Theory of shear-induced migration in dilute polymer solutions near solid boundaries

Abstract

In this work, a continuum theory is developed for the behavior of flowing dilute polymer solutions near solid surfaces, using a bead-spring dumbbell model of the dissolved polymer chains. Hydrodynamic interactions between the chains and the wall lead to migration away from the wall in shear flow. At steady state, this hydrodynamic effect is balanced by molecular diffusion; an analytical expression for the resulting concentration profile is derived. It is shown that the depletion layer thickness is determined by the normal stresses that develop in flow and can be much larger than the size of the polymer molecule. The transient development of this depletion layer is also studied, as well as the spatial development downstream from an entrance. Numerical and similarity solutions in these cases show that the developing concentration profile generally displays a maximum at an intermediate distance from the wall.

Pressure-driven transport of confined DNA polymers in fluidic channels

“…The model also neglects forces normal to the flow direction that may arise from hydrodynamic coupling of the polymer segments to the channel walls (26,27) or from the fluid inertia itself (28). Theory (29) and simulations (26,27) predict that hydrodynamic interactions result in the migration of polymers toward the channel center to a degree that increases with Wi and h, an effect that has been experimentally confirmed for 48.5-kbp DNA in very large (h ϭ 126 m) channels (30). These effects are not expected to be significant for most of the range of small h tested in our experiments, but their onset at the highest Wi ϳ 5 and h ϳ 4 m tested may explain the small discrepancy between our model predictions and the lengthdependent ͞ observed there.…”

Reduction of the effective shear viscosity in polymer solutions due to crossflow migration in microchannels: Effective viscosity models based on DPD simulations

“…Confined polymers between flat walls without flow offer analytic treatments [9,13,14], as does simplified dumbbell models in shear flow [15]. For more realistic cases of migration with long polymer chains, there are a number of empirical results from experiments [7,10], DPD simulations [16,17,18,19,20] and Brownian and molecular dynamics simulations [6,21,22] that qualitatively describe the depletion layer behavior within the given parameter range.…”

Pressure driven flow of polymer solutions in nanoscale slit pores

“…Theories have therefore been based on simplified systems rather than on polymer solutions. Previous theoretical and com-putational studies that focused on the density profiles of polymers in uniform shear flow (i.e., Couette flow) or pressure driven flow (i.e., Poiseuille flow) have been conflicting [9,10,12,13,14]. Previous Brownian dynamics simulations showed a migration of the polymer chains towards the wall [9,10].…”

“…For example, the understanding of the structure and dynamics of polymeric molecules in micro-channels is important to DNA sequencing in channels with widths ranging from 10 to 50µm [2], DNA delivery through micro-capillaries in gene therapy, and to lab-on-chip applications that involve polymers [3]. Issues of particular interest pertinent to polymer solutions in the presence of laminar flow is the mass distribution of polymers across the channel, the polymers conformational distribution, and the effect of the polymer chains on the profile of the solution velocity field [1,2,4,5,6,7,8,9,10,11,12,13,14,15].…”

“…In these studies, however, wallmonomer hydrodynamic interactions are not accounted for. A recent kinetic theory by Ma and Graham [12] of an infinitesimally dilute solution of dumbbells predicts a migration of the dumbbell particles away from the wall towards the mid-section of the channel. A key reason for the migration of the dumbbells away from the wall is attributed to the hydrodynamic interaction between the wall and the dumbbell, which leads to a deterministic migration from the wall, while the effect of the Brownian motion is to homogenize the solution and therefore to counter the effect of the wall-monomer hydrodynamic interaction.…”