Simulation of micron-scale drop impact

Abstract

The numerical simulation of droplet impact is of interest for a vast variety of industrial processes, where practical experiments are costly and timeconsuming. In these simulations, the dynamic contact angle is a key parameter, but the modeling of its behavior is poorly understood so far. One of the few models which considers the overall physical context of the involved 'moving contact line problem' is Shikhmurzaev's interface formation model [1]. In addition to keeping the problem well-posed, all surface and bulk parameters, such as the contact angle, are determined as part of the solution rather than being prescribed functions of contact line speed. In this article, we couple an asymptotic version of the interface formation model with our three-dimensional incompressible two-phase Navier-Stokes solver. Additionally, we employ a simple constant contact angle approach. We compare the results of these two numerical models with those from laboratory experiments for the micron-scale droplet impact on substrates with a variety of wetting characteristics. With our sophisticated asymptotic interface formation model, the droplet shapes, heights and diameters compare very well with practical experiments.

Moving contact lines and dynamic contact angles: a ‘litmus test’ for mathematical models, accomplishments and new challenges

“…Further applications included dynamic wetting by a drop impacting on a homogeneous substrate [120] and on a substrate with varying wettability [121], metastable regimes of dynamic wetting [122], flow-induced Marangoni effect [123], and, rather unexpectedly, viscous flows over chemically patterned surfaces [124,125] where no free surfaces are involved. There are now even works studying the interface formation model itself from a purely mathematical point of view addressing the issue of classical solvability of problems formulated in its framework [126,127].…”

Solução numérica do modelo Oldroyd-B para valores pequenos da razão de viscosidades: aplicação em escoamentos com superfícies livres

“…Trabalhos envolvendo a dinâmica de uma gota newtoniana são mais recorrentes na literatura, principalmente quando considera-se a influência da tensão superficial (FRANCOIS;SHYY, 2003;GUNJAL;RANADE;CHAUDHARI, 2005;LUNKAD;BUWA;NIGAM, 2007;FANG et al, 2008;COYAJEE;BOERSMA, 2009;BERBEROVIC, 2010;SHIN;CHERGUI;JURIC, 2017;GRIEBEL;KLITZ, 2019). No âmbito de escoamentos viscoelásticos, alguns códigos numéricos que consideram resolver escoamentos transientes com superfícies livres, optam por simular numericamente o problema do impacto de uma gota sobre uma placa plana (drop impact) como teste inicial para verificar o desempenho do método numérico em aproximar e mover a superfície do fluido ao longo do tempo (TOMÉ et al, 2002;OISHI et al, 2011;XU et al, 2012;FIGUEIREDO et al, 2014;DENG, 2016;YU, 2018).…”