Seminar über aktuelle Fragen zur Dynamik komplexer Fluide: Oscillating Contact Lines of Newtonian and Viscoplastic Fluids

The spreading of Newtonian and non-Newtonian liquid droplets occurs in a number of applications such as inkjet and 3D printing. In the talk, we will present our recent study on the spreading of droplets on a pre-wetted surface. We will briefly review the classic findings on the problem using Newtonian lubrication theory and then discuss the limitations. Next, we will present a solution of Stokes equation for the same problem, where an entirely different behavior appears for large Capillary numbers, Ca. We validate the theoretical results experimentally. We use digital holographic microscopy, a method based on interferometry that allows us to measure the surface profile of the droplet with sub-micron accuracy. In short, we find three important Capillary numbers. First, an extremely small Ca, where the oscillations disappear because of gravity. A moderate one, where the oscillations become the most pronounced and eventually a large Ca, where the oscillations disappear again.

We extend the theoretical results for a particular non-Linear fluid, known as viscoplastic fluid (a.k.a yield-stress material). Such material, if not sufficiently stressed, behaves like a solid, but once the stress exceeds a critical value (the yield stress), it deforms like a viscous fluid. We derive the viscoplastic thin film equations and present the numerical and asymptotic solutions. We again observe the oscillations in the surface profiles, this time not only during the spreading but also in the final shape, when the deformation solidifies because of the yield stress. Asymptotically, we show a completely different origin of the oscillations is viscoplastic fluids. The experimental validation of the results is currently a work in progress.