Experimental, numerical and analytical investigation of droplet oscillation of a viscoelastic fluid

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Oscillating droplets occurring in innumerous production and energy conversion processes are a subject of scientific interest. The deviation from a sphere increases the surface, which enhances the rate of transfer for mass, momentum and energy. Liquids involved in production processes of bio- and chemical engineering, particularly, polymer powders by spray drying and in the aeration of liquids with dissolved proteins and bacteria, may exhibit viscoelastic behaviors. In the present project we intend to jointly develop a deeper understanding of the motions within viscoelastic droplets and, as a long-term goal, to explain their influences on transport processes across the interface. For this we will employ sophisticated experimental, numerical and analytical methods. Most important, the droplet deformations involved are allowed to include nonlinear fluid behavior.For this, new numerical methods based on Discontinuous Galerkin method (DG) will be developed, which allow an hp-accurate simulation. Different from classical approaches, the key goal is a sub-cell accurate sharp-interface hp-accurate simulation. A broad variety of specific tools have already been developed for this. The numerical difficulties for simulating viscoelastic models are less severe in the context of DG compared to classical numerical methods, e.g. FVM. Additionally, tensor-polynomial basis ideas, very successfully employed for algebraic stress models in the context of turbulence, will also be adopted. Therein it led to fast and robust schemes, which, due to the close similarity of equations, will also be employed for the present viscoelastic models.Additionally, a weakly nonlinear analytical approach will be developed such that it can represent the time dependency of the oscillation frequency. Nonlinearity is essential, as the oscillation frequency decreases with increasing oscillation amplitude, and, further, 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 an important aspect in the decay of oscillations. These results will be a crucial benchmark for the DG-based numerical scheme.Both analytical and numerical approaches will be compared to experimental results. In order to do so, experiments will deliver both material parameters as well as dynamical results such as oscillation frequencies, droplet shapes, etc. In the linear limit, the dampened drop shape oscillations themselves will be used for determining the polymeric deformation retardation time scale of the test liquid needed for the computations.The present proposal is part of a two-phase project where in the second phase it is intended to study mass and energy transfer across the droplet-surface. Physically this corresponds to a non-material interface, resulting in different difficulties both numerically as well as experimentally. These effects constitute key design parameters for many applications.