, 4, 5) and others (8, 22, 23) for potential flow is developed to solve for all persistent steady equilibria, and characterize parameter boundaries where steady states cease to exist, which predicts the transition to tumbling limit cycles.

Analysis and modeling of edge fluctuations and transport mechanism in the Maryland Centrifugal Experiment

The Maryland Centrifugal Experiment [R. F. Ellis et al., Phys. Plasmas 12, 055704 (2005)] is a mirror machine designed to have a plasma axially confined by supersonic rotation and dominantly interchange stable by the radial shear in the azimuthal velocity. Nevertheless, residual fluctuations still persist. To investigate the presence of such fluctuations, an azimuthal array of 16 magnetic pickup coils at the edge region of the plasma has been employed. A comprehensive analysis of the magnetic fluctuations reveals that, under the imposed shear flow, only m=0 and m=2 modes are dominant; yet, the observed frequency spectrum is broadband. Using higher order spectral analysis, clear evidence of nonlinear mode coupling is detected. It is also observed that the amplification of magnetic fluctuations leads to enhanced transport consistent with the drop of the plasma density and voltage. As a result, the magnetic fluctuations start to decrease in amplitude as the central plasma pressure drops. In return, the anomalous radial particle and momentum transport are reduced; thus, the plasma confinement improves. As the plasma pressure starts to build up, the plasma voltage increases, destabilizing the m=2 interchange mode. The cycle of enhanced transport and intermittent fluctuations repeats itself. A two-dimensional magnetohydrodynamics code in slab geometry is employed to investigate the dynamics of the primary interchange instability and to assess the level of transport. For very low sheared rotation, a broad spatial spectrum of unstable modes is obtained. As the sheared rotation is increased, the high mode numbers become stabilized and low mode numbers dominate the spectrum. Both the experimental data obtained from the azimuthal array probes and the simulations in case of parabolic shear flow show clear evidence of nonlinear mode coupling, explaining the broadband frequency spectrum for low mode numbers. A detailed comparison of spatiotemporal dynamics of simulations with the experimental data is presented.

Convective Dynamos with Penetration, Rotation, and Shear

We investigate the dynamo properties of Boussinesq, penetrative convection in the presence of rotation and large-scale velocity shear flows. Several numerical experiments are conducted in a local Cartesian computational domain in which the relative stability of the lower stable layer, the rotation rate, the supercriticality of the convection, and the strength of the imposed shear flow are varied. Once a statistically steady hydrodynamic state is achieved for any set of parameters, a weak seed magnetic field is added and the subsequent dynamo evolution is followed. In all cases studied, the weak seed field is initially amplified exponentially and then eventually saturates in a stationary magnetohydrodynamic (MHD) state. Even in the presence of penetration, rotation, and shear, the field is predominantly small-scale. We analyze the reasons for this and make suggestions as to possible further mechanisms that may lead to large-scale field generation.

Shear-driven release of a bud from a multicomponent vesicle

The authors study the response of a multicomponent budded vesicle to an imposed shear flow using dissipative particle dynamics. Under certain circumstances, phase separation in the vesicle membrane leads to the formation of a minority domain which deforms into a nearly spherical bud in order to reduce its interfacial energy. The authors show that an imposed shear force has a varying effect on the vesicle, tending either to separate the bud from the vesicle or to stretch the bud open, depending on the vesicle orientation. The authors examine the interplay of membrane bending rigidity, line tension, and shear in determining the behavior of the vesicle. With the appropriate design, vesicles can be made to release buds in a controlled manner in response to shear. The authors outline a regime in which bud release is favorable.

Role ofE ×B Shear Flow in Transport Barrier Oscillations

Transport barriers at the plasma edge are key elements of high confinement regimes in fusion devices. In typical configurations, such barriers are not stable but exhibit quasi-periodic relaxation oscillations. In the first part of this work, a one dimensional model for such relaxation oscillations is investigated. This model has been derived from three dimensional turbulence simulations in the presence of a transport barrier generated by an imposed shear flow. A proper orthogonal decomposition of the spatio-temporal behavior in this model then leads to a reduced set of ordinary equations for the amplitudes of the relevant modes. These modes are found to be different from linear eigenmodes. The zero dimensional model reproduces barrier oscillations. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Single Drop Dynamics under Shearing Flow in Systems with a Viscoelastic Phase

AbstractIn this article, we discuss the dynamics of a single drop immersed in an immiscible liquid, under an imposed shear flow. The two situations of a viscoelastic matrix with a Newtonian drop and of a viscoelastic drop in a Newtonian matrix are considered, both systems being characterized by a viscosity ratio equal to one, and by the same elasticity parameter. Experimental data are taken with a rheo‐optical computer‐assisted shearing device, allowing for drop observation from the vorticity direction of the shear flow. Data favourably compare with predictions of the recently proposed Maffettone‐Greco model, where the drop is described as a deforming ellipsoid.

Brownian dynamics simulations of polyelectrolyte adsorption in shear flow

Brownian dynamics simulations are used to study the adsorption of an isolated polyelectrolyte molecule onto an oppositely charged flat surface in the absence and the presence of an imposed shear flow. The polyelectrolyte is modeled as a freely jointed bead-rod chain where excluded volume interactions are incorporated by using a hard-sphere potential. The total charge along the backbone is distributed uniformly among all the beads, and the beads are allowed to interact with one another and the charged surface through screened Coulombic interactions. The simulations are performed by placing the molecule a fixed distance above the surface, and the adsorption behavior is then studied as a function of screening length. In the absence of an imposed flow, the chain is found to lie flat and extended on the adsorbing surface in the limit of weak screening, whereas in the limit of strong screening it desorbs from the surface and attains free-solution behavior. For intermediate screening, only a small portion of the chain adsorbs and it becomes highly extended in the direction normal to the surface. An imposed shear flow tends to orient the chain in the direction of flow and also leads to increased contact of the chain with the surface.

Nano-structure computation with coupled momentum phase ordering kinetics models

When a system such as a binary liquid is cooled rapidly from a homogeneous phase into a two-phase region, domains of the two equilibrium phases form and grow (coarsen) with time. In the absence of external forcing, such as by gravity or an imposed shear flow, a dynamical-scaling regime emerges in which the domain morphology is statistically self-similar at different times, with an overall length-scale (coarsening scale) that grows with time. In the first part of the paper, the scaling phenomenology will be reviewed and the time-dependence of the coarsening scale will be discussed in the context of a number of different physical systems and scaling regimes. In the second part, the influence of external drives, in particular gravity and shear flow, will be addressed and recent results reviewed. In particular, we find that multiple length scales emerge since in the shear case the system coarsens more rapidly in the mean flow direction while in the gravity case the coarsening is more rapid in the direction of the gravity. We characterized the scales by calculations of the anisotropic growth laws. Further for the shear we show that it is possible to control the asymptotic morphology of the phase separation in order to obtain either lamellae or cylindrical structures and potentially create for example nano-conductive wires or materials with particular optical properties. Investigating gravitational effects we find that scaling laws are significantly affected even for small density mismatch or low gravity, and the growth mechanism has some similarities to the sedimentation process.

Shear-modulated electroosmotic flow on a patterned charged surface

The effect of imposing shear flow on a charge-modulated electroosmotic flow is theoretically investigated. The flow structures exhibit either saddle points or closed streamlines, depending on the relative strength of an imposed shear to the applied electric field. The formation of closed streamlines could be advantageous for trapping nondiffusive particles at desired locations. Different time periodic alternating flows and their corresponding particle trajectories are also examined to assess strategies for creating efficient mixing.

Kinetic Structure Simulations of Nematic Polymers in Plane Couette Cells. I: The Algorithm and Benchmarks

The Doi--Hess theory coupled with an anisotropic Marrucci--Greco distortional elasticity potential provides a kinetic, mean field description of the coupling between hydrodynamics, molecular orientation by excluded volume, and elastic distortions of flowing nematic liquid crystalline polymers (LCPs). In this paper we provide the first numerical algorithm and implementation of kinetic-scale models for structure formation in confined, planar Couette cells. The model and algorithm extend kinetic simulations of Larson and Ottinger [Macromolecules, 24 (1991), pp. 6270--6282], Faraoni et al. [J. Rheol., 43 (1999), pp. 829--843], Grosso et al. [Phys. Rev. Lett., 86 (2001), pp. 3184--3187], and Forest et al. [Rheol. Acta, 43 (2004), pp. 17--37; Rheol. Acta, 44 (2004), pp. 80--93] for homogeneous nematic polymers in imposed shear flows. The focus here is one-dimensional flow and LCP structures that form between oppositely moving, parallel plates, a classical model problem that has been studied in detail with continuum models [P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, Clarendon Press, Oxford, 1993; G. Marrucci, Macromolecules, 24 (1991), pp. 4176--4182; G. Marrucci and F. Greco, Flow behavior of liquid crystalline polymers, in Advances in Chemical Physics, Vol. 86, Wiley, New York, pp. 331--404] and a variety of mesoscopic, second-moment orientation tensor models [T. Tsuji and A. D. Rey, J. Non-Newt. Fluid Mech., 73 (1997), pp. 127--152; R. Kupfermann, M. Kawaguchi, and M. M. Denn, J. Non-Newt. Fluid Mech., 91 (2000), pp. 255--271; G. Sgalari, G. L. Leal, and J. Feng, J. Non-Newt. Fluid Mech., 102 (2002), pp. 361--382; D. Grecov and A. D. Rey, Phys. Rev. E, 68 (2003), 061704; M. G. Forest et al., J. Rheol., 48 (2004), pp. 175--192; Z. Cui, M. G. Forest, and Q. Wang, On weak plane Couette and Poiseuille flows of nematic polymers, SIAM J. Appl. Math., submitted]. The model consists of a Smoluchowski equation for the space-time evolution of the orientational probability distribution function, coupled with a momentum flow balance equation, a constitutive equation for the extra stress, and the continuity equation. The Smoluchowski equation is first reduced to a finite set of partial differential equations in time and space for spherical harmonic amplitudes. Then we discretize the spatial variables (by the method of lines) using high-order finite differences, which reduces the full system to a large set of ordinary differential equations. Adaptive grid generation techniques are implemented. To provide an accurate and stable time integration, we employ the newly developed spectral deferred correction algorithm. We close with an application of the kinetic theory and numerical code to explore steady state flow-molecular structures in slow planar Couette experiments (low Deborah number) and low Ericksen number, where distortional elasticity dominates short-range excluded volume effects.

Gravitational Effects on Structure Development in Quenched Complex Fluids

When binary liquid mixtures are cooled rapidly from a homogeneous phase into a two-phase system, domains of the two equilibrium phases form and grow (coarsen) with time. In the absence of an external forcing due to gravity or an imposed shear flow, a dynamic scaling regime emerges in which the domain morphology is statistically self-similar at different times with a length-scale that grows with time. In the presence of gravity, however, multiple length scales develop, with the system coarsening more rapidly in the direction of the force. The late-time behavior of such a system is characterized in this study by the calculation of anisotropic growth laws. Gravitation effects significantly affect scaling laws, even with small density mismatch, and the growth mechanism has some similarities to the sedimentation process. However, very few numerical studies have been made of such effects; this is one of the first.

Computational Modeling of Cell Adhesion and Movement Using a Continuum-Kinetics Approach

Adhesion of leukocytes to substrate involves the coupling of disparate length and timescales between molecular mechanics and macroscopic transport, and existing models of cell adhesion do not use full cellular information. To address these challenges, a multiscale computational approach for studying the adhesion of a cell on a substrate is developed and assessed. The cellular level model consists of a continuum representation of the field equations and a moving boundary tracking capability to allow the cell to change its shape continuously. At the receptor-ligand level, a bond molecule is mechanically represented by a spring. Communication between the macro/micro- and nanoscale models is facilitated interactively during the computation. The computational model is assessed using an adherent cell, rolling and deforming along the vessel wall under imposed shear flows. Using this approach, we first confirm existing numerical and experimental results. In this study, the intracellular viscosity and interfacial tension are found to directly affect the rolling of a cell. Our results also show that the presence of a nucleus increases the bond lifetime, and decreases the cell rolling velocity. Furthermore, it is found that a cell with a larger diameter rolls faster, and decreases the bond lifetime. This study shows that cell rheological properties have significant effects on the adhesion process contrary to what has been hypothesized in most literature.

Numerical Modeling of the Solar Tachocline. II. Forced Turbulence with Imposed Shear

We report the first three-dimensional, global-scale numerical simulations of stably stratified turbulence in the solar tachocline driven by penetrative convection. We adopt a thin-shell geometry and approximate the effects of penetrative convection via random, small-scale forcing. After the simulations have been evolved for some time, a differential rotation is introduced and maintained against viscous dissipation by an additional forcing term. The imposed shear is stable over the timescales considered (Richardson numbers range from ~250 to 1000). We investigate the characteristics of the turbulence before and after adding the imposed differential rotation. The random forcing is varied to generate different types of turbulent wave fields, dominated by rotational r-modes or irrotational g-modes. Nonlinear transfer among modes does occur, but we find little evidence for a quasi-two-dimensional inverse cascade. Coupling between the randomly forced turbulence and the imposed shear flow gives rise to Reynolds stresses that transport momentum poleward and outward. This implies diffusive (down-gradient) latitudinal transport and antidiffusive (countergradient) vertical transport. Overall, the latitudinal transport dominates and acts to dissipate the imposed shear. This could have important implications for the structure of the solar tachocline and the global angular momentum distribution in the solar interior.

Coarsening dynamics of phase-separating systems.

When a system such as a binary liquid is cooled rapidly from a homogeneous phase into a two-phase region, domains of the two equilibrium phases form and grow ('coarsen') with time. In the absence of an external drive, such as gravity or an imposed shear flow, a dynamical-scaling regime emerges in which the domain morphology is statistically self-similar at different times, up to an overall length-scale (coarsening scale) that grows with time. In the first part of the paper, the scaling phenomenology will be reviewed and the time-dependence of the coarsening scale will be discussed in the context of a number of different physical systems and scaling regimes. In the second part, the influence of an external drive, in particular a shear flow, will be addressed and recent developments reviewed. Interesting open questions include the late-time behaviour under shear and whether the coarsening continues indefinitely or is ultimately arrested by the shear flow.

Shear‐Induced Diffusion in Dilute Suspensions of Charged Colloids

We propose a model for the nonequilibrium enhancement of colloidal self‐diffusion in an externally imposed shear flow in charged systems. The diffusion enhancement is calculated in terms of electrostatic, two‐body interactions between the particles in shear flow. In the high‐shear rate, low‐volume fraction limit in which the model is valid, we compare these calculations to the experiments of Qiu et al. [PRL 61, 2554 (1988)] and simulations of Chakrabarti et al. [PRE 50, R3326 (1994)] and find good agreement on scaling and magnitude to within experimental uncertainty of the electrostatic parameters.

Towards Monodomains of Self-Organized Comb-Shaped Polymeric Supramolecules

AbstractWe have previously shown that hierarchical self-organization is achieved upon physically bonding amphiphilic molecules to diblock copolymers. Here we discuss the effect of imposed shear flow to achieve overall alignment of the locally self-organized structures. We will first present shear aligned polystyrene-block-poly(4-vinyl pyridine) diblock copolymers (PS-b-P4VP), where pentadecyl phenol (PDP) has been hydrogen bonded to the pyridines. Depending on the selected molecular weights, eg. hexagonal arrangement of PS cylinders in the lamellar matrix of P4VP(PDP) can be obtained with high overall order of both structures. This is a template to obtain discrete PS nanorods, which have P4VP corona once the PDP molecules have been cleaved off by a solvent treatment. Selecting a relatively high molecular weight PS block and a short P4VP block leads to mesoporous materials with emptied cylinders with P4VP brushes at the walls. The glassy state of the PS matrix prevents the pores from collapsing. The pyridine groups of PS-b-P4VP can be protonated using eg. toluene sulphonic acid and the resulting polymeric salt has been complexed using PDP. The weight fractions have been selected so that the polyelectrolyte/amphiphile complex self-organizes into cylindrical domains with hexagonal packing. Shear alignment leads to high overall order. SAXS in combination with structural models suggests that within the cylinders there are parallel self-organized layers. The conductivity is anisotropic. We will also discuss dielectric reflectors based on self-organized block polyelectrolytes consisting PS-b-P4VP where DBSA has been complexed to P4VP. In this case, plasticization due to the oligomeric side chains promotes a facile structure formation at long periodicities in comparison to concepts based on eg. blends of high molecular weight polymers and block copolymers. Finally, plasticized comb-shaped supramolecules based on rigid conjugated poly(p-pyridine) are discussed. Even gentle shearing leads to highly aligned lamellar structures, which show efficient polarized photoluminescence.

Computer simulations of domain growth in off-critical quenches of two-dimensional binary mixtures

The phase separation of two-dimensional binary mixtures has been studied through numerical Langevin simulations based on a Ginzburg–Landau free energy. We have considered not symmetric mixtures with and without imposed shear flow. In the sheared case our main results are as follows: (1) domains are distorted by the flow; (2) the structure factor has four peaks; (3) excess viscosity shows a peak whose position is independent of shear rate but its height decreases increasing shear rate.

Factors determining crystal--liquid coexistence under shear.

The interaction between an imposed shear flow and an order--disorder transition underlies a broad range of phenomena. Under the influence of shear flow, a variety of soft matter is observed to spontaneously form bands characterized by different local order---for example, thermotropic liquid crystals subjected to shear flow exhibit rich phase behaviour. The stability of order under the influence of shear flow is also fundamental to understanding frictional wear and lubrication. Although there exists a well developed theoretical approach to the influence of shear flow on continuous transitions in fluid mixtures, little is known about the underlying principles governing non-equilibrium coexistence between phases of different symmetry. Here we show, using non-equilibrium molecular dynamics simulations of a system of spherical particles, that a stationary coexistence exists between a strained crystal and the shearing liquid, and that this coexistence cannot be accounted for by invoking a non-equilibrium analogue of the chemical potential. Instead of such thermodynamic arguments, we argue that a balancing of the crystal growth rate with the rate of surface erosion by the shearing melt can account for the observed coexistence.

Interface fluctuations, Burgers equations, and coarsening under shear

We consider the interplay of thermal fluctuations and shear on the surface of the domains in various systems coarsening under an imposed shear flow. These include systems with nonconserved and conserved dynamics, and a conserved order parameter advected by a fluid whose velocity field satisfies the Navier-Stokes equation. In each case the equation of motion for the interface height reduces to an anisotropic Burgers equation. The scaling exponents that describe the growth and coarsening of the interface are calculated exactly in any dimension in the case of conserved and nonconserved dynamics. For a fluid-advected conserved order parameter we determine the exponents, but we are unable to build a consistent perturbative expansion to support their validity.