Mass transfer oscillating flows

As Re increases further and vortices are shed, the local rate of mass transfer aft of separation should oscillate. Although no measurements have been made for spheres, mass transfer oscillations at the shedding frequency have been observed for cylinders (B9, D6, SI2). At higher Re the forward portion of the sphere approaches boundary layer flow while aft of separation the flow is complex as discussed above. Figure 5.17 shows experimental values of the local Nusselt number Nuj c for heat transfer to air at high Re. The vertical lines on each curve indicate the values of the separation angle. It is clear that the transfer rate at the rear of the sphere increases more rapidly than that at the front and that even at very high Re the minimum Nuj. occurs aft of separation. Also shown in Fig. 5.17 is the thin concentration boundary layer... 

In a supersonic gas flow, the convective heat transfer coefficient is not only a function of the Reynolds and Prandtl numbers, but also depends on the droplet surface temperature and the Mach number (compressibility of gas). 154 156 However, the effects of the surface temperature and the Mach number may be substantially eliminated if all properties are evaluated at a film temperature defined in Ref. 623. Thus, the convective heat transfer coefficient may still be estimated using the experimental correlation proposed by Ranz and Marshall 505 with appropriate modifications to account for various effects such as turbulence,[587] droplet oscillation and distortion,[5851 and droplet vaporization and mass transfer. 555 It has been demonstrated 1561 that using the modified Newton s law of cooling and evaluating the heat transfer coefficient at the film temperature allow numerical calculations of droplet cooling and solidification histories in both subsonic and supersonic gas flows in the spray. 

For sufficiently large electrodes with a small vibration amplitude, aid < 1, a solution of the hydrodynamic problem is possible [58, 59]. As well as the periodic flow pattern, a steady secondary flow is induced as a consequence of the interaction of viscous and inertial effects in the boundary layer [13] as shown in Fig. 10.10. It is this flow which causes the enhancement of mass-transfer. The theory developed by Schlichting [13] and Jameson [58] applies when the time of oscillation, w l is small in comparison with the time taken for a species to diffuse across the hydrodynamic boundary layer (thickness SH= (v/a>)ln diffusion timescale 8h/D), i.e., when v/D t> 1. Re needs to be sufficiently high for the calculation to converge but sufficiently low such that the flow does not become turbulent. Experiment shows that, for large diameter wires (radius, r, — 1 cm), the condition is Re 2000. The solution Sh = 0.746Re1/2 Sc1/3(a/r)1/6, where Sh (the Sherwood number) = kmr/D and km is the mass-transfer coefficient,... 

Current densities were recorded as a function of time for a large number of flow rates. For Re < 50, the mass-transfer rate was steady. When Re > 200, more than one frequency of oscillation in mass-transfer rate was encountered. In the range 50 < Re < 200, only one dominant frequency was observed. The frequency of oscillation is a function of Re. The experimental and simulated frequencies as a function of Re for both d/h = 0.25 and d/h = 0.5 are in close agreement. 

By viscous interaction with the continuous phase, oscillating shape variations of liquid drops and gas bubbles occur, and for Re 1. mobile surface fluid particles in free-rising or falling conditions move in a wobbling or spirial-like manner, which has a marked influence on mass transfer rates. As before, we can arrive at different correlations for different bulk flow regions. These are summarized below ... 

Bubble formation and orifice activity are two important factors determining stability. Synchronous bubble formation, where almost all holes are active instantaneously, tends to produce a uniform bubble and gas holdup distribution. The uniform bubble distribution leads to a more stable homogeneous flow regime, less liquid recirculation, and higher gas holdup and gas-liquid mass transfer. Asynchronous orifice operation is often accompanied by alternating or oscillating orifice activity, which leads to flow instability. The instability creates more bubble-bubble interaction and leads to lower gas holdup and gas-liquid mass transfer. Hence, the gas distributor affects the critical superficial gas velocity at which the transition regime is detected. 

In upflow operation the liquid to particle Sherwood number is higher than in downflow operation and increases remarkably with gas flow, indicating the large contribution of the liquid turbulence caused by bubble motion. Recently attempts were made to analyse the situation also theoretically and a unified correlation has been developed for heat and mass transfer from single spheres, packed beds as well as tube wall, taking into account the diffusion of solute into a liquid film,oscillating with response to the bub-... 

Figure 12.2 Schematic diagram of an apparatus consisting of two CSTRs for studying physically coupled oscillating reactions. A needle valve controls the flow between the reactors. Inputs to the reactors are independently controlled. Drop detectors ensure that liquid flows out of the two reactors at the same rate so that there is no net mass transfer from one to the other. Reprinted, in part, with permission from Crowley, M. F. Epstein, I. R. 1989. Experimental and Theoretical Studies of a Coupled Chemical Oscillator Phase Death, Multistability, and In-Phase and Out-Of-Phase Entrainment, J. Phys. Chem. 93, 2496-2502. CC 1989 American Chemical Society.)...

Another example of the OBRs use with solid particles is as a photochemical reactor with solids suspension, in this case the vortical flow patterns being used to suspend catalytic titania particles to convert organics in wastewater. The tita-nia needs to be activated by ultraviolet, and the reaction requires the presence of oxygen, so air is bubbled through. The gas-liquid mass transfer is enhanced by the oscillation of the fluid, as it increases hold-up time (bubble residence time) and reduces bubble size (increasing surface area and further increasing hold-up time). The flow patterns simultaneously ensure good exposure of the titania particles to the radiation from an axially located ultraviolet lamp. 

In this book we considered mass transfer and elemental migration between the atmosphere, hydrosphere, soils, rocks, biosphere and humans in earth s surface environment on the basis of earth system sciences. In Chaps. 2, 3, and 4, fundamental theories (thermodynamics, kinetics, coupling model such as dissolution kinetics-fluid flow modeling, etc.) of mass transfer mechanisms (dissolution, precipitation, diffusion, fluid flow) in water-rock interaction of elements in chemical weathering, formation of hydrothermal ore deposits, hydrothermal alteration, formation of ground water quality, seawater chemistry. However, more complicated geochemical models (multi-components, multi-phases coupled reaction-fluid flow-diffusion model) and phenomenon (autocatalysis, chemical oscillation, etc.) are not considered. 

Sahoo, S.N., 2013. Heat and mass transfer effect on MHD flow of a viscoelastic fluid through a porous medium bounded by an oscillating porous plate in sUp flow regime. Int. J. Chem. Eng., 380679. 

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