Pumping viscoelastic two-fluid media

TL;DR

This paper analyzes how viscoelastic two-fluid media respond to wave-driven fluid transport, revealing wave number and viscosity dependencies, and identifying regimes where viscoelastic effects significantly alter flow compared to Newtonian fluids.

Contribution

It provides an analytical study of wave-driven flow in viscoelastic two-fluid models, clarifying the regimes where viscoelasticity influences transport and the boundary between these regimes.

Findings

Transport is wave number and viscosity dependent.

Two regimes identified: Newtonian-like and gel-like behavior.

Boundary between regimes clarified.

Abstract

Using a two-fluid model for viscoelastic polymer solutions, we study analytically fluid transport driven by a transverse, small amplitude traveling wave propagation. The pumping flow far from the waving boundary is shown to be strongly wave number and viscosity dependent, in contrast to a viscous Newtonian fluid. We find the two qualitatively different regimes: In one regime relevant to small wave numbers, the fluidic transport is almost the same as the Newtonian case, and uniform viscoelastic constitutive equations provide a good approximation. In the other regime, the pumping is substantially decreased because of the gel-like character. The boundary separating these two regimes is clarified. Our results suggest possible needs of two-fluid descriptions for the transport and locomotion in biological fluids with cilia and flagella.