Liquid mixing diffusion

Solids-liquid-gas mixing 275 Solids-liquid mixing 275 Solids—solids mixing 275 Sonic velocity 150, 156,158, 189 Sorel effect, thermal diffusion 589 Spalding, D. B, 393,562 Sparrow, E. M. 465, 564 Specific energy, open channel flow 98... 

Confined flows typically exhibit laminar-flow regimes, i.e. rely on a diffusion mixing mechanism, and consequently are only slowly mixed when the diffusion distance is set too large. For this reason, in view of the potential of microfabrication, many authors pointed to the enhancement of mass transfer that can be achieved on further decreasing the diffusional length scales. By simple correlations based on Fick s law, it is evident that short liquid mixing times in the order of milliseconds should result on decreasing the diffusion distance to a few micrometers. 

The liquid-liquid free interface diffusion (FID) method, in which protein and precipitant solutions are carefully superimposed and left to slowly mix diffusively, was least used in the past due to handling difficulties. However, in the last 4 years the free interface technique has experienced a revival for both screening and optimization procedures. The... 

The values of k a for CO, desorption in a stirred-tank fermentor, calculated from the experimental data on physically dissolved CO, concentration (obtained by the above-mentioned method) and the CO2 partial pressure in the gas phase, agreed well with the k a values estimated from the k a for O, absorption in the same fermentor, but corrected for any differences in the liquid-phase diffusivities [11]. Perfect mixing in the liquid phase can be assumed when calculating the mean driving potential. In the case of large industrial fermentors, it can practically be assumed that the CO, partial pressure in the exit gas is in equilibrium with the concentration of CO, that is physically dissolved in the broth. The assumption of either a plug flow or perfect mixing in the gas phase does not have any major effect... 

One of the most important processes involved in the scale-up of liquid parenteral preparations is mixing [1]. For liquids, mixing can be defined as a transport process that occurs simultaneously in three different scales, during which one substance (solute) achieves a uniform concentration in another substance (solvent). On a large, visible scale, mixing occurs by bulk diffusion, in which the elements are blended by the pumping action of the mixer s impeller. On the microscopic scale, elements that are in proximity are blended by eddy currents, and they 43... 

Equation (4.11) applies provided that the gas phase resistance to the transfer of HTO is limiting. This requires that the accommodation coefficient of molecules at the surface, the solubility, and the liquid phase diffusion, or mixing, within the drop, are all sufficiently high. 

This micro mixer is based on a bi-laminated stream which has to pass a considerably narrowed flow passage having the function of reducing the diffusion distance and thereby speeding up liquid mixing [114—116],... 

P 31] liquid mixing times were calculated based on assuming diffusion as the only mixing mechanism and considering Fick s law which takes into account the diffusion constant and the diffusion distance [114]. 

M 44a] [P 40] Numerical errors which are due to discretization of the convective terms in the transport equation of the concentration fields introduce an additional, unphysical diffusion mechanism [37]. Especially for liquid-liquid mixing with characteristic diffusion constants of the order of 1CT9 m2 s 1 this so-called numerical diffusion (ND) is likely to dominate diffusive mass transfer on computational grids. 

First, we note that miscibility and compatibility mean the same thing. The former refers generally to liquid systems, whereas, the latter usually designates solid systems. There are two aspects of the question of miscibility Will the two liquids mix (thermodynamics), and how long would this process take (kinetics) The second aspect is important in polymer-polymer and polymer-monomer systems, because of the low diffusivities involved. Thermodynamically, the mixture will be stable if, at temperature T,... 

Ammonia is absorbed in a falling film of water in an absorption apparatus and the film is disrupted and mixed at regular intervals as it flows down the column. The mass transfer rate is calculated from the penetration theory on the assumption that all the relevant conditions apply. It is found from measurements that the mass transfer rate immediately before mixing is only 16 per cent of that calculated from the theory and the difference has been attributed to the existence of a surface film which remains intact and unaffected by the mixing process. If the liquid mixing process takes place every second, what thickness of surface film would account for the discrepancy Diffusivity of ammonia in water = 1.76 x 10 9 m2/s. 

In the bubble column the velocity profile of recirculating liquid is shown in Fig. 27, where the momentum of the mixed gas and liquid phases diffuses radially, controlled by the turbulent kinematic viscosity Pf When I/l = 0 (essentially no liquid feed), there is still an intense recirculation flow inside the column. If a tracer solution is introduced at a given cross section of the column, the solution diffuses radially with the radial diffusion coefficient Er and axially with the axial diffusion coefficient E. At the same time the tracer solution is transported axially Iby the recirculating liquid flow. Thus, the tracer material disperses axially by virtue of both the axial diffusivity and the combined effect of radial diffusion and the radial velocity profile. 

In solid-liquid mixing design problems, the main features to be determined are the flow patterns in the vessel, the impeller power draw, and the solid concentration profile versus the solid concentration. In principle, they could be readily obtained by resorting to the CFD (computational fluid dynamics) resolution of the appropriate multiphase fluid mechanics equations. Historically, simplified methods have first been proposed in the literature, which do not use numerical intensive computation. The most common approach is the dispersion-sedimentation phenomenological model. It postulates equilibrium between the particle flux due to sedimentation and the particle flux resuspended by the turbulent diffusion created by the rotating impeller. 

The application of CFD in the modeling of solid-liquid mixing is fairly recent. In 1994, Bakker et al. developed a two-dimensional computational approach to predict the particle concentration distribution in stirred vessels. In their model, the velocity field of the liquid phase is first simulated taking into account the flow turbulence. Then, using a finite volume approach, the diffusion-sedimentation equation along with the convective terms is solved, which includes Ds, a... 

A different numerical strategy to simulate multiphase mixing was introduced by Mann and Mann and Hackett. The idea of the method, called the network-of-zone, is to subdivide the flow domain in a set of small cells assumed to be mixed perfectly. The cells are allowed to exchange momentum and mass with their neighboring cells by convective and diffusive fluxes. Brucato and Rizzuti and Brucato et al. applied this idea to the modeling of solid-liquid mixing. An unsteady mass balance for the particles was derived to estimate the solid distribution in the vessel, namely ... 

Liquid mixing in bubble columns is a result of global convective re-circulation of the liquid phase and turbulent diffusion due to eddies generated by the rising bubbles. By structuring the gas and the liquid flow, HyperCat reduces the axial dispersion for both phases leading to a large reduction in axial dispersion coefficients (Dax)- The real benefit of this reduced dispersion is that it is not a function of the colunm diameter (Dc) as is the case with conventional bubble colunm reactors. 

The pertial liquid mixing case is or considerable interest in desiga. Various models for representing peitial mixing have been proposed for most instances the eddy diffusion model appears approprinte. This model uses a dimensionless Peclet number... 

There are several types of situations covered by Eq, (21.16). The simplest case is zero convective flow and equimolal counterdiffusion of A and B, as occurs in the diffusive mixing of two gases. This is also the case for the diffusion of A and B in the vapor phase for distillations that have constant molal overflow. The second common case is the diffusion of only one component of the mixture, where the convective flow is caused by the diffusion of that component. Examples include evaporation of a liquid with diffusion of the vapor from the interface into a gas stream and condensation of a vapor in the presence of a noncondensable gas. Many examples of gas absorption also involve diffusion of only one component, which creates a convective flow toward the interface. These two types of mass transfer in gases are treated in the following sections for the simple case of steady-state mass transfer through a stagnant gas layer or film of known thickness. The effects of transient diffusion and laminar or turbulent flow are taken up later. 

Dififusiou of Liquids—Dialysis.—If a liquid be carefull floated upon the surface of a second liquid, of greater density, with which it is capable of mixing, two distinct layers will at first be formed. Even at perfect rest, mixture will begin immediately, and progress slowly until the two liquids have diffused into each other to form a single liquid whose density is the same throughout. 

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