FWF - Tropfenschwingungen - Experiments, numerics and analytics of droplet oscillation of a viscoelastic fluid

Liquid droplets occur in numerous production and energy conversion processes. Due to initial deformations from the spherical shape they tend to oscillate, so that their surface periodically increases and decreases and motions in the drop and the ambient gas are induced. This may enhance the rates of evaporation of the drops and their aerodynamic drag and therefore in-fluence the dynamics and lifetime of the drops. Liquids involved in production processes of bio- and chemical engineering, e.g., polymer solutions in spray drying and protein and bacte-ria suspensions in aerated vessels, may be viscoelastic. In the present project we will jointly develop a deeper understanding of the motions within viscoelastic droplets and, as a long-term goal, explain their influences on transport processes across the interface. The motions are allowed to have large amplitudes, so that they are nonlinear. In the project we plan to both develop new numerical methods allowing for an accurate repre-sentation of the droplet surface, and investigate a weakly nonlinear analysis for its ability to represent the nonlinearity of the motion. The hypotheses for this part of the work are that the numerical method may allow for a sub-cell accurate sharp interface, and that the weakly non-linear approach represents the nonlinearity of the motion such that its influence on transport processes is accurately represented. Nonlinearity is essential, since the oscillation frequency decreases with increasing oscillation amplitude and the times spent in the oblate and prolate states of deformation are no longer equal. The coupling of the oscillation modes in nonlinear motion is important in the decay of oscillations. These results will be a crucial benchmark for the numerical scheme. Both numerical and analytical approaches will be compared to experimental results achieved with individual oscillating droplets. In order to do so, experiments will deliver both dynamic results such as oscillation frequencies, droplet shapes, etc., as well as material parameters. In the linear limit, the dampened drop shape oscillations themselves will be used for determining a characteristic time scale of the viscoelastic liquid needed for the computations. The present proposal is a part of a two-phase project with the second phase intended to study transfer processes across the droplet surface. Physically this corresponds to an interface that is con-tinuously formed and destroyed, resulting in various difficulties, both numerically as well as experimentally. These processes are of central importance in the design of the applications.