We conducted a numerical study on the translocation of a biopolymer from the cis side to the trans side of a membrane through a synthetic nano-pore driven by an external electric field in the presence of hydrodynamic interactions (HIs). The motion of the polymer is simulated by 3D Langevin dynamics technique using a worm-like chain model of N identical beads, while HI between the polymer and fluid are incorporated by the lattice Boltzmann equation. The translocation process is induced by electrophoretic force, which sequentially straightens out the folds of the initial random configuration of the polymer chain on the cis side. Our simulation results on translocation time and velocity are in good quantitative agreement with the corresponding experimental ones when the surface charge on the nano-pore and the HI effect are considered explicitly. We found that the translocation velocity of each bead inside the nano-pore mainly depends upon the length of the straightened portion of the polymer in forced motion near the pore. We confirmed this by a theoretical formula. After performing simulations with different pore lengths, we observed that translocation velocity mainly depends upon the applied potential difference rather than upon the electric field inside the nano-pore.

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We conducted a numerical study on the motion of a solid sphere settling under gravity in a viscous fluid using the lattice Boltzmann method combined with the smoothed profile method (SPM). The coupling of lattice Boltzmann fluid and a spherical particle is treated by introducing a body force term to the Boltzmann kinetic equation. For verification, we applied our numerical code to the simulation of flow over a static sphere and compared the results with previously published data. Later, we simulated the sedimentation process of a sphere inside a closed container. Our simulation results of the sphere's settling velocity and fluid velocity contours at various Reynolds numbers are in good agreement with the corresponding experimental results. Finally, we analyzed the accuracy of the present SPM for different forms for the smoothed profile function at various interface thicknesses and grid sizes.

We present a numerical simulation of two-phase flow in a three-dimensional cross-junction microchannel by using the lattice Boltzmann method (LBM). At first, we validated our LBM code with the velocity profile in a 3-dimensional rectangular channel. Then, we developed a lattice Boltzmann code based on the free energy model to simulate the immiscible binary fluid flow. The parallelization of the developed code is implemented on a PC cluster using the MPI program. The numerical results of two-phase flow in the microchannel reveal droplet formation process, which compares well with corresponding experimental results. The size of droplet decreases with increase of the flow-rate ratio and the capillary number. The movement of a droplet through the microchannel induces three-dimensional circulating flow inside the droplet. This complex flow is thought to enhance the mixing and reaction of reagents.