Direct numerical simulation of an arbitrarily shaped particle at a fluidic interface

A consistent formulation is presented for the direct numerical simulation of an arbitrarily shaped colloidal particle at a deformable fluidic interface. The rigid colloidal particle is decomposed into a collection of solid spherical beads and the three-phase boundaries are replaced with smoothly spreading interfaces. The major merit of the present formulation lies in the ease with which the geometrical decomposition of the colloidal particle is implemented, yet allows the dynamic simulation of intricate three-dimensional colloidal shapes in a binary fluid. The dynamics of a rodlike, a platelike, and a ringlike particle are presently tested. It is found that platelike particles attach more rapidly to a fluidic interface and are subsequently harder to dislodge when subject to an external force. Using the Bond number, i.e., the ratio of the gravitational force to the reference capillary force, a spherical particle with equal affinity for the two fluids breaks away from a fluidic interface at the critical value $\text{Bo}=0.75$. This value is in line with our numerical experiments. It is here shown that a plate and a ring of equivalent masses detach at greater critical Bond numbers approximately equal to $\text{Bo}=1.3$. Results of this study will find applications in the stabilization of emulsions by colloids and in the recovery of colloidal particles by rising bubbles.

Figure 1

Schematics of a solid assembly at a fluidic interface. The assembly is shown in the body frame and in the inertial frame.

Figure 2

Relative terminal velocity as a function of the number of beads in the three-dimensional chain (top). The reference data obtained with the open-source program hydrlib [25] are used to calculate the relative errors (bottom).

Figure 3

Three-dimensional solid assemblies used in the two simulation sets S2 and S3.

Figure 4

Orientation $\alpha$ of each solid assembly as a function of time. At the time $t/t_0=0$ the center of mass is placed at the fluidic interface initially set in horizontal position.

Figure 5

Evolution of the fluidic interface for various Bond numbers. The time step between two successive isolines colored in gray is constant. The 3D plots and the field midsections $\psi$ are shown for the plate (S3) at time $t_3$ and $t_{16}$, respectively.

Figure 6

Relative vertical displacement of the assembly in the bottom fluid as a function of the Bond number. Data associated with a detachment are not shown.

Figure 7

Vertical velocity component ${\text{V}}_y$ as a function of the particle altitude, where ${\left({\text{V}}_x{\text{V}}_y{\text{V}}_z\right)}^{\top }={\mathbf{V}}_{\text{S}}$. The data are shown for $\theta ={90}^{\circ }.$