Mobility of a Slender Object in Entangled Polymer Solution

Accurate physical modeling of heterogeneouscomplexfluids is paramount to understanding active and passivetransport in biological and biomimetic environments. In thepresent paper we employ the phenomenological two-fluid model toderive frictional resistance of a rigid object moving through anentangled polymer solution. Depending on the interaction betweenthe particle and the incompressible polymer network, we introducefour different types of boundary conditions involving velocity andelastic stress of the polymer at the particle surface. For stronglyadherent polymer we show, by employing the no-slip boundarycondition, that the generalized Stokes relation (GSR) holds forarbitrarily shaped particle, implying that its frictional resistance is the same as the hydrodynamic (Stokes) resistance, being linearlyproportional to the bulk viscosity,eta b, of the entangled polymer solution. For particles pretreated to hinder polymer adhesion weshowed, by assuming either direct or indirect (solvent-mediated) repulsive interaction between the particle and the polymernetwork, that GSR does not hold in general and that frictional resistance becomes mesh-size-dependent. In the latter case,approximate closed-form expressions for translational (i.e., longitudinal and transverse) frictional resistances of a slender rigidparticle are obtained employing the classical Oberbeck's solution of the Stokes equations for prolate spheroid and the 2D solution ofthe Brinkman equations for an infinitely long cylinder. We demonstrate, in particular, that for high values of the bulk viscosity typicalfor biological and biomimetic gels eta b???100 eta, with eta being the solvent viscosity, the frictional anisotropy (i.e., the ratio of transverseto longitudinal resistances) could reach values >10, in qualitative agreement with experimental observations and numericalfindings.

Automated summary

Accurate physical modeling of heterogeneous complex fluids is important for understanding transport in biological and biomimetic environments. This paper investigates the frictional resistance of a rigid object moving through an entangled polymer solution using a two-fluid model. Different boundary conditions and their effects on frictional resistance are analyzed. The study shows that the generalized Stokes relation holds for strongly adherent polymer, but not for particles pre-treated to hinder polymer adhesion.