Motion of a sphere through a polymer solution

T.H. Fan, J.K.G. Dhont, R. Tuinier

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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.

Original languageEnglish
Article number011803
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number1
Publication statusPublished - 2007
Externally publishedYes


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