Hele-Shaw drop deformation in quadratic extensional flow

The four-roll mill and microfluidic experiments have often used linear extensional flow to study deformation, break-up and coalescence behavior. There, however, is no experimental evidence of higher order flows being used to study emulsion drops. Here, we consider the deformation of a Hele-Shaw drop exposed to a quadratic flow that forms inside a microfluidic hexagonal chamber. A Hele-Shaw drop was held at the center of the chamber and at the stagnation point of the flow ‘indefinitely’, using a computer-controlled six-port extensional flow device, and the dynamic deformation of the drop was recorded at the applied stresses. For quadratic Hele Shaw flow, in the limits of small deformation, the drop deforms into a triangle with round corners as opposed to an ellipse in a linear extensional flow. The deformation is calculated in the limit of small capillary number, and the theory matches with experiment. This is the new way of deforming drops on a quadratic platform experimentally, and may lead to measurements such as interfacial tension and breakup.