Breakup dynamics of toroidal droplets in shear-thinning fluids

Toroidal droplets are inherently unstable and transform into spherical droplets via the Rayleigh-Plateau instability for cylindrical jets. We exploit this similarity to study the break-up dynamics of a Newtonian liquid jet surrounded by rheologically non-linear materials. We find that break-up takes longer compared to break-up in the presence of simple fluids. Interestingly, the breakup dynamics can be explained by considering the linear theory for Newtonian liquids and incorporating the non-linearities of our material through the strain-rate-dependent viscosity. Finally, we show that the scaling factor required to relate the viscosity to the growth rate associated to the Rayleigh-Plateau instability is given by the elastic modulus of the outer material, illustrating that both the viscoelasticity and shear-thinning behavior of the outer material are essential in the dynamics of the problem.