Motion of a sphere through a polymer solution

We present analytical solutions of the hydrodynamic resistance force a spherical particle experiences when it moves through a polymer solution containing nonadsorbing chains. Polymer depletion results in a reduced polymer concentration and fluid viscosity near the particle surface. The nonuniform physical properties in the fluid phase affect the transport behavior of a translating and rotating sphere as compared with the case of uniform properties. Based on Stokes’ stream function theory, we develop a simplified two-layer approximation by using a step function to represent the viscosity profile. The presence of the polymer solution is formulated in terms of correction functions to the translational and rotational friction of a sphere in a pure solvent. The results are in fair agreement with systematic measurements of the friction of a colloidal sphere when it moves through a polymer solution. The analysis also predicts an apparent slip length in terms of the viscosity ratio and thickness of the depletion layer.