The interaction of elastomeric coatings with viscous flows: how incompressible is PDMS?

Elastic substrates bounding fluid flows are common in many experimental and industrial settings; their principal purpose is usually to drive or suppress the flow of fluid. In particular, PDMS is one of the most frequently used materials in microfluidic platforms, since it is easily designed into complex channel shapes. The deformation of such PDMS and other elastomeric layers is becoming increasingly recognised, but the model appropriate for describing its deformation depends on how close to incompressible the coating is. While the Poisson ratio is usually quoted as being in the range of 0.49 – 0.5, the precise value may change the behaviour of the coating and have knock-on consequences. We will present a model for thin, near-incompressible elastic foundations, and discuss how its application to examples of fluid-structure interaction problems at low Reynolds number can depend sensitively on how incompressible the coating is.