Deformation of a Hele–Shaw drop undergoing quadratic flow

Abstract

A Hele–Shaw quadratic flow in the form of a six-port microfluidic device is employed to study the deformation of a single channel-spanning or Hele–Shaw Newtonian drop suspended in a Newtonian medium. An initially circular drop in a quadratic flow deforms into a regular triarcle, i.e., a rounded-corner triangle. Theoretically, the deformation is calculated in the limit of small capillary number, which is defined as Ca=Cμa4/(4γb2), where C is the quadratic flow rate, μ is the suspending fluid viscosity, a is the drop radius, γ is the interfacial tension, and b is the channel depth. The theory matches reasonably well with the experiment for small capillary numbers. This is the new way of deforming drops on a Hele–Shaw quadratic platform experimentally and may lead to measurements such as complex interfacial properties and breakup.