Azimi Yancheshme A, Palmese GR, Alvarez NJ. A generalized scaling theory for spontaneous spreading of Newtonian fluids on solid substrates.
J Colloid Interface Sci 2023;
636:677-688. [PMID:
36680958 DOI:
10.1016/j.jcis.2023.01.025]
[Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/25/2022] [Revised: 01/03/2023] [Accepted: 01/05/2023] [Indexed: 01/09/2023]
Abstract
HYPOTHESIS
There exists a generalized solution for the spontaneous spreading dynamics of droplets taking into account the influence of interfacial tension and gravity.
EXPERIMENTS
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.
FINDINGS
We show that the spreading process is governed by three important parameters: the Bo number, viscous timescale τviscous, and static advancing contact angle, θs. More specifically, there exists a master spreading curve for a specific Bo and θs by scaling the spreading time with the τviscous. Moreover, we developed a correlation for prediction of the equilibrium shape of the droplets as a function of both Bo and θs. 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.
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