Abstract
This paper presents a numerical study of the viscoelastic effects on drop deformation under two configurations of interest: steady shear flow and complex flow under gravitational effects. We use a finite element method along with Brownian dynamics simulation techniques that avoid the use of closed-form, constitutive equations for the “micro-”scale, studying the viscoelastic effects on drop deformation using an interface capturing technique. The method can be enhanced with a variance-reduced approach to the stochastic modeling, along with machine learning techniques to reconstruct the shape of the polymer stress tensor in complex problems where deformations can be dramatic. The results highlight the effects of viscoelasticity on shape, the polymer stress tensor, and flow streamlines under the analyzed configurations.
Highlights
We describe the main ideas, mathematical background, and computational implementation of the FEM-based, Machine Learning (ML)-enhanced method used to perform the series of numerical experiments carried out in Section 3 to gain insight into the impact that viscoelasticity may have on drop deformation
The configuration is represented in Figure 1: a drop of a viscous fluid of radius a placed at the center of a domain [2L × 2H ], with H = 4a and L = 8a, experiences a steady, shear flow of rate γ = V/H produced by the top and bottom lids moving at velocity V in opposite directions
This pattern is more evident when using the Hooke instead of the FENE dumbbell model, due to the larger stresses produced by the former model during drop deformation: the minimum value of the circularity decreases for both c = 1 and c = 5, and we observe a lower local maximum at t u 2.2 for c = 5, De = 3, with the drop showing a lack of deformation at the latter stages of the simulation (t ≥ 2.75)
Summary
Bubble and drop dynamics in non-Newtonian fluids are a topic of undeniable interest within the community [1], owing largely to the number of real-world situations that may benefit from a comprehensive knowledge of the underlying physics: from drop formation mechanisms [2], to biomedical equipment involving droplet manipulation [3] or engineering devices in which breakup plays a central role [4,5], from droplet impact on liquid surfaces [6] to the study of drop dynamics within polymer gels and solutions [7,8]; a deeper understanding of this type of multiphase flows would improve existing manufacturing processes, and encourage the development of new applications and spur breakthroughs in scientific research.To study the multiphase flow of polymeric liquids, one should choose an appropriate discretization method capable of providing an accurate description of the interface. Level Set (LS) methods [16,17] capture the interface as the zero isocontour of a certain scalar function, which is advected by the flow, with noticeable mass loss and shape degradation if excessive diffusion is introduced during the advection stage. Despite these shortcomings, the LS method is widely used for interface problems undergoing dramatic deformation and topological changes and can be readily enhanced via “hybrid” schemes such as the Particle Level Set (PLS) method [18] that are able
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