Capillary filling dynamics of viscoelastic fluids

We consider the filling of a capillary by a viscoelastic fluid described by the Phan-Thien-Tanner (PTT) constitutive behavior. By considering both vertical capillary filling and horizontal capillary filling, we demarcate the role played by gravity and fluid rheology towards long-time oscillations in the capillary penetration depth. We also consider the isothermal filling of the capillary for a closed channel and thus bring out the fundamental differences in the nature of capillary filling for PTT and Newtonian fluids for closed channels in comparison to open channels. Through a scaling analysis, we highlight a distinct viscoelastic regime in the horizontal capillary filling which is in contrast to the Washburn scaling seen in the case of Newtonian fluids. Such an analysis with a very general constitutive behavior is therefore expected to shed light on many areas of microfluidics which focus on biofluids that are often well described by the PTT constitutive behavior.