Dynamics of drop impact onto a solid sphere: spreading and retraction

Abstract

In this paper, drop impact onto a sphere is numerically investigated at moderate Reynolds and Weber numbers. It is naturally expected that the aspect ratio of the sphere to the drop, $\unicode[STIX]{x1D706}_{r}$, would make a big difference to drop spreading and retraction on the sphere, compared with drop impact onto a flat substrate. To quantitatively assess the effect of $\unicode[STIX]{x1D706}_{r}$, a diffuse-interface immersed-boundary method is adopted after being validated against experiments. With the help of numerical simulations, we identify the key regimes in the spreading and retraction, analyse the results by scaling laws, and quantitatively evaluate the effect of $\unicode[STIX]{x1D706}_{r}$ on the impact dynamics. We find that the thickness of the liquid film spreading on the sphere can be well approximated by $h_{L,\infty }(1+3/4\unicode[STIX]{x1D706}_{r}^{-3/2})$, where $h_{L,\infty }$ represents the film thickness of drop impact on a flat substrate. At the early stage of spreading, the temporal variation of the wetted area is independent of $\unicode[STIX]{x1D706}_{r}$ when the time is rescaled by the thickness of the liquid film. Drops are observed to retract on the sphere at a roughly constant speed, and the predictions of theoretical analysis are in good agreement with numerical results.

Curved surface effect on high-speed droplet impingement

“…Some researchers also emphasised that when the curvature of a curved surface is equivalent to that of the impinging droplet, the curved surface effect is particularly significant (Burson-Thomas et al 2019a), and the flat surface can be regarded as a surface with zero curvature. However, most studies have mainly focused on impingement at relatively low speeds (Khojasteh et al 2017;Liu et al 2017;Zhu et al 2017;Li et al 2018;Chen et al 2019). Scant research has explored a high-speed droplet's impingement on a curved surface to interpret the curved surface effect on the droplet's evolution, which can be helpful to understand the fluid induction surface damage mechanism.…”

Axisymmetric evolution of gravity-driven thin films on a small sphere

“…The impact of a droplet on a solid sphere often leads to a liquid film on the sphere, where inertia dominates the evolution at the early stage and viscosity takes over at the late stage (Bakshi, Roisman & Tropea 2007). The wetting dynamics accompanied by the advancing contact line plays an important role in the formation of liquid films (Zhu et al 2017). In the condition of continuous liquid supply, Wild & Potter (1972) and Belousov & Belousov (2010) experimentally measured the film thickness on a sphere.…”

“…The wetting dynamics accompanied by the advancing contact line plays an important role in the formation of liquid films (Zhu et al. 2017). In the condition of continuous liquid supply, Wild & Potter (1972) and Belousov & Belousov (2010) experimentally measured the film thickness on a sphere.…”

Simulation of droplet impacting a square solid obstacle in microchannel with different wettability by using high density ratio pseudopotential multiple-relaxation-time (MRT) lattice Boltzmann method (LBM)

“…Most of the phenomena that droplets hit on a solid obstacle can be divided into the level of the droplets impacting horizontal wall [3][4][5][6], spherical surface [7,8] and inclined wall [9,10]. If the size and shape of solid obstacles are taken into account, solid obstacles can be categorized as spherical obstacles [7,8,11] , cylindrical obstacles and rectangular obstacles [12][13][14]. Significant amount of researches have been reported to explore the characteristics of spreading, wetting, spattering, crushing, consequent pressure change and velocity change when droplet impacting on the solid obstacle through theoretical analysis, experimental study and numerical simulation.…”