Implementation of Lees-Edwards periodic boundary conditions for direct numerical simulations of particle dispersions under shear flow

A general methodology is presented to perform direct numerical simulations of particle dispersions in a shear flow with Lees-Edwards periodic boundary conditions. The Navier-Stokes equation is solved in oblique coordinates to resolve the incompatibility of the fluid motions with the sheared geometry, and the force coupling between colloidal particles and the host fluid is imposed by using a smoothed profile method. The validity of the method is carefully examined by comparing the present numerical results with experimental viscosity data for particle dispersions in a wide range of volume fractions and shear rates including nonlinear shear-thinning regimes.     

The shear hysteresis in lamellar structure of surfactant–water binary system

We study the shear effect on the lamellar structure of surfactants in water using dissipative particle dynamics simulations. Starting from a lamellar structure without shear flow, we increase the shear rate and then decrease it stepwisely. A weak shear changes the lamellar plane to be parallel to the shear direction though the lamellar normal has no specific direction on the plane normal to the shear direction. By increasing the shear rate, the lamellar normal eventually flips to the vorticity direction regardless of the initial configuration. Lamellar normal would stay along the vorticity direction on decreasing the shear rate. The hysteresis is also found in shear-stress. By varying the shear rate, the time needed to reach the final unique state is significantly shortened compared with that observed with a constant shear rate. We find a correlation between the excess shear-stress and the tilt angle of surfactant in lamellar.     

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.     

Triplet correlation in sheared suspensions of Brownian particles

Triplet microstructure of sheared concentrated suspensions of Brownian monodisperse spherical particles is studied by sampling realizations of a three-dimensional unit cell subject to periodic boundary conditions obtained in accelerated Stokesian dynamics simulations. Triplets are regarded as a bridge between particle pairs and many-particle clusters thought responsible for shear thickening. Triplet-correlation data for weakly sheared near-equilibrium systems display an excluded volume effect of accumulated correlation for equilateral contacting triplets. As the Peclet number increases, there is a change in the preferred contacting isosceles triplet configuration, away from the "closed" triplet where the particles lie at the vertices of an equilateral triangle and toward the fully extended rod-like linear arrangement termed the "open" triplet. This transition is most pronounced for triplets lying in the plane of shear, where the open triplets' angular orientation with respect to the flow is very similar to that of a contacting pair. The correlation of suspension rheology to observed structure signals onset of larger clusters. An investigation of the predictive ability of Kirkwood's superposition approximation (KSA) provides valuable insights into the relationship between the pair and triplet probability distributions and helps achieve a better and more detailed understanding of the interplay of the pair and triplet dynamics. The KSA is seen more successfully to predict the shape of isosceles contacting triplet nonequilibrium distributions in the plane of shear than for similar configurations in equilibrium hard-sphere systems; in the sheared case, the discrepancies in magnitudes of distribution peaks are attributable to two interaction effects when pair average trajectories and locations of particles change in response to real, or "hard," and probabilistically favored ("soft") neighboring excluded volumes and, in the case of open triplets, due to changes in the correlation of the farthest separated pair caused by the fixed presence of the particle in the middle.     

CFD modeling for flow and mass transfer in spacer-obstructed membrane feed channels

The effect of spacer geometry on fluid dynamics and mass transfer in feed channels of spiral wound membranes has been investigated. Three-dimensional computational fluid dynamics (CFD) simulations reveal significant influence of spacer geometric parameters such as filament spacing, thickness and flow attack angle on wall shear rates and mass transfer coefficients. The spacers with filaments in axial and transverse direction induce higher shear stresses at the top membrane surface when compared to the bottom; the mass transfer rates are almost equal. The distribution of mass transfer coefficients become uniform when the spacing between axial filaments is increased or transverse filament thickness is decreased. For spacers with filaments inclined to the channel axis, the flow structure depends on spacing and flow attack angle. The fluid follows a zigzag path when spacing is greater while it begins to line-up with the filaments when spacing is reduced or flow attack angle is increased. The flow when aligned with the filaments increases the wall shear stress but confines the region of higher mass transfer coefficient values to a narrower portion. The zigzag flow movement increases these values on a major portion of membrane surface which enhances the mass transfer rates.     

Vertical anisotropic microfibers for a gecko-inspired adhesive

Geckos are able to adhere strongly and release easily from surfaces because the structurally anisotropic fibers on their toes naturally exhibit force anisotropy based on the direction of articulation. Here, semicircular fibers, with varying amounts of contact area on the two faces, are investigated to ascertain whether fiber shape can be used to gain anisotropy in shear and shear adhesion forces. Testing of 10-μm-diameter polydimethylsiloxane (PDMS) fibers against a 4-mm-diameter flat glass puck show that shear and shear adhesion forces were two to five times greater when in-plane movement caused the flat face, rather than the curved face, of the fiber to come in contact with the glass puck. The directional adhesion and shear force anisotropy results are close to theoretical approximations using the Kendall peel model and clearly demonstrate how fiber shape may be used to influence the properties of the adhesive. This result has broad applicability, and by combining the results shown here with other current vertical and angled designs, synthetic adhesives can be further improved to behave more like their natural counterparts.     

Controlled stacking of charged block copolymer micelles

Using poly(acrylic acid)-b-poly(methyl acrylate)-b-polystyrene (PAA-b-PMA-b-PS) triblock copolymers or a mixture of different molecular weight PAA-b-PS diblock copolymers, stacks of polymeric micellar assemblies, such as disks and Y-shaped cylinders, were formed through intermicellar interactions. Whereas micelles hierarchically stacked together, micellar interactions within the stack defined a uniform micelle geometry and size for up to micrometers in length. The kinetic pathway dependence and stability of the stacked assemblies were studied, and possible intermicellar interactions between micelles within the stacks are proposed.     

Shear-Induced "Melting" of an Aqueous Foam

We present diffusing-wave spectroscopy measurements of bubble dynamics in a continuously sheared aqueous foam. At slow strain rates, isolated clusters of bubbles intermittently rearrange from one solidly packed configuration to another, even though the macroscopic flow appears continuous. At fast rates, bubbles instead move smoothly and continuously throughout the entire foam. In other words, shear flow that appears macroscopically laminar is similarly laminar down to the bubble scale; effectively the foam "melts." The crossover to this regime can be understood in terms of elastic energy accumulation and viscous dissipation mechanisms. In particular, the strain rate needed for shear-induced melting to occur is set by the ratio of a yield strain to the rearrangement event duration. To explore the implications for macroscopic flow, we compare these bubble-scale dynamics directly with viscosity measurements. Copyright 1999 Academic Press.     

Design and fabrication of gecko-inspired adhesives

Recently, there has been significant interest in developing dry adhesives mimicking the gecko adhesive system, which offers several advantages compared to conventional pressure-sensitive adhesives. Specifically, gecko adhesive pads have anisotropic adhesion properties; the adhesive pads (spatulae) stick strongly when sheared in one direction but are non-adherent when sheared in the opposite direction. This anisotropy property is attributed to the complex topography of the array of fine tilted and curved columnar structures (setae) that bear the spatulae. In this study, we present an easy, scalable method, relying on conventional and unconventional techniques, to incorporate tilt in the fabrication of synthetic polymer-based dry adhesives mimicking the gecko adhesive system, which provides anisotropic adhesion properties. We measured the anisotropic adhesion and friction properties of samples with various tilt angles to test the validity of a nanoscale tape-peeling model of spatular function. Consistent with the peel zone model, samples with lower tilt angles yielded larger adhesion forces. The tribological properties of the synthetic arrays were highly anisotropic, reminiscent of the frictional adhesion behavior of gecko setal arrays. When a 60° tilt sample was actuated in the gripping direction, a static adhesion strength of ~1.4 N/cm(2) and a static friction strength of ~5.4 N/cm(2) were obtained. In contrast, when the dry adhesive was actuated in the releasing direction, we measured an initial repulsive normal force and negligible friction.     

Structure of a semidilute polymer solution under steady shear

We use Brownian dynamics computer simulations to investigate the structure of a semidilute polymer solution undergoing a steady, uniform shear flow. We find that the contributions to structure factor from intra- and interchain correlations, which cancel each other almost completely for an equilibrium semidilute solution, are modified in different ways by the shear flow. Incomplete cancellation of these contributions leads to anisotropic patterns that resemble those observed in light scattering experiments on sheared semidilute solutions [Wu et al., Phys. Rev. Lett. 66, 2408 (1991)]. For small wave vectors the structure factor change is dominated by the interchain contribution. We also monitor the distortion of the pair correlation function and show that for small distances it is dominated by the intrachain contribution. Finally, we investigate nonlinear shear viscosity and find that, like the short-distance part of the distortion of the pair correlation function, it is predominantly of intrachain origin.     

Molecular diffusion and slip boundary conditions at smooth surfaces with periodic and random nanoscale textures

The influence of periodic and random surface textures on the flow structure and effective slip length in Newtonian fluids is investigated by molecular dynamics (MD) simulations. We consider a situation where the typical pattern size is smaller than the channel height and the local boundary conditions at wetting and nonwetting regions are characterized by finite slip lengths. In the case of anisotropic patterns, transverse flow profiles are reported for flows over alternating stripes of different wettability when the shear flow direction is misaligned with respect to the stripe orientation. The angular dependence of the effective slip length obtained from MD simulations is in good agreement with hydrodynamic predictions provided that the stripe width is larger than several molecular diameters. We found that the longitudinal component of the slip velocity along the shear flow direction is proportional to the interfacial diffusion coefficient of fluid monomers in that direction at equilibrium. In case of random textures, the effective slip length and the diffusion coefficient of fluid monomers in the first layer near the heterogeneous surface depend sensitively on the total area of wetting regions.     

Dynamical heterogeneity in a highly supercooled liquid under a sheared situation

In the present study, we performed molecular dynamics simulations and investigated dynamical heterogeneity in a supercooled liquid under a steady shear flow. Dynamical heterogeneity can be characterized by three quantities: the correlation length ξ(4)(t), the intensity χ(4)(t), and the lifetime τ(hetero)(t). We quantified all three quantities by means of the correlation functions of the particle dynamics, i.e., the four-point correlation functions, which are extended to the sheared condition. Here, to define the local dynamics, we used two time intervals t = τ(α) and τ(ngp); τ(α) is the α-relaxation time, and τ(ngp) is the time at which the non-Gaussian parameter of the Van Hove self-correlation function is maximized. We discovered that all three quantities (ξ(4)(t), χ(4)(t), and τ(hetero)(t)) decrease as the shear rate γ of the steady shear flow increases. For the time interval t = τ(α), the scalings ξ(4)(τ(α))~γ(-0.08), χ(4)(τ(α))~γ(-0.26), and τ(hetero)(τ(α))~γ(-0.88) were obtained. The steady shear flow suppresses the heterogeneous structure as well as the lifetime of the dynamical heterogeneity. In addition, we demonstrated that all three quantities in the sheared non-equilibrium state can be mapped onto those in the equilibrium state through the α-relaxation time τ(α). This finding means that the same relation between τ(α) and three quantities holds in both the equilibrium state and the sheared non-equilibrium state and therefore proposes that the dynamical heterogeneity can play a similar role in the drastic change of τ(α) due to not only the temperature but also the shear rate.     

Orientation-induced crystallization in isotactic polypropylene melt by shear deformation

Development of orientation-induced precursor structures (nuclei) prior to crystallization in isotactic polypropylene melt under shear flow was studied by in-situ synchrotron small-angle X-ray scattering (SAXS) and rheo-optical techniques. SAXS patterns at 165°C immediately after shear (rate = 60 s⁻¹, t_s = 5 s) showed emergence of equatorial streaks due to oriented structures (microfibrils or shish) parallel to the flow direction and of meridional maxima due to growth of the oriented layer-like structures (kebabs) perpendicular to the flow. SAXS patterns at later times (t = 60 min after shear) indicated that the induced oriented structures were stable above the nominal melting point of iPP. DSC thermograms of sheared iPP samples confirmed the presence of two populations of crystalline fractions; one at 164°C (corresponding to the normal melting point) and the other at 179°C (corresponding to melting of oriented crystalline structures). Time-resolved optical micrography of sheared iPP melt (rate = 10 s⁻¹, t_s = 60 s, T = 148°C) provided further information on orientation-induced morphology at the microscopic scale. The optical micrographs showed growth of highly elongated micron size fibril structures (threads) immediately after shear and additional spherulities nucleated on the fibrils at the later stages. Results from SAXS and rheo-optical studies suggest that a stable scaffold (network) of nuclei, consisting of shear-induced microfibrillar structures along the flow direction superimposed by layered structures perpendicular to the flow direction, form in polymer melt prior to the occurance of primary crystallization. The scaffold dictates the final morphological features in polymer.     

Computational modelling of declination loops under shear flow

Optical observations of sheared lyotropic and thermotropic liquid crystals have shown them to have a rich microstructure dominated by disclination loops and networks. In thermotropic liquid crystalline polymers it has been possible to freeze in the microstructures, which are then sectioned and analysed by optical and electron microscopy, to enable the identification of the predominant types of disclinations. In this work a computational model is presented which simulates the development of texture in liquid crystalline materials. The model has been designed so that it is possible to study large localised distortions which are subjected to a flow field. In the aspect of the work reported here, simulations have been used to study the influence of simple shear on individual disclination loops placed in an otherwise undeformed sample. The subsequent deformation of the loop is shown to be dependent on the angle that the rotation vector of the loop makes with the vorticity direction.     

Bond-orientational analysis of hard-disk and hard-sphere structures

We report the bond-orientational analysis results for the thermodynamic, random, and homogeneously sheared inelastic structures of hard-disks and hard-spheres. The thermodynamic structures show a sharp rise in the order across the freezing transition. The random structures show the absence of crystallization. The homogeneously sheared structures get ordered at a packing fraction higher than the thermodynamic freezing packing fraction, due to the suppression of crystal nucleation. On shear ordering, strings of close-packed hard-disks in two dimensions and close-packed layers of hard-spheres in three dimensions, oriented along the velocity direction, slide past each other. Such a flow creates a considerable amount of fourfold order in two dimensions and body-centered-tetragonal (bct) structure in three dimensions. These transitions are the flow analogs of the martensitic transformations occurring in metals due to the stresses induced by a rapid quench. In hard-disk structures, using the bond-orientational analysis we show the presence of fourfold order. In sheared inelastic hard-sphere structures, even though the global bond-orientational analysis shows that the system is highly ordered, a third-order rotational invariant analysis shows that only about 40% of the spheres have face-centered-cubic (fcc) order, even in the dense and near-elastic limits, clearly indicating the coexistence of multiple crystalline orders. When layers of close-packed spheres slide past each other, in addition to the bct structure, the hexagonal-close-packed (hcp) structure is formed due to the random stacking faults. Using the Honeycutt-Andersen pair analysis and an analysis based on the 14-faceted polyhedra having six quadrilateral and eight hexagonal faces, we show the presence of bct and hcp signatures in shear ordered inelastic hard-spheres. Thus, our analysis shows that the dense sheared inelastic hard-spheres have a mixture of fcc, bct, and hcp structures.     

Assessment of phenomenological models for viscosity of liquids based on nonequilibrium atomistic simulations of copper

The shear viscosity of liquid copper is studied using nonequilibrium molecular-dynamics simulations under planar shear flow conditions. We examined variation of viscosity as function of shear rate at a range of pressures (ca. 0 - 40 GPa). We analyzed these results using eight different phenomenological models and find that the observed non-Newtonian behavior is best described by the Powell-Eyring (PE) model: eta(gamma) = (eta(0)-eta(infinity))sinh(-1)(taugamma)(taugamma) + eta(infinity), where gamma is the shear rate. Here eta(0) (the zero-shear-rate viscosity) extracted from the PE fit is in excellent agreement with available experimental data. The relaxation time tau from the PE fit describes the shear response to an applied stress. This provides the framework for interpreting the shear flow phenomena in complex systems, such as liquid metal and amorphous metal alloys.     

Coupling between protein-laden films and a shearing bulk flow

Two-dimensional protein crystallization on lipid monolayers at a quiescent air/water interface is now a well-established process, but it only operates under a very restricted set of conditions and on a very slow time scale. We have recently been able to significantly extend the conditions under which the proteins will crystallize as well as speed up the process by subjecting the interface to a shearing flow. Here, we investigate the two-way coupling between a protein-laden film and the bulk flow that provides the interfacial shear. This flow in a stationary open cylinder is driven by the constant rotation of the floor. Using the Boussinesq-Scriven surface model for a Newtonian interface coupled to the Navier-Stokes equations for the bulk flow, we find that the surface shear viscosity of protein-laden films under most conditions is small or negligible. This is the case for films subjected to constant shearing flow, regardless of the duration of the flow. However, when the film is intermittently sheared, significant surface shear viscosity is evident. In these cases, the surface shear viscosity is not uniform across the film.     

Shear modulated percolation in carbon nanotube composites

A novel time-dependent percolation transition has been observed in sheared carbon nanotube (CNT) composites. At a fixed CNT filler loading, the electrical conductivities of CNT composites can change abruptly as much as 8 orders of magnitude as the shear processing time increases. Microstructure characterization shows that the CNTs have aligned along the shear flow direction, which leads to the dramatic increase of the percolation threshold and thereby the dramatic decreases of the electrical conductivities. Our results highlight the great importance of understanding the response of CNT dispersion states to the processing conditions.     

Effect of flow on polymer-polymer miscibility

The effect of shear flow on the phase behaviour of partially miscible blends exhibiting a lower critical solution temperature behaviour has been investigated. Miscibility limits were detected, with and without the application of flow, as changes from optical clarity to turbidity using light scattering and as the appearance of double glass transition temperatures. Light scattering data were collected on a rheo-optical device that was designed to monitor phase changes in polymer blends undergoing shear flow between parallel glass plates in a temperature controlled environment. Glass transition temperatures of some quenched sheared blends were measured using a differential scanning calorimeter in order to confirm the conclusions from the light scattering data. It was found that shear induced demixing and shear induced mixing may be observed within the same blend depending on the magnitude of the applied flow. Miscibility gaps and closed miscibility loops may appear in the phase diagrams. At certain temperatures and shear rates unusual scattering patterns were observed and these were associated with a “ripple” morphology when directly viewed through the microscope.     

A Langevin dynamics simulation study of the tribology of polymer loop brushes

The tribology of surfaces modified with doubly bound polymer chains (loops) has been investigated in good solvent conditions using Langevin dynamics simulations. The density profiles, brush interpenetration, chain inclination, normal forces, and shear forces for two flat substrates modified by doubly bound bead-necklace polymers and equivalent singly bound polymers (twice as many polymer chains of 12 the molecular weight of the loop chains) were determined and compared as a function of surface separation, grafting density, and shear velocity. The doubly bound polymer layers showed less interpenetration with decreasing separation than the equivalent singly bound layers. Surprisingly, this difference in interpenetration between doubly bound polymer and singly bound polymer did not result in decreased friction at high shear velocity possibly due to the decreased ability of the doubly bound chains to deform in response to the applied shear. However, at lower shear velocity, where deformation of the chains in the flow direction is less pronounced and the difference in interpenetration is greater between the doubly bound and singly bound chains, some reduction in friction was observed.