Polymer Migration Research Articles

Stress-gradient induced migration of polymers in thin films flowing over smoothly corrugated surfaces

We consider the two dimensional, steady flow of a dilute polymer solution over a solid substrate with periodic topography under the action of a body force. We examine how the distribution of polymer is affected by flow conditions, physical properties and substrate geometry and how it affects the dynamics of the free-surface. The Mavrantzas–Beris two-fluid Hamiltonian model is used in order to account for polymer migration due to stress gradients. The model is solved via the mixed finite element method combined with a quasi-elliptic grid generation technique. Results for polymer concentration, stress and velocity fields are presented as a function of the non-dimensional parameters of the problem. The basic phenomena that appear in the case of polymer migration in undulating channels (Tsouka et al., 2014), also appear in free surface flows. Increasing the elastic stresses, increases migration of macromolecules towards the free surface, developing a polymer-depleted layer especially over the substrate maxima, which finally gives rise to “apparent” slip. Increasing the cavity steepness also enhances migration and the thickness of the depletion layer and induces strong variation in the stresses away from the substrate wall, especially in low polymer concentrations. All these phenomena cannot be captured by the homogenous Oldroyd-B model. The evaluation of the Stokes number shows that flow resistance decreases as elasticity increases, increases monotonically up to an asymptote with the capillary number, and exhibits a non-monotonic dependence on the Reynolds number. Moderate inertial effects can give rise to large deformations of the free surface, developing waves with complex shapes. If we use a similarly modified ePTT model, we observe that its inherent shear-thinning is enhanced by the stress induced migration and tends to reduce the gradients on both polymeric stresses and polymer concentration along the film.

The effect of wall depletion and hydrodynamic interactions on stress-gradient-induced polymer migration

We generalize our recent continuum theory for the stress-gradient-induced migration of polymers [Zhu et al., J. Rheol., 2016, 60, 327-343] by incorporating the effect of solid boundaries on concentration variations. For a model flow in a channel with periodic slip wall velocity, which can in principle be produced by an electric field in the presence of a sinusoidal wall charge, we obtain theoretical results for the steady-state distribution of dilute solutions of polymer dumbbells using a systematic perturbation analysis in Weissenberg number Wi. We find that the presence of a thin wall depletion zone changes the lowest order solution from second to first in Wi and drastically affects the concentration field far from the depletion layer, due both to a coupling of the second derivative of the velocity field to the concentration gradient, and to convection of the polymer-depleted fluid in this layer into the bulk of the fluid. Additional effects induced by wall hydrodynamic interaction (HI) are assessed by incorporating polymer flux from the wall-HI migration theory of Ma and Graham into our continuum theory. We establish the range of validity of our theory by comparing the theoretical results with Brownian dynamics (BD) simulations: excellent agreement is achieved for relatively small molecules, while the theory breaks down when the Gradient number Gd is greater than 0.5, where Gd is the ratio of polymer coil size to the length scale over which the velocity gradient changes. The BD simulations are also extended to the case of long Hookean chains with numbers of springs per chain ranging from 1 to 32, where it is found that for fixed Gd and Wi, the results are nearly identical, showing that all important phenomena are captured by a simple dumbbell model, thus supporting the continuum theory which was derived for the case of dumbbells. In addition, the Stochastic Rotation Dynamics (SRD) method is employed to evaluate the role of HI on the migration pattern, producing effects consistent with the continuum theory incorporating the wall-migration flux. In general, we demonstrate that the polymer concentrates in drastically different regions of the channel depending on Gd and Wi.

Hydrodynamic Aspects of the Toms Effect

The physicomathematical model of migration of polymers in a liquid turbulent flow in a pipe is based on a comparison of forces transverse to the motion of the mainstream flow: the Saffman, Magnus, and turbophoresis forces. It has been shown that the polymer particles are grouped near a certain boundary within the limits of the boundary layer. On this basis, the authors have made assumptions on the mechanism of suppression of turbulent pulsations and decrease in the viscous friction near the wall, which makes up the Toms effect. The proposed model satisfies, at least, qualitatively, various actually observed manifestations of the effect.

Mini-tablets versus pellets as promising multiparticulate modified release delivery systems for highly soluble drugs

Whether mini-tablets (tablets, diameters ≤6mm) belong to single- or multiple-unit dosage forms is still questionable. Accordingly, Pharmacopoeial evaluation procedures for mini-tablets are lacking. In this study, the aforementioned points were discussed. Moreover, their potential for oral controlled delivery was assessed. The antidepressant venlafaxine hydrochloride (Vx), a highly soluble drug undergoing first pass effect, low bioavailability and short half-life was selected as a challenging payload. In an attempt to weigh up mini-tablets versus pellets as multiparticulate carriers, Vx-loaded mini-tablets were compared to formulated pellets of the same composition and the innovator Effexor®XR pellets.Formulations were prepared using various polymer hydrogels in the core and ethyl cellulose film coating with increasing thickness. Mini-tablets (diameter 2mm) showed extended Vx release (<60%, 8h). Indeed, release profiles comparable to Effexor®XR pellets were obtained. Remarkably higher coating thickness was required for pellets to provide equivalent retardation. Ethyl cellulose in the core ensured faster release due to polymer migration to the surface and pore formation in the coat. mini-tablets showed higher stability to pellets upon storage. Industrially speaking, mini-tablets proved to be superior to pellets in terms of manufacturing, product quality and economical aspects. Results point out the urgent need for standardized evaluation procedures for mini-tablets.

Formation of compositional gradient profiles by using shear-induced polymer migration phenomenon under Couette flow field

We investigated whether a graded-index profile, specified by the polymer compositional gradient, could be formed using shear-induced polymer migration phenomenon in a polymer solution. For the presented model system, we generated a shear flow by rotating a glass rod at the center of a polystyrene/methylmethacrylate (PS/MMA) solution and measured the degree of polymer migration by the shear flow field by examining the concentration of polymer solution along the radial direction from the rotating axis to the periphery. Through model experiments, we formed a compositional gradient and controlled its profile in the solution by varying the concentration of polymer solution, molecular weight of polymer, and shear rate. Finally, we solidfied the gradient profiles by the polymerization of the PS/MMA solution and confirmed that the gradient profiles were maintained with a compositional gradient twice larger than the mother PS/MMA solution.

ChemInform Abstract: Dihydrogen Catalysis: A Remarkable Avenue in the Reactivity of Molecular Hydrogen

AbstractReview: 157 refs.

Interdiffusion behavior under a temperature gradient field in a poly(ethylene-co-hexene)/poly(ethylene-co-butene) system

The in-plane thermal gradient accelerates polymer migration through the enhancement in polymer diffusion along the direction of the temperature gradient.

Dihydrogen Catalysis: A Remarkable Avenue in the Reactivity of Molecular Hydrogen

Molecular hydrogen is the simplest and most abundant compound in the universe and is involved in numerous industrial chemical processes. In conventional chemistry, dihydrogen typically plays the role of a reductant and a reagent for homogeneous and heterogeneous hydrogenation processes such as the industrial and enzymatic ammonia formation, reduction of metallic ores and hydrogenation of unsaturated fats and oils. However, there are also processes in which molecular hydrogen participates as promoter, and even as catalyst. The catalytic role of the dihydrogen in free-valence migration in irradiated polymers and the interstellar isomerization of the formyl cation (protonated carbon monoxide) are well-documented examples of such processes. Recently, this issue has received new attention. Dihydrogen has been shown to play the role of a dehydrogenation catalyst (involving particularly metallocomplexes and inorganic materials), a relay (pass-on) transfer molecular agent and a transporter of protons.This review article, combined with original results, is focused on the mechanisms of the chemical processes where dihydrogen demonstrates catalytic behavior. We will call these processes (with somewhat broader meaning of the term) “dihydrogen catalysis” (DHC) which also includes the reactions mediated by transition metal dihydrides. Dihydrides are tentatively considered as pre-activated dihydrogen, coordinated to a metal center or implanted into a solid surface/support.DHC reactions are classified into five major reaction types: (i) dihydrogen-assisted relay transport of H-atoms (H2-RT); (ii) dihydrogen-assisted stepwise relay transport of H-atoms or of a free valence (sH2-RT); (iii) dihydrogen-assisted proton transport (H2-PT); (iv) dihydrogen-assisted dehydrogenation (H2-DeH); and (v) pre-activated dehydrogenation (PA-DeH). The classification of these mechanisms is based on a detailed analysis of numerous potential energy surfaces studied by DFT and ab initio methods in conjunction with available experimental data. The H2-RT, H2-DeH, and PA-DeH processes occur via cyclic transition states. The relay H2-RT transport involves the H-H-H triad linked to both H-donor and H-acceptor centers, whereas the transition state ring in the H2-DeH dehydrogenation processes involves a H-H-H-H tetrad with the dihydrogen catalyst located in the middle. The H2-PT mechanism provides the transport of a proton mediated by dihydrogen combined in a triangular (H3+)-carrier unit.There are also practically important processes stimulated by dihydrogen such as the hydrogen spillover and hydrogen build-up in electronics, in which the catalytic role of dihydrogen is ambiguous, either because of the uncertainties in mechanisms, or prevailing traditional views. Some examples are briefly discussed in the framework of the concept of dihydrogen catalysis, some being provided with theoretical support (in part calculated by us), and others being merely hypothesized to provide suggestions to an interested reader.

Multiscale modeling of polymer flow-induced migration and size separation in a microfluidic contraction flow

We study polymer migration in a periodic pressure-driven sudden contraction-expansion flow with contraction dimension comparable to the polymer radius of gyration, for which several polymer migration mechanisms can be important: (1) sieving by the thin channel of polymers too large to easily enter them; (2) deformation-hydrodynamic coupling, including wall-hydrodynamic interaction, which causes polymers to drift away from the walls towards the center of the channel; (3) streamline-curvature-induced migration, in which polymers traveling along curved streamlines migrate towards the center of curvature; and (4) depletion-convection coupling, in which depletion layers in thin channels are convected across wide side chambers, creating a one-sided diffusion barrier that leads to depletion from the side chamber. We use both Stochastic Rotation Dynamics (SRD), which includes hydrodynamic interaction (HI), and simple Brownian dynamics (BD), with HI omitted and flow field given by finite element analysis. The similarity in results from SRD and BD at Weissenberg number Wi less than 10 (where Wi is based on the shear rate in the narrow region of the contraction channel) shows that HI (Mechanism 2) has only a weak effect on polymer migration in our tight geometry. At Wi>1, the polymer migrates towards the centerline in the wide region, due mainly to streamline-curvature-induced (SCI) migration (Mechanism 3), but also to depletion-convection-induced migration (Mechanism 4). And we demonstrate these two mechanisms more explicitly in a pressure-driven flow in a grooved channel that is significantly wider than the polymer. SCI migration dominates in the contraction geometry, and produces a migration velocity proportional to Wi2. Using the central limit theorem, we accurately predict the position and width of a band of polymer passing through N periodic contractions, thereby demonstrating the potential for SCI migration as a mechanism of size separation in a multi-step planar contraction channel. We find that the best separation is achieved at Wi around 2, where SCI migration has the greatest resolving power between polymers of different size. We also find that sieving (Mechanism 1) is dominant at low Wi less than unity, where the chains with large radius of gyration are delayed in their entry to the thin channel, relative to shorter polymers. This sieving separation mechanism differs from that of size-exclusion chromatography which yields faster migration by the shorter chains. Our strategy of combining simulation methods with the central limit theorem could also be used to predict separation efficiencies of a wide variety of polymers and colloids in microfluidic geometries.

Stress-gradient induced migration of polymers in corrugated channels

We study the flow of a dilute polymer solution in a wavy channel under steady-state flow conditions by employing the nonequilibrium thermodynamics two-fluid model [Mavrantzas and Beris, Phys. Rev. Lett. 69, 273–276 (1992)], allowing for the coupling between polymer concentration and polymer stresses. The resulting highly complex system of partial differential equations describing inhomogeneous transport phenomena in the fluid are solved with an efficient implementation of the mixed finite-element method. We present numerical results for polymer concentration, stress, velocity, and fluxes of polymer as a function of the nondimensional parameters of the problem (the Deborah number De, the Peclet number Pe, the Reynolds number Re, the ratio of the solvent viscosity to the total fluid viscosity β, and the constriction ratio of the channel width cr). We find that the constricted part of the wall is depleted of polymer, when the polymer diffusion length scale, expressed by the ratio of De/Pe, increases. The migration is more pronounced for macromolecules characterized by longer relaxation times and takes place toward the expanding part of the channel or toward the centerplane. Migration is also enhanced by the width variability of the channel: The more corrugated the channel, the stronger the transfer of polymer to the centerplane. This increases the spatial extent of polymer depletion near the wall or induces a zone of sharp variation in polymer stress and concentration, which moves away from the channel wall, especially in lower polymer concentration. The development of a polymer-depleted layer smooths out the boundary layer which is known to arise with Boger fluids at the walls of such corrugated channels or tubes and gives rise to an “apparent” slip in the constricted section of the wall and to a very low value of the drag force on the wall. When and where boundary layers arise, they scale as (1/De) for the stresses and as (De/Pe)1/3 for the concentration.

Effect of particle size on salt-induced diffusiophoresis compared to Brownian mobility.

For ternary polymer-salt-water systems at low polymer concentration (0.5%, w/w), we have experimentally investigated the effect of polymer size on polymer diffusiophoresis (i.e., polymer migration induced by a salt concentration gradient) and salt osmotic diffusion (i.e., salt migration induced by a polymer concentration gradient). Specifically, Rayleigh interferometry was employed to measure ternary diffusion coefficients for aqueous solutions of poly(ethylene glycol) (PEG) and KCl at 25 °C. Our investigation focused on four polymer molecular masses (from 10 to 100 kg mol(-1)) and two salt concentrations (0.25 and 0.50 M). To describe and examine our experimental results, we introduced a normalized diffusiophoresis coefficient as the ratio of polymer diffusiophoresis to polymer Brownian mobility. This coefficient was found to increase with polymer molecular mass, thereby demonstrating that the relative importance of polymer diffusiophoresis compared to its intrinsic Brownian mobility increases with particle size. The observed behavior was linked to preferential hydration (water thermodynamic excess) and hydration (bound water) of the macromolecule. The ratio of salt osmotic diffusion to binary salt-water diffusion approximately describes the nonuniform spatial distribution of salt along a static polymer concentration gradient at equilibrium. The significance of polymer diffusiophoresis, especially at high PEG molecular mass, was examined by considering a steady-state diffusion problem showing that salt concentration gradients can produce large enhancements and depletions of polymer concentration. This work is valuable for understanding and modeling the effect of salt concentration gradients on diffusion-based transport of polymers with applications to interfacial processes.

A New Type of Time-Temperature Integrator Based on Doping Front Migration in Conductive Polymers

A New Type of Time-Temperature Integrator Based on Doping Front Migration in Conductive Polymers

Experimental and Numerical Study of Gel Particles Movement and Deposition in Porous Media After Polymer Flooding

Gel particle, a promising conformance control technology, is recently applying to after-polymer-flooding reservoirs by reusing the remaining polymer in porous media. However, there is no available numerical model which is useful for simulating the conformance control. A series of lab experiments are conducted to explore the main characters of gel particles movements after polymer flooding. Four main mechanisms, namely, swelling, synergy with remaining polymer, shear breaking, and deformation migration, are recognized and described by mathematical formulas. Based on the physical experiments, a numerical model is established to simulate gel particles propagation after polymer flooding. In particular, gel particles are treated as an additional component in aqueous phase. The interaction between the particle gels and the remaining polymer is simplified by aqueous viscosity relationship and particle gel grain size variation. Two transport forms, plugging and deformation migration, are embodied in the model, and the local pressure gradient controls which form the propagation belongs to. The retention of particle gels will cause pore volume decrease and therefore reduce the permeability of thief zones to bypassing water to less swept zones. An iterative method is employed to decouple the gel particle profile control model, which is robust and fairly time-saving. In particular, the flow model is numerically solved by the IMPSAT method and the gel particles continuity equation is explicitly solved by using an operator splitting technique. The newly developed model is validated by history matching results of 1D experiments and actual application case. The results suggest that the presented model is helpful to optimize parameters for profile control for gel particle profile control technology.

Tumbling, stretching and cross-stream migration of polymers in rectilinear shear flow from dissipative particle dynamics simulations

Solutions of flexible polymer chains with harmonic bonds undergoing rectilinear flow in slit pores are investigated via dissipative particle dynamics (DPD) simulations. We found that when DPD with low Schmidt number (Sc∼1) is used, the polymer chains tend to migrate across the streamlines towards the walls. However, a cross-stream migration towards the centerline is observed when DPD with relatively high values of Schmidt number (Sc∼10) is used. The effect of chain length and Weissenberg number, defined as Wi=Γ̇τrel, where Γ̇ and τrel are the shear rate and polymer longest relaxation time, respectively, are investigated. The polymer chains exhibit a large number of orientational and extensional fluctuations, with the distributions of both latitude and azimuthal angles exhibiting power-law decays in agreement with experiments, theory and previous simulations. The polymer chains exhibit tumbling kinetics characterized by an exponential distribution of tumbling times. The characteristic time scale is proportional to the longest relaxation time of the polymer chains at equilibrium. The power spectral density of the extension, while monotonically decaying for large chain length or large Weissenberg number, exhibits a shallow peak for short chains, implying that shear flow induces nearly repetitive tumbling of the polymer chains. The time scale corresponding to the peak of the extension power spectral density is also proportional to the longest chain relaxation time.

Cross-streamline migration of a semiflexible polymer in a pressure driven flow

Experiments and simulations on single α-actin filaments in the Poiseuille flow through a microchannel show that the center-of-mass probability density across the channel assumes a bimodal shape as a result of pronounced cross-streamline migration. We reexamine the problem and perform Brownian dynamics simulations for a bead-spring chain with bending elasticity. Hydrodynamic interactions between the pointlike beads are taken into account by the two-wall Green tensor of the Stokes equations. Our simulations reproduce the bimodal distribution only when hydrodynamic interactions are taken into account. Numerical results on the orientational order of the end-to-end vector of the model polymer are also presented together with analytical hard-needle expressions at zero flow velocity. We derive a Smoluchowski equation for the center-of-mass distribution and carefully analyze the different contributions to the probability current that causes the bimodal distribution. As for flexible polymers, hydrodynamic repulsion explains the depletion at the wall. However, in contrast to flexible polymers, the deterministic drift current mainly determines migration away from the centerline and thereby depletion at the center. Diffusional currents due to a position-dependent diffusivity become less important with increasing polymer stiffness.

Precise Control and Consecutive Modulation of Spin Transition Temperature Using Chemical Migration in Porous Coordination Polymers

Precise control of spin transition temperature (T(c)) is one of the most important challenges in molecular magnetism. A Hofmann-type porous coordination polymer {Fe(pz)[Pt(II)(CN)(4)]} (1; pz = pyrazine) exhibited cooperative spin transition near room temperature (T(c)(up) = 304 K and T(c)(down) = 284 K) and its iodine adduct {Fe(pz)[Pt(II/IV)(CN)(4)(I)]} (1-I), prepared by oxidative addition of iodine to the open metal sites of Pt(II), raised the T(c) by 100 K. DSC and microscopic Raman spectra of a solid mixture of 1-I and 1 revealed that iodine migrated from 1-I to 1 through the grain boundary after heating above 398 K. We have succeeded in precisely controlling the iodine content of {Fe(pz)[Pt(CN)(4)(I)(n)]} (1-In; n = 0.0-1.0), which resulted in consecutive modulation of T(c) in the range 300-400 K while maintaining the hysteresis width. Furthermore, it was demonstrated that iodine migration in the solid mixture was triggered by the spin transition of 1-I. The magnetically bistable porous framework decorating guest interactive open-metal-site in the pore surface makes it possible to modulate T(c) ad arbitrium through unique postsynthetic method using iodine migration.

Semiflexible polymer conformation, distribution and migration in microcapillaryflows

The flow behavior of a semiflexible polymer in microchannels is studied usingmultiparticle collision dynamics, a particle-based hydrodynamic simulationtechnique. Conformations, distributions, and radial cross-streamline migrationare investigated for various bending rigidities, with persistence lengthsLp in therange 0.5 ≤ Lp/Lr ≤ 30. The flow behavior is governed by the competition between a hydrodynamic liftforce and steric repulsion from the wall, which lead to migration away from thewall, and a locally varying flow induced orientation, which drives the polymeraway from the channel center and towards the wall. The different dependences ofthese effects on the polymer bending rigidity and the flow velocity results in acomplex dynamical behavior. However, a generic effect is the appearance of amaximum in the monomer and the center-of-mass distributions, which occurs at thechannel center for small flow velocities, but moves off-center at higher velocities.

Direct Surface Force Measurements of Polyelectrolyte Multilayer Films Containing Nanocrystalline Cellulose

Polyelectrolyte multilayer films containing nanocrystalline cellulose (NCC) and poly(allylamine hydrochloride) (PAH) make up a new class of nanostructured composite with applications ranging from coatings to biomedical devices. Moreover, these materials are amenable to surface force studies using colloid-probe atomic force microscopy (CP-AFM). For electrostatically assembled films with either NCC or PAH as the outermost layer, surface morphology was investigated by AFM and wettability was examined by contact angle measurements. By varying the surrounding ionic strength and pH, the relative contributions from electrostatic, van der Waals, steric, and polymer bridging interactions were evaluated. The ionic cross-linking in these films rendered them stable under all solution conditions studied although swelling at low pH and high ionic strength was inferred. The underlying polymer layer in the multilayered film was found to dictate the dominant surface forces when polymer migration and chain extension were facilitated. The precontact normal forces between a silica probe and an NCC-capped multilayer film were monotonically repulsive at pH values where the material surfaces were similarly and fully charged. In contrast, at pH 3.5, the anionic surfaces were weakly charged but the underlying layer of cationic PAH was fully charged and attractive forces dominated due to polymer bridging from extended PAH chains. The interaction with an anionic carboxylic acid probe showed similar behavior to the silica probe; however, for a cationic amine probe with an anionic NCC-capped film, electrostatic double-layer attraction at low pH, and electrostatic double-layer repulsion at high pH, were observed. Finally, the effect of the capping layer was studied with an anionic probe, which indicated that NCC-capped films exhibited purely repulsive forces which were larger in magnitude than the combination of electrostatic double-layer attraction and steric repulsion, measured for PAH-capped films. Wherever possible, DLVO theory was used to fit the measured surface forces and apparent surface potentials and surface charge densities were calculated.

Comparison of lattice-Boltzmann and Brownian-dynamics simulations of polymer migration in confined flows

This paper compares results from lattice-Boltzmann and brownian-dynamics simulations of polymer migration in confined flows bounded by planar walls. We have considered both a uniform shear rate and a constant pressure gradient. Lattice-Boltzmann simulations of the center-of-mass distribution agree quantitatively with brownian-dynamics results, contradicting previously published results. The mean end-to-end distance of the extended polymer is more sensitive to grid resolution Δx and time-step Δt. Nevertheless, for sufficiently small Δx and Δt, convergent results for the polymer stretch are obtained which agree with brownian dynamics within statistical uncertainties. The brownian-dynamics simulations incorporate a mobility matrix for a confined polymer that is both symmetric and positive definite for all physically accessible configurations.

Analysis of the Migration of Rigid Polymers and Nanorods in a Rotating Viscometric Flow

The dynamics and rheology of a rigid polymer or nanorod suspended in a Newtonian, viscous fluid under torsional flow have been studied. Our theoretical analysis predicts that rigid rods migrate in the radial direction according to their orientational configuration which is controlled by the competition between the shear flow, which tends to align the rods in the direction of flow, and Brownian motion, which tends to randomize the orientation. Steady and transient distributions of the center-of-mass in a dilute solution are derived from a kinetic theory and are confirmed by performing a Brownian dynamics simulation. The migration shifts the distribution toward the axis of rotation and enhances the shear-thinning behavior of the suspension.