Method of submerged Stokeslets for slip flow about ensembles of particles.

A boundary singularity method with submerged Stokeslets is applied to the low Reynolds number flows about a set of spheres. Newtonian fluid is considered with no slip or partial slip boundary conditions at the wall. The validity of the method for Stokes flows about representative sets of spheres is investigated. The considered cases include (i) a uniform flow about a stationary set of particles typical for filtration and chemical vapor deposition, (ii) a flow induced by particles moving toward each other typical for self-assembly processes and (iii) a flow induced by spinning particles typical for micro-pump applications. The dependence of the flowfield on the number of Stokeslets is investigated in order to establish the needed number of Stokeslets. Comparison of flow field for the no-slip (Kn = 0) and partial-slip boundary conditions (Kn = 0.1) shows that the partial slip at the particles' surface significantly affect the velocity field and pressure distribution.

Multi-time step modeling of plume dynamics in nanosecond-scale carbon ablation.

The time span of plume dynamics in laser ablation of carbon ranges from nanoseconds to milliseconds. Multi-time step approach is developed to study the plume dynamics over this entire range with minimum requirements of numerical computational resources. This approach is applied to study one of the important aspects of nanosecond-scale laser ablation, namely the shielding of incident laser beam with previously ejected plumes. Capturing the shielding effect requires smaller than nanosecond-scale time step because of large velocity and pressure gradients in plume. Use of this time step over the entire domain needs enormous amount of computer time to cover the whole time span of plume dynamics. Multi-time step modeling for such an application is therefore useful. In general, for nanosecond-scale laser ablation this shielding is caused by ionized particles and by gas molecules. It is shown for carbon plume resulting from the nanosecond-scale lasers that the degree of ionization is small. Ionization of ablated carbon is estimated by Saha equation for the given initial plume conditions. The shielding of incident laser beam is therefore calculated by normal molecular absorption. The laser-light intensity that reaches the target for subsequent pulses is evaluated.

Combined thermal and gas dynamics numerical model for laser ablation of carbon.

One of the major methods of production of carbon nanotubes is the laser ablation process. In this process, a powerful nanosecond-scale laser beam illuminates a target. The resulting explosion produces a plume of rapidly expanding gaseous carbon with embedded metallic catalysts, on whose surfaces the nanotubes are formed. The time-scale of a single laser pulse is of the order of nanoseconds whereas the plume development and growth of nanotubes take up to several milliseconds. The synthesis process largely depends on the plume properties, i.e., on the temperature, pressure, and density of the expanding plume. In turn, the plume propagation depends on the ablation speed, pressure, and density. In the current study, a combined thermal and gas dynamics model is proposed, implemented and tested. The proposed model is based on combined conduction heat transfer within the solid target, carbon sublimation process described by equilibrium thermodynamics, and process of plume development described by continuous gas dynamics. The carbon sublimation model is based on Clausius-Clapeyron equation and conservation of energy for differential control volume. The parameters of the injected plume are defined by this thermal model. The validity of viscous and inviscid models of plume dynamics is discussed. The ability of finite-volume discretizations to capture the plume dynamics and its roll-up is compared for various numerical schemes. To evaluate the accuracy of numerical modeling of plume dynamics, we compare finite-volume discretization based on Relaxing TVD scheme with that based on the upwind scheme with Roe averaging at the cell interface and non-linear ENO scheme for second-order flux formulas.