Oblique impact dynamics of micron particles onto a liquid surface

Micron particles rotate and their trajectories deviate from the impact direction when impacting the liquid surface obliquely; thus their impact dynamics is largely different from that of vertical impact, which remains to be studied in depth. In this study we established a three-dimensional simulation method by solving the coupled equations of particle motion and fluid flow and adopting a dynamic meshing technique and slip velocity boundary condition that accurately reproduced the particle motion and gas-liquid interface evolution during oblique impact. Our results, based on detailed flow field and acting forces and moments analyses, demonstrate that the particle's nonaxisymmetric wetting leads to the nonaxisymmetric distribution of fluid pressure and shear stress along the particle surface, and thus deviates the dominating forces at different impact stage from its direction of motion, which makes the particle trajectory deviate from the impact direction and also generates a viscous moment that rotates the particle. We also illustrate how the impact angle and Weber number modulate the flow field around the particle as well as the acting forces and finally influence the particle motions. These findings provide a deep understanding of the dynamics of the nonaxisymmetric impact of the micron particle on liquid surfaces, which is a ubiquitous scenery in nature and industry.

Figure 1

Schematic of a micron particle impacting a liquid surface.

Figure 2

Illustrations of (a) the computational domain and (b) the mesh at the symmetric plane.

Figure 3

Comparison of (a) the particle trajectory colored based on the dimensionless time $T\left(=t{u}_0/d_p\right)$, with × representing the position where the particle is submerged, (b) the particle's trajectory deviation $\mathrm{\Delta }s$ (the positive value means the particle's trajectory deviates downward) and rotational angular velocity ω, and (c) the evolution of the angular position of the TPCL ϕ and the inclination of the TPCL plane ${\alpha }_T$ between the simulations and experiments [29]: $\alpha =43.8^{\circ }$, $d_p=306.0\mu \mathrm{m}$, $u_0=2.84\mathrm{m}/\mathrm{s}$, $\mathrm{We}=34$, and $\mathrm{Re}=867$. The black dashed line in (a) represents the impact direction, while the inset figure plots the enlarged view near the particle submerged position.

Figure 4

Time series of the gas-liquid interface obtained numerically and experimentally [29]: $\alpha =43.8^{\circ }$, $d_p=306.0\mu \mathrm{m}$, $u_0=2.84\mathrm{m}/\mathrm{s}$, $\mathrm{We}=34$, and $\mathrm{Re}=867$.

Figure 5

(a), (c) The penetration depth ($h_p$) and maximum trajectory deviation ($\mathrm{\Delta }{s}_m$) of the particle and (b), (d) the maximum angular velocity of the particle (${\omega }_m$) and maximum inclination of the TPCL plane (${\alpha }_{Tm}$) as functions of (a), (b) α ($\mathrm{We}=34$, $\mathrm{Re}=867$) and (c), (d) We ($\alpha ={45}^{\circ }$, $\mathrm{Re}=867$). The open points and the solid points represent the oscillation mode and the submergence mode, respectively.

Figure 6

The shear stress vector distribution on the particle surface at two moments representing the initial and late impact stage (the gray curved surface represents the gas-liquid interface): $\alpha =43.8^{\circ }$, $\mathrm{We}=34$, and $\mathrm{Re}=867$.

Figure 7

Time evolution of the moment acting on the particle during impact with different impact angles (× represents the time of particle submergence): $\mathrm{We}=34$ and $\mathrm{Re}=867$.

Figure 8

Time evolution of the magnitude (a) and direction (b) of the forces acting on the particle during impact: $\alpha =43.8^{\circ }$, $\mathrm{We}=34$, and $\mathrm{Re}=867$.

Figure 9

Pressure distribution of the fluid around the particle at two typical moments: $\alpha =43.8^{\circ }$, $\mathrm{We}=34$, and $\mathrm{Re}=867$. The gray curved surface represents the gas-liquid interface, and the black line represents the fluid streamline.

Figure 10

The time evolution of the components parallel (${}_{//}$) and perpendicular ($\perp$) to the impact direction of the hydrodynamic force $F_h$, surface tension force $F_s$, and total external force $F_t$ at different impact angles ($\mathrm{We}=34$ and $\mathrm{Re}=867$): (a) $\alpha ={60}^{\circ }$ and (b) $\alpha ={30}^{\circ }$.