Mass transfer shear flow

Flow Past Bodies. A fluid moving past a surface of a soHd exerts a drag force on the soHd. This force is usually manifested as a drop in pressure in the fluid. Locally, at the surface, the pressure loss stems from the stresses exerted by the fluid on the surface and the equal and opposite stresses exerted by the surface on the fluid. Both shear stresses and normal stresses can contribute their relative importance depends on the shape of the body and the relationship of fluid inertia to the viscous stresses, commonly expressed as a dimensionless number called the Reynolds number (R ), EHp/]1. The character of the flow affects the drag as well as the heat and mass transfer to the surface. Flows around bodies and their associated pressure changes are important. 

Solid-Liquid Mass Transfer There is potentially a major effect of both shear rate and circulation time in these processes. The sohds can either be fragile or rugged. We are looking at the slip velocity of the particle and also whether we can break up agglomerates of particles which may enhance the mass transfer. When the particles become small enough, they tend to follow the flow pattern, so the slip velocity necessary to affect the mass transfer becomes less and less available. 

Each stage of particle formation is controlled variously by the type of reactor, i.e. gas-liquid contacting apparatus. Gas-liquid mass transfer phenomena determine the level of solute supersaturation and its spatial distribution in the liquid phase the counterpart role in liquid-liquid reaction systems may be played by micromixing phenomena. The agglomeration and subsequent ageing processes are likely to be affected by the flow dynamics such as motion of the suspension of solids and the fluid shear stress distribution. Thus, the choice of reactor is of substantial importance for the tailoring of product quality as well as for production efficiency. 

The optimum flow rate for most SEC separations using conventional PLgel column dimensions (internal diameter 7.5 mm) is 1.0 ml/min. It may be of some benefit to work with lower flow rates, particularly for the analysis of higher molecular weight polymers where the reduced flow rate improves resolution through enhanced mass transfer and further reduces the risk of shear... 

In a drop extractor, liquid droplets of approximate uniform size and spherical shape are formed at a series of nozzles and rise eountercurrently through the continuous phase which is flowing downwards at a velocity equal to one half of the terminal rising velocity of the droplets. The flowrates of both phases are then increased by 25 per cent. Because of the greater shear rate at the nozzles, the mean diameter of the droplets is however only 90 per cent of the original value. By what factor will the overall mass transfer rate change ... 

Sundararajan et al. [131] in 1999 calculated the slurry film thickness and hydrodynamic pressure in CMP by solving the Re5molds equation. The abrasive particles undergo rotational and linear motion in the shear flow. This motion of the abrasive particles enhances the dissolution rate of the surface by facilitating the liquid phase convective mass transfer of the dissolved copper species away from the wafer surface. It is proposed that the enhancement in the polish rate is directly proportional to the product of abrasive concentration and the shear stress on the wafer surface. Hence, the ratio of the polish rate with abrasive to the polish rate without abrasive can be written as... 

The velocity, viscosity, density, and channel-height values are all similar to UF, but the diffusivity of large particles (MF) is orders-of-magnitude lower than the diffusivity of macromolecules (UF). It is thus quite surprising to find the fluxes of cross-flow MF processes to be similar to, and often higher than, UF fluxes. Two primary theories for the enhanced diffusion of particles in a shear field, the inertial-lift theory and the shear-induced theory, are explained by Davis [in Ho and Sirkar (eds.), op. cit., pp. 480-505], and Belfort, Davis, and Zydney [/. Membrane. Sci., 96, 1-58 (1994)]. While not clear-cut, shear-induced diffusion is quite large compared to Brownian diffusion except for those cases with very small particles or very low cross-flow velocity. The enhancement of mass transfer in turbulent-flow microfiltration, a major effect, remains completely empirical. 

For turbulent flow, we shall use the Chilton-Colburn analogy [12] to derive an expression for mass transfer to the spherical surface. This analogy is based on an investigation of heat and mass transfer to a flat plate situated in a uniform flow stream. At high Schmidt numbers, the local mass transfer rate is related to the local wall shear stress by... 

The Chilton-Colburn analogy can be also used to estimate the local mass transfer rate in laminar flow where the wall shear stress is related to the azimuthal velocity gradient by... 

Shah and Nelson [33] introduced a convective mass transport device in which fluid is introduced through one portal and creates shear over the dissolving surface as it travels in laminar flow to the exit portal. They demonstrated that this device produces expected fluid flow characteristics and yields mass transfer data for pharmaceutical solids which conform to convective diffusion equations. 

For the turbulent motion in a tube, the mass transfer coefficient k is proportional to the diffusion coefficient at the power of 2/3. It is easy to realize by inspection that this value of the exponent is a result of the linear dependence of the tangential velocity component on the distance y from the wall. For the turbulent motion in a tube, the shear stress t r0 = const near the wall, whereas for turbulent separated flows, the shear stress is small at the wall near the separation point (becoming zero at this point) and depends on the distance to the wall. Thus, the tangential velocity component has, in the latter case, no longer a linear dependence on y and a different exponent for the diffusion coefficient is expected. For separated flows, it is possible to write under certain conditions that [90]... 

Mechanical forces can disturb the elaborate structure of the enzyme molecules to such a degree that de-activation can occur. The forces associated with flowing fluids, liquid films and interfaces can all cause de-activation. The rate of denaturation is a function both of intensity and of exposure time to the flow regime. Some enzymes show an ability to recover from such treatment. It should be noted that other enzymes are sensitive to shear stress and not to shear rate. This characteristic mechanical fragility of enzymes may impose limits on the fluid forces which can be tolerated in enzyme reactors. This applies when stirring is used to increase mass transfer rates of substrate, or in membrane filtration systems where increasing flux through a membrane can be accompanied by increased fluid shear at the surface of the membrane and within membrane pores. Another mechanical force, surface... 

The reduction in apparent viscosity, particularly in the intake region of the rotor blade, results in a considerable improvement of the flow, and greatly accelerates heat- and mass-transfer processes compared with the same processing at low shear rates or in unstressed conditions. It should therefore be obvious that these machines, which produce an agitated film mechanically, are specially suitable for processing non-Newtonian viscous materials. 

When two phases are mixed together (gas-liquid, immiscible liquid-liquid), a fine dispersion of bubbles or drops and a high specific interfacial area are produced because of the intensive turbulence and shear. For this reason, resistance to interphase mass transfer is considerably smaller than in conventional equipment. In addition, a wide range of gas-liquid flow ratios can be handled, whereas in stirred tanks the gas-flow rate is often limited by the onset of flooding. Mass transfer coefficients (kLa) can be 10-100 times higher than in a stirred tank. 

Bubble Dynamics and Mass Transfer in Shear Flow, 430... 

BUBBLE DYNAMICS AND MASS TRANSFER IN SHEAR FLOW... 

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