Scaling law behaviour of the retraction of a Newtonian droplet after a strain jump in a Newtonian matrix

Abstract

We performed 3D visualisation of a Newtonian droplet embedded in an immiscible Newtonian liquid after a strain jump with a home-built counter-rotating shear device. The use of different linear polyurethanes for the droplet liquid allowed us to cover almost three decades of viscosity ratios (K) and to obtain a distinct interface with PDMS matrices with the same interfacial tension for all droplet/matrix pairs. During the droplet retraction, the major axis (L) showed universal time dependence. The apparent Hencky strain of L decayed linearly at large deformations and exponentially at small deformations. After large strain steps, the droplet axis along the vorticity direction (W) deflated and then inflated and the time dependence could be well described by a log normal function. The full width at half maximum was proportional to the droplet relaxation time for all K. The amplitude and the position of the minimum of W were proportional to the affine deformation. The results revealed interesting scaling law behaviour of the droplet retraction after large strain jumps.