Article,
On the correspondence between creeping flows of viscous and viscoelastic fluids
Journal of Non-Newtonian Fluid Mechanics, (2007)
Abstract
From the wealth of exact solutions for Stokes flow of simple viscous fluids C. Pozrikidis, Introduction to Theoretical and Computational Fluid Dynamics, Oxford University Press, Oxford, 1997, pp. 222-311, the classical ''viscous-viscoelastic correspondence'' between creeping flows of viscous and linear viscoelastic materials yields exact viscoelastic creeping flow solutions. The correspondence is valid for an arbitrary prescribed source: of force, flow, displacement or stress; local or nonlocal; steady or oscillatory. Two special Stokes singularities, extended to viscoelasticity in this way, form the basis of modern microrheology T.G. Mason, D.A. Weitz, Optical measurements of the linear viscoelastic moduli of complex fluids, Phys. Rev. Lett. 74 (1995) 1250-1253: the Stokeslet (for a stationary point source of force) and the solution for a driven sphere. We amplify these viscoelastic creeping flow solutions with a detailed focus on experimentally measurable signatures: of elastic and viscous responses to steady and time-periodic driving forces; and of unsteady (inertial) effects. We also assess the point force approximation for micron-size driven beads. Finally, we illustrate the generality in source geometry by analyzing the linear response for a nonlocal, planar source of unsteady stress. (C) 2007 Elsevier B.V. All rights reserved.
