Thermocapillary effects on viscoelastic drops suspended in axisymmetric pressure driven flows

Dynamics and deformation of a viscoelastic drop in another immiscible viscoelastic medium in the presence of externally imposed pressure and temperature gradients are analyzed asymptotically in the present work. Both of the phases obey the linear Phan-Thien-Tanner constitutive model, capable of accounting for shear thinning behavior in polymeric fluids. The first two asymptotic corrections to the leading order Newtonian behavior are reported here, in the limit of small Deborah and Capillary numbers, which, respectively, characterize the extent of viscoelasticity and interfacial deformation. We establish that the viscoelastic properties of the inner phase strongly influence the migration velocity and the interfacial deformation of the drop. Our analysis reveals the possibility of realizing a maximum migration velocity for an intermediate viscosity of the interior phase, provided it has stronger viscoelastic characteristics than the suspending medium. We further compute the critical thermal gradient required to completely arrest the drop's motion and demonstrate that the same depends on the Deborah number as well as the viscosity of the inner phase. The viscoelastic stresses also dictate the deformation as the drop's shape changes from prolate to oblate when those stresses become significant. Our results may find potential applications in areas such as polymer processing and handling of biologically relevant media in medical diagnostics.