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We have developed a lattice-Boltzmann method which can be used to simulate nearly spherical and non-coalescing bubbly flows. The method directly recovers the slip boundary condition so one only needs to solve the flow in the continuous phase. Compared with two-component numerical methods, the new single-component is faster and more robust. With the new method we are able to simulate and study many of the fundamental properties of a homogeneous bubbly suspension, such as hindered rising velocity, velocity variance and microstructures. (Figure: Simulation of Stokes drag on an array of bubbles. The y-axis shows the drag of the array non-dimensionalized using the Stokes drag of an isolated bubble. The x-axis is the volume fraction. The simulation results (symbols) are in excellent agreement with the theoretical prediction (lines) by Sangani & Acrivos (1982).)

In batch settling process, particle settling velocity decreases with increasing solid concentration. The added resistance comes from the hydrodynamic interaction among particles. The level of hindrance was firstly systematically studied by Richardson and Zaki, who proposed a power-law relation:

In this equation, u is the mean settling velocity, u_t is the terminal velocity of an isolated particle, Φ is the volume fraction, and n is a parameter depending on the Reynolds number. There are evidences that this formula is not so correct at the dilute limit. The change in settling velocity in the dilute limit is more rapid than predicted by this simple power-law.

Our simulations reveal that in the region where the settling velocity deviates from Richardson-Zaki, there is a significant amount of anisotropy in the suspension. On the other hand, in the region where settling velocity obeys R-Z, the suspension is random.

The anisotropy in the suspension comes from the wake interaction between pairs of particles. A particle in the wake of another particle travels faster. As it catches the leading particle, the pair pivots to a horizontal orientation and the particles then repel one another. As the result, when the suspension reaches stable state, particles will be swept away from each other's wake and most of them will be aligned horizontally.

Spherical beads packed into microfluid channels form a microscale packed-bed reactor. However, in this study we are not studying the rate of mass transfer from the beads to the fluid. We are using the beads as a mean to disturb the otherwise parallel flow field to enhance the mixing of two chemical species in microchannels.

We study the mixing by simulating the complex flow field using the lattice-Boltzmann method. The motion of tracers consists of a convective motion proportional to the local fluid velocity, and a random motion determined from the tracer diffusivity. (Figure: Mixing of tracer-labeled and non-labeled streams in a microchannel packed with spherical beads. This demonstration shows the release of tracer in the upper ½ of the channel and the passage of tracers through the packed bed.)

We are studying the stability of an unbounded, initially homogeneous dilute particle-gas suspension subject to a simple shear flow for particle Stokes numbers that are small but non-zero. It is well known that the inertia of aerosol particles causes them to be thrown out of vortices and to accumulate in regions of high strain rate. This leads a decrease in the particle concentration in regions where the perturbation velocity reinforces the vorticity of the imposed shear flow and an increase in particle concentration in regions where the perturbation velocity tends to cancel the vorticity of the imposed flow. The gravitational force acting on this inhomogeneous density field reinforces the perturbation velocity leading to a growth of the perturbation. The shearing motion turns the wave vector of the disturbance flow eventually arresting the growth. However, if the shear is weak compared with the gravitational settling, the perturbation grows exponentially larger than its initial value before this arrest occurs. We believe that secondary instabilities may continue the growth of particle concentration fluctuations.

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Micro-scale inertia breaks the degenerate closed-streamline configuration that occurs in shear flow past a neutrally buoyant torque-free particle in the inertialess limit. The broken symmetry leads to the open streamlines illustrated in the figure, allowing heat/mass to be convected away in an efficient manner in sharp contrast to the inertialess diffusion-limited scenario. Inertial forces scale with the particle Reynolds number Re and the dimensionless transfer rate, characterized by the Nusselt number, is Nu = C(RePe)^1/3 when Re>>1 and Pe>>1. Here, the Peclet number Pe measures the relative importance of the convective and the diffusive transfer mechanisms. The constant C is a function of the flow in the vicinity of the particle, and equals 4.09(1+λ)^2/3 for a two dimensional linear flow, where λ depends on the relative magnitudes of extension and vorticity; λ=0 for simple shear flow.

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