Viscoelastic Effects on Drop Deformation Using a Machine Learning-Enhanced, Finite Element method

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.

The Elasticity of Polymer Melts and Solutions in Shear and Extension Flows

“…Any deformation in the polymer processing inevitably leads to molecular orientation that can be treated in terms of elasticity (stored energy) wherein normal stresses (under the extension flow) create a much higher effect than shear stresses (under the shear flow) that is clearly demonstrated in the simplest model of the deformation of a liquid drop inside a surrounding liquid under different modes of the flow [ 12 , 13 , 14 ]. Elastic (recoverable) force for a liquid droplet is surface tension while for polymers and in particular for polymer blends, the source of elasticity is molecular motion directed to the recovery of the equilibrium conformation and having the statistic (entropic) nature.…”

High-resolution fluid–particle interactions: a machine learning approach

“…As demonstrated, the coarse-scale modelling cannot show the fine-scale features and often suffices for a general, and crude, representation. With the recent developments in machine learning (ML) methods and their successful application to classical engineering problems, various advances have been made to accelerate numerical methods (Kachrimanis, Karamyan, & Malamataris 2003;Ariana, Vaferi, & Karimi 2015;Benvenuti, Kloss, & Pirker 2016;Chaurasia & Nikkam 2017;Liang et al 2018a,b;Figueiredo et al 2019;Brevis, Muga, & van der Zee 2020;Prieto 2020). This capacity has also been extended to problems related to fluid dynamics and granular flow (Radl & Sundaresan 2014;Kutz 2017;Wan & Sapsis 2018;Fukami, Fukagata & Taira 2019;Li et al 2020a;Park & Choi 2020;Aghaei Jouybari et al 2021) where its applications towards the former has been extensively reviewed (Brenner, Eldredge, & Freund 2019;Brunton, Noack, & Koumoutsakos 2020;Fukami, Fukagata, & Taira 2020a).…”