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Translational and rotational drag coefficients for a disk moving in a liquid membrane associated with a rigid substrate

Published online by Cambridge University Press:  21 April 2006

Evan Evans  and
Erich Sackmann
Evan Evans
Affiliation:
Physics Department, Technical University of Munich, D-8046 Garching b. München, West Germany Departments of Pathology and Physics, University of British Columbia, Vancouver, BC, Canada V6T 1W5
Erich Sackmann
Affiliation:
Physics Department, Technical University of Munich, D-8046 Garching b. München, West Germany
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Abstract

A simple phenomenological drag relation is used to characterize weak dynamic coupling of a liquid membrane to an adjacent solid substrate. With this linear velocity-dependent drag relation, the inertialess equations of motion for membrane flow are easily solved for steady translation and rotation of a disk-like particle. The resulting drag coefficients exhibit functional dependencies on the dimensionless particle size very similar to the relations obtained for particle motion in a membrane bounded by semi-infinite liquid domains (Hughes et al. 1981), although the scaling of particle size is different. Within this phenomenological approach, diffusivities of molecular probes in membranes can be used to investigate the intrinsic molecular drag at a solid-liquid membrane interface and to estimate properties of thin lubricating liquid layers between membrane and substrate.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 194 , September 1988 , pp. 553 - 561
Copyright
© 1988 Cambridge University Press

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