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兴趣的主题。与球体的偏离增加了表面，从而提高了质量、动量和能量的传递速率。生物和化学工程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和溶解蛋白质和细菌的液体曝气，可能表现出粘弹性行为。在目前的项目中，我们打算共同深入了解粘弹性液滴内的运动，并作为一个长期目标，解释它们对跨界面传输过程的影响。为此，我们将采用复杂的实验、数值和分析方法。最重要的是，所涉及的液滴变形允许包括非线性流体行为。为此，将发展基于间断伽辽金法（DG）的新的数值方法，以实现hp精度的模拟。与传统方法不同，该方法的关键目标是实现亚单元精确的锐界面仿真。为此已经开发了各种各样的特定工具。与经典数值方法（如FVM）相比，在DG环境下模拟粘弹性模型的数值困难不那么严重。此外，张量-多项式基思想，非常成功地应用于湍流背景下的代数应力模型，也将被采用。由此产生了快速和鲁棒的方案，由于方程的密切相似性，这些方案也将用于目前的粘弹性模型。此外，将开发一种弱非线性分析方法，使其能够表示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，而且，在扁圆和长形变形状态下花费的时间不再相等。非线性运动中振动模态的耦合是振动衰减的一个重要方面。这些结果将成为基于dg的数值方案的关键基准。分析方法和数值方法都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力学结果，如振荡频率，液滴形状等。在线性极限下，阻尼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。目前的提案是一个两阶段项目的一部分，在第二阶段，它打算研究质量和能量在液滴表面的传递。物理上，这对应于非物质界面，导致数值和实验上的不同困难。这些影响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.