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A two–dimensional flow model has been developed to simulate mass transport in a microchannel bioreactor with a porous wall. A two–domain approach, based on the finite volume method, was implemented. For the fluid part, the governing equation used was the Navier–Stokes equation; for the porous medium region, the generalized DarcyBrinkman–Forchheimer extended model was used. For the porous–fluid interface, a stress jump condition was enforced with a continuity of normal stress, and the mass interfacial conditions were continuities of mass and mass flux. Two parameters were defined to characterize the mass transports in the fluid and porous regions. The porous Dainkohler number is the ratio of consumption to djffusion of the substrates in the porous medium. The fluid Damkohler number is the ratio of the substrate consumption in the porous medium to the substrate convection in the fluid region. The concentration results were found to be well correlated by the use of a reaction–convection distance parameter which incorporated the effects of axial distance, substrate consumption, and convection. The reactor efficiency reduced with reaction–convection distance parameter because of reduced reaction (or flux), and smaller local effectiveness factor due to the lower concentration in Michaelis–Menten type reactions. The reactor was more effective, and hence, more efficient with the smaller porous Damkohler number The generalized results could find applications for the design of bioreactors with a porous wall. [ABSTRACT FROM AUTHOR]

The swirling flow in an enclosed conical frustum chamber with a rotating bottom wall was studied by a numerical model based on the steady, axisymmetric Navier–Stokes equations. The flow behavior was investigated over a wide range of parameters, that is, the Reynolds number up to 2500, the aspect ratio up to 3.5, and the slope angle of the sidewall from 60° to 180°. The vortex breakdown boundary curves were summarized. It was found that vortex breakdown is delayed or even suppressed in the convergent chamber (chamber section narrowing upward). However, for the divergent chamber, the onset of vortex breakdown is precipitated by an initial increase in the slope angle while delayed by a further increase in the slope angle. The flow separation along the inclined sidewall may occur in the divergent chamber with a big slope angle. For an even bigger slope angle, this separation bubble directly combined with the corner vortex at the upper right corner, forming a large recirculation region. The present results suggested that, although vortex breakdown can occur in the divergent chamber with any slope angle, it cannot occur in a convergent chamber with a small slope angle as well as in a conical chamber. [ABSTRACT FROM AUTHOR]

Microchannel bioreactors have applications for manipulating and investigating the fluid microenvironment on cell growth and functions in either single culture or co-culture. This study considers two different types of cells distributed randomly as a co-culture at the base of a microchannel bioreactor: absorption cells, which only consume species based on the Michaelis-Menten process, and release cells, which secrete species, assuming zeroth order reaction, to support the absorption cells. The species concentrations at the co-culture cell base are computed from a three-dimensional numerical flow-model incorporating mass transport. Combined dimensionless parameters are proposed for the co-culture system, developed from a simplified analysis under the condition of decreasing axial-concentration. The numerical results of species concentration at the co-culture cell-base are approximately correlated by the combined parameters under the condition of positive flux-parameter. Based on the correlated results, the critical value of the inlet concentration is determined, which depends on the effective microchannel length. For the flow to develop to the critical inlet concentration, an upstream length consisting only of release cells is needed; this upstream length is determined from an analytical solution. The generalized results may find applications in analyzing the mass transport requirements in a co-culture microchannel bioreactor. [ABSTRACT FROM AUTHOR]

The effects of the conical lids on vortex breakdown have been investigated numerically. The boundaries for the onset of vortex breakdown are plotted in terms of the Reynolds number, the aspect ratio H1/R, where H1 is the height of the side wall, and the height ratio H2/H1, where H2 is the height of the axis. The concave-cone lid (H2/H1>1) delays or even completely suppresses vortex breakdown, while the convex-cone lid (H2/H1<1) precipitates the onset of vortex breakdown. The attached bubbles were found in the chamber with the convex-cone lid at a smaller height ratio. The critical aspect ratio, below which vortex breakdown cannot occur, decreases with the increase of the height ratio. The results indicate that a conical lid can enlarge the vortex breakdown boundaries and this might be of practical interest when using this device for mixing. The results also suggest that the actual shape of the lid has an influence on suppressing or intensifying vortex breakdown. [ABSTRACT FROM AUTHOR]

Microchannel bioreactors have been used in many studies to manipulate and investigate the fluid microenvironment around cells. In this study, substrate concentrations and shear stresses at the base were computed from a three-dimensional numerical flow-model incorporating mass transport. Combined dimensionless parameters were developed from a simplified analysis. The numerical results of substrate concentration were well correlated by the combined parameters. The generalized results may find applications in design analysis of microchannel bioreactors. The mass transport and shear stress were related in a generalized result. Based on the generalized results and the condition of dynamic similarity, various means to isolate their respective effects on cells were considered. [ABSTRACT FROM AUTHOR]

The behavior of a droplet impinging onto a solid substrate can be influenced significantly by the horizontal motion of the substrate. The coupled interactions between the moving wall and the impacting droplet may result in various outcomes, which may be different from the usual normal droplet impact on a stationary wall. In this paper, we present a method to suppress drop rebound on hydrophobic surfaces via transverse wall oscillations, normal to the impact direction. The numerical investigation shows that the suppression of droplet rebound has a direct relationship with the oscillation phase, amplitude, and frequency. For a particular range of oscillation frequencies and amplitudes, a lateral shifting of the droplet position is observed along the oscillating direction. While large oscillation amplitude favors the process of droplet deposition, a high frequency promotes droplet rebound from the oscillating wall. A linear trend in the transition region between deposition and rebound is observed from a scaled phase diagram of the oscillation amplitude versus frequency. We provide a systematic investigation of drop deposition and elucidate the mechanism of rebound suppression through the temporal evolution of the nonaxial kinetic energy and the velocity flow field. [ABSTRACT FROM AUTHOR]