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

在无数的生产和能量转换过程中发生的振荡液滴是一个科学感兴趣的主题。偏离球体增加了表面，从而提高了质量、动量和能量的传递速率。在生物和化学工程的生产过程中涉及的液体，特别是通过喷雾干燥的聚合物粉末以及在溶解有蛋白质和细菌的液体的充气中涉及的液体，可以表现出粘弹性行为。 在本项目中，我们打算共同开发粘弹性液滴内的运动的更深入的理解，并作为一个长期的目标，以解释其对跨界面的传输过程的影响。为此，我们将采用先进的实验，数值和分析方法。最重要的是，液滴变形可以包含非线性流体行为，为此，将开发基于间断Galerkin方法（DG）的新的数值方法，该方法可以实现hp精度的模拟。与经典方法不同，该方法的关键目标是子单元精确的尖锐界面hp精确的模拟。已经为此开发了各种各样的具体工具。数值模拟粘弹性模型的困难是不太严重的背景下，DG相比，经典的数值方法，如有限体积法。此外，张量多项式的基础思想，非常成功地用于代数应力模型在湍流的情况下，也将被采用。在这里，它导致快速和强大的格式，由于密切相似的方程，也将被用于目前的粘弹性模型。此外，弱非线性分析方法将被开发，使其能够代表振荡频率的时间依赖性。非线性是必不可少的，因为振荡频率随着振荡幅度的增加而降低，并且，此外，在扁长和长扁形变状态中花费的时间不再相等。非线性运动中振动模式的耦合是振动衰减的一个重要方面。这些结果将是基于DG的数值方法的一个重要基准。分析和数值方法将与实验结果进行比较。为了做到这一点，实验将提供材料参数以及动态结果，如振荡频率，液滴形状等。阻尼的液滴形状振荡本身将用于确定计算所需的测试液体的聚合物变形延迟时间尺度。第二阶段的项目，在第二阶段的目的是研究质量和能量转移通过液滴表面。在物理上，这对应于一个非物质的接口，导致在不同的困难，无论是在数值上，以及实验。这些效应构成了许多应用的关键设计参数。

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.