STABILITY OF FLOW PAST DEFORMABLE SOLIDS

Abstract

Flow past deformable solids occur in many practically important situations and settings. Examples include biological systems such as blood flow and air flow wherein the flow occurs inside soft and deformable vessels and engineering systems like microfluidic devices where soft elastomers like poly dimethyl siloxane PDMS is used to fabricate the channels. Flow past deformable solids is classified into two main groups 1. External flows 2. Internal flows External flows consist of boundary layer flows and is very common in marine and aerodynamics applications whereas internal flows are common in biological systems and in microfluidic devices etc. The distinction between flow past rigid solids and flow past soft and deformable solids can be made based on the following aspects. For the case of flow past rigid solids there is no coupling between the fluid and the solid but in case of deformable solids there is interaction between deformation of solid and the deformation on the free surface when there is boundary layer flow. This coupling effect can be put to use to suppress the interfacial instabilities arising in the case of flow past rigid planes by employing soft and deformable plane instead of rigid planes. For flow inside sub- millimeter conduits made of soft and deformable materials the transition of laminar flow to turbulent flow occurs at low Reynolds number as compared to the flow through rigid tubes and channels. In case of rigid channels and rigid tubes the transition Reynolds number is 1200 and 2100 respectively. Verma and Kumaran (2013) have showed that this transition Reynolds number could be as low as 200 for the case of a very soft and deformable channels.