Choking the flow in soft Hele-Shaw cells: the role of elastomer geometry

Abstract

We investigate flow-induced choking in soft Hele-Shaw cells comprising a fluid-filled gap in between a rigid plate and a confined block of elastomer. Fluid injected from the centre of the circular rigid plate flows radially outwards, causing the elastomeric block to deform, before exiting through the cell rim. The pressure in the fluid deforms the elastomer, increasing the size of the gap near the inlet, and decreasing the gap near the cell rim, because of volume conservation of the solid. At a critical injection flow rate, the magnitude of the deformation becomes large enough that the flow is occluded entirely at the rim. Here, we explore the influence of elastomer geometry on flow-induced choking and, in particular, the case of a thick block with radius smaller than its depth. We show that choking can still occur with small-aspect-ratio elastomers, even though the confining influence of the back wall that bounds the elastomer becomes negligible; in this case, the deformation length scale is set by the radial size of the cell rather than the depth of the block. Additionally, we reveal a distinction between flow-induced choking in flow-rate-controlled flows and flow-rate-limiting behaviour in pressure-controlled flows.