Azimi Yancheshme Amir, Palmese Giuseppe R, Alvarez Nicolas J
Chemical and Biological Engineering, Drexel University, Philadelphia, PA 19104, USA.
J Colloid Interface Sci. 2023 Apr 15;636:677-688. doi: 10.1016/j.jcis.2023.01.025. Epub 2023 Jan 8.
There exists a generalized solution for the spontaneous spreading dynamics of droplets taking into account the influence of interfacial tension and gravity.
This work presents a generalized scaling theory for the problem of spontaneous dynamic spreading of Newtonian fluids on a flat substrate using experimental analysis and numerical simulations. More specifically, we first validate and modify a dynamic contact angle model to accurately describe the dependency of contact angle on the contact line velocity, which is generalized by the capillary number. The dynamic contact model is implemented into a two-phase moving mesh computational fluid dynamics (CFD) model, which is validated using experimental results.
We show that the spreading process is governed by three important parameters: the Bo number, viscous timescale τ, and static advancing contact angle, θ. More specifically, there exists a master spreading curve for a specific Bo and θ by scaling the spreading time with the τ. Moreover, we developed a correlation for prediction of the equilibrium shape of the droplets as a function of both Bo and θ. The results of this study can be used in a wide range of applications to predict both dynamic and equilibrium shape of droplets, such as in droplet-based additive manufacturing.
考虑界面张力和重力的影响，存在一种适用于液滴自发扩散动力学的广义解。
本文利用实验分析和数值模拟，针对牛顿流体在平坦基底上的自发动态扩散问题，提出了一种广义标度理论。具体而言，我们首先验证并修正了一个动态接触角模型，以准确描述接触角对接触线速度的依赖性，该依赖性由毛细管数进行广义化。将动态接触模型应用于两相移动网格计算流体动力学（CFD）模型，并利用实验结果对其进行了验证。
我们表明，扩散过程由三个重要参数控制：邦德数、粘性时间尺度τ和静态前进接触角θ。具体来说，对于特定的邦德数和接触角θ，通过用τ对扩散时间进行标度，存在一条主扩散曲线。此外，我们建立了一个关联式，用于预测液滴平衡形状与邦德数和接触角θ二者的函数关系。本研究结果可广泛应用于预测液滴的动态和平衡形状，如基于液滴的增材制造。
