Analytical Consideration for the Maximum Spreading Factor of Liquid Droplet Impact on a Smooth Solid Surface

Abstract

Based on the energy conservation approach, this study develops a universal model to predict the maximum spreading factor of liquid droplet impact on a smooth solid surface. Validated with the present simulations and experiments in the literature, this model effectively overcomes the limitation of previous models in the viscous regime and greatly reduces the computing errors from over 30% to below 6%. It is demonstrated that the underestimated maximum spreading factor by previous models results from the overestimation of viscous dissipation. By replacing the conventional model of spreading time, t m = 8D 0 /3U 0 , with a more precise one, t m = 1.47τ i We −0.44 , the formulation to compute the viscous dissipation of entire spreading is improved. Finally, we examine the applicability of present model in the capillary regime and good performance is also shown.

How an Oxide Layer Influences the Impact Dynamics of Galinstan Droplets on a Superhydrophobic Surface

“…The highly distorted interface induces the generation of capillary waves. , According to the red dashed circle in Figure a, the spreading factor begins to oscillate during late spreading, which may result from the capillary waves that repeatedly propagate upward and downward. To confirm our speculation, numerical simulation based on an effective, sharp-interface, continuum-level modeling method is implemented, which has been validated and widely used to investigate the impact dynamics in our previous work. − This modeling approach is originally developed by Chamakos et al , , who also presented the details of the modeling setup. Up to now, it is still challenging to incorporate the influence of the oxide layer into a continuum-level modeling method.…”

“…Comparison of the experimental maximum spreading factor (solid symbols) with the ones predicted by the models of Clanet et al. (β max ∼ We 1/4 ), Pasandideh-Fard et al (eq ), Ukiwe and Kwok (eq ), and Du et al (eq ). …”

“…In the past few decades, numerous relations associated with impact parameters have been established to estimate β max . ,,− Although these models have shown good performance for ordinary Newtonian fluids, whether they can predict well the maximum spreading factor of Galinstan droplets is unknown. Clanet et al found that the spreading phase could be divided into two regimes by the impact parameter P = We / Re 4/5 and β max follows a different scaling law in these two regimes.…”

“…One of the most classic models is eq , which is proposed by Pasandideh-Fard et al By considering the surface energy provided by the lateral area and modifying the viscous dissipation term, Ukiwe and Kwok and Du et al. established eqs and , respectively. Here, θ Y and θ A are the Young’s contact angle and the advancing contact angle, respectively. …”

“…The spreading time t max is another critical parameter that characterizes the spreading phase, which determines the viscous dissipation of the entire spreading. ,,, Figure a shows the variation of spreading time with impact velocity. To eliminate the influence of the droplet volume, the spreading time is scaled by the initial diameter of a droplet.…”