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The Quarterly Journal of Mechanics and Applied Mathematics 1995 48(1):39-55; doi:10.1093/qjmam/48.1.39
© 1995 by Oxford University Press
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FLOW IN A CONTRACTILE TUBE AS A MODEL FOR PLASMODIAL STREAMING

D. A. SMITH

( Department of Physics, Monash University Clayton 3168, Australia )

Analytic solutions are obtained for two versions of the creeping-flow problem for Navier-Stokes fluid in an elastically deformable tube, driven by oscillatory inhomogeneous tension in the tube. In version I, the tube possesses dilatational elastic stiffness and solutions are obtained by Stokes's stream function. The amplitudes of radial oscillations, and of the applied force needed to maintain constant tube length, are enhanced by Marangoni effects arising from flow-induced surface stresses, but are still much smaller than observed in strands of the slime-mould Physarum polycephalum because of the low frequency of oscillation (~=0·01 Hz). Low-frequency radial motions of the surface can be obtained if the surface tube displays shear viscosity and the period of oscillation is comparable with the shear relaxation time. Solutions are found in the low-frequency limit (version II) where the bulk fluid is in hydrostatic equilibrium.


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