Maximum spreading of droplet-particle collision covering a low Weber number regime and data-driven prediction model

Abstract

In the present study, the maximum spreading diameter of a droplet impacting with a spherical particle is numerically studied for a wide range of impact conditions: Weber number (We) 0-110, Ohnesorge number (Oh) 0.0013-0.7869, equilibrium contact angle ( θeqi) 20{degree sign}-160{degree sign}, and droplet-to-particle size ratio (Ω) 1/10-1/2. A total of 2600 collision cases are simulated to enable a systematic analysis and prepare a large dataset for training of a data-driven prediction model. The effects of four impact parameters (We, Oh, θeqi, and Ω) on the maximum spreading diameter ( β*max) are comprehensively analyzed, and particular attention is paid to the difference of β*max between the low and high Weber number regimes. A universal model for prediction of β*max, as a function of We, Oh, θeqi, and Ω, is also proposed based on a deep neural network. It is shown that our data-driven model can predict the maximum spreading diameter well, showing an excellent agreement with the existing experimental results as well as our simulation dataset within a deviation range of {plus minus} 10%.

Energetics of spreading droplets and role of capillary waves at low Weber numbers below 10

“…In this section, therefore, a brief introduction of our simulation methods is given rather than a fully detailed description. Readers can refer to our previous studies for more detailed information on our numerical formulations [23,39,47,48] and method validation.…”

“…In addition, in digital microfabrication technology, a molten liquid droplet can often undergo low speed impact to ensure a precise deposition on three-dimensional micro-structures [22]. In such collision cases, at low Weber number, the capillary effects and associated phenomena play dominant roles in spreading dynamics [23]. This is the author's peer reviewed, accepted manuscript.…”

“…However, the online version of record will be different from this version once it has been copyedited and typeset. PLEASE CITE THIS ARTICLE AS DOI: 10.1063/5.0138378 [23] shown that the maximum spreading of a millimetric droplet can reach above its initial droplet diameter measured before contact [23,43], although the initial impact velocity is zero.…”

Prediction of the morphological evolution of a splashing drop using an encoder–decoder

“…In recent years, with the increasing availability and accessibility of data, data-driven approaches-and machine learning in particular-have attracted increasing attention among fluid researchers as a faster and cheaper alternative or complement to experimental and numerical studies [32][33][34][35][36][37][38][39]. Regarding drop impacts, several machine-learning-based studies have been carried out [40][41][42][43]. Notably, a number of studies on predicting the maximum spreading factor of a non-splashing drop under various conditions were published in 2022.…”

“…Also, Tembely et al compared the performances of the linear regression model, decision tree, random forest, and gradient boost regression model on predicting the maximum spreading of a drop on surfaces of various wettabilities [41]. Even for droplet-particle collisions, Yoon et al used a multi-layer feedforward neural network (FNN) to predict the maximum spreading diameter under a significantly wide range of impact conditions [42]. Other than the maximum spreading diameter, such physical parameters-based machine learning was also applied for the investigations of the drop impact force and the splashing mechanisms.…”