Submicron Flow of Polymer Solutions: Slippage Reduction due to Confinement

Abstract

Pressure-driven flows of high molecular weight polyacrylamide solutions are examined in nanoslits using fluorescence photobleaching. The effective viscosity of polymer solutions decreases when the channel height decreases below the micron scale. In addition, the apparent slippage of the solutions is characterized macroscopically on similar surfaces. Though slippage can explain qualitatively the effective viscosity reduction, a quantitative comparison shows that the slip length is greatly reduced below the micron scale. This result indicates that chain migration is suppressed in confined geometries.

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

“…The reduction of effective viscosity becomes significant for narrower channels in the micron range (e.g., sandstone reservoirs), because the depleted volume becomes a larger fraction of the total fluid volume. A reduction of the effective viscosity by a factor of at least two is found experimentally for HPAM flow in channels with plane walls when the channel width is reduced from ten to one micron [10].…”

“…Cuenca and Bodiguel [10] found relatively large reductions in effective viscosity with reduced channel width in the sub-micron range for HPAM polymer. This is also the behavior we find in the simulations, where δ/h ≃ 0.2 for the narrower channels around 10 nm, and drops to about δ/h ≃ 0.05 for widths of 40 nm (Figure 3).…”

“…The Newtonian approximation is valid for polymer solutions if W i is near and below unity (Appendix C). For thin depletion layers where δ/h ≪ 1, it has been shown earlier that the effective viscosity is approximately [10,49] …”

“…where µ 0 e is the effective viscosity for a homogeneous polymer solution throughout the flow volume (no depletion layer), and f d is an increasing function of the depleted volume fraction δ/h [48,10]. In the following, we develop algebraic models for the correction factor f d , accounting for depletion layers that span a significant fraction of the channel volume.…”

“…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. Ready-to-apply models for the depletion layer thickness δ as function of the Weissenberg number W i, the channel width h, ion contents/salinity, and adsorption properties are still lacking as far as we are aware.…”