Bulk flow force

In the bulk flow-force combination of (c), there can be cases where, instead of two fluid phases, one can have one fluid phase and another solid phase. Categories (b) and (c) provide a broader and more useful framework than the category of bulk flow perpendicular to the force direction illustrated by Giddings (1991) using a few examples. 

Chapter 7 will consider separations achieved under the bulk flow-force combination of (b). Separation systems utilizing the configurations of (c) are treated in Chapter 8. (There will be occasional examples of two combinations of bulk flow and force directions.) Chapters 6, 7 and 8 will generally employ one separator vessel. Reactive separations will be treated immediately alongside non-reactive separations as often as possible. Different feed introduction modes will be considered as required in all three configurations, (a), (b) and (c). Multistage separation schemes, widely used in the processes of gas absorption, distillation, solvent extraction, etc., are studied in Chapter 8 when only one vessel is used. When multiple devices are used to form a separation cascade, an introductory treatment is provided in Chapter 9. 

Equations (13-111) to (13-114), (13-118) and (13-119), contain terms, Njj, for rates of mass transfer of components from the vapor phase to the liquid phase (rates are negative if transfer is from the liquid phase to the vapor phase). These rates are estimated from diffusive and bulk-flow contributions, where the former are based on interfacial area, average mole-fraction driving forces, and mass-... 

Intraparticle convection can also occur in packed beds when the adsorbent particles have very large and well-connected pores. Although, in general, bulk flow through the pores of the adsorbent particles is only a small frac tion of the total flow, intraparticle convection can affec t the transport of veiy slowly diffusing species such as macromolecules. The driving force for convec tion, in this case, is the... 

An important mixing operation involves bringing different molecular species together to obtain a chemical reaction. The components may be miscible liquids, immiscible liquids, solid particles and a liquid, a gas and a liquid, a gas and solid particles, or two gases. In some cases, temperature differences exist between an equipment surface and the bulk fluid, or between the suspended particles and the continuous phase fluid. The same mechanisms that enhance mass transfer by reducing the film thickness are used to promote heat transfer by increasing the temperature gradient in the film. These mechanisms are bulk flow, eddy diffusion, and molecular diffusion. The performance of equipment in which heat transfer occurs is expressed in terms of forced convective heat transfer coefficients. 

Theoretical representation of the behaviour of a hydrocyclone requires adequate analysis of three distinct physical phenomenon taking place in these devices, viz. the understanding of fluid flow, its interactions with the dispersed solid phase and the quantification of shear induced attrition of crystals. Simplified analytical solutions to conservation of mass and momentum equations derived from the Navier-Stokes equation can be used to quantify fluid flow in the hydrocyclone. For dilute slurries, once bulk flow has been quantified in terms of spatial components of velocity, crystal motion can then be traced by balancing forces on the crystals themselves to map out their trajectories. The trajectories for different sizes can then be used to develop a separation efficiency curve, which quantifies performance of the vessel (Bloor and Ingham, 1987). In principle, population balances can be included for crystal attrition in the above description for developing a thorough mathematical model. 

The mechanism by which analytes are transported in a non-discriminate manner (i.e. via bulk flow) in an electrophoresis capillary is termed electroosmosis. Eigure 9.1 depicts the inside of a fused silica capillary and illustrates the source that supports electroosmotic flow. Adjacent to the negatively charged capillary wall are specifically adsorbed counterions, which make up the fairly immobile Stern layer. The excess ions just outside the Stern layer form the diffuse layer, which is mobile under the influence of an electric field. The substantial frictional forces between molecules in solution allow for the movement of the diffuse layer to pull the bulk... 

On the basis of each of the theories discussed, the rate of mass transfer in the absence of bulk flow is directly proportional to the driving force, expressed as a molar concentration difference, and, therefore ... 

Explain how hydrostatic forces and osmotic forces regulate the bulk flow of fluid across the capillary wall... 

The third mechanism of capillary exchange is bulk flow. In this case, water and dissolved solutes move across capillaries due to hydrostatic pressure and osmotic pressure. When the balance of these two forces causes fluid to move out of the capillary, it is referred to as filtration. When these forces cause fluid to move into the capillary, it is referred to as reabsorption. 

Figure 15.7 Starling principle a summary of forces determining the bulk flow of fluid across the wall of a capillary. Hydrostatic forces include capillary pressure (Pc) and interstitial fluid pressure (PJ. Capillary pressure pushes fluid out of the capillary. Interstitial fluid pressure is negative and acts as a suction pulling fluid out of the capillary. Osmotic forces include plasma colloid osmotic pressure (np) and interstitial fluid colloid osmotic pressure (n,). These forces are caused by proteins that pull fluid toward them. The sum of these four forces results in net filtration of fluid at the arteriolar end of the capillary (where Pc is high) and net reabsorption of fluid at the venular end of the capillary (where Pc is low).

Bulk or forced flow of the Hagan-Poiseuille type does not in general contribute significantly to the mass transport process in porous catalysts. For fast reactions where there is a change in the number of moles on reaction, significant pressure differentials can arise between the interior and the exterior of the catalyst pellets. This phenomenon occurs because there is insufficient driving force for effective mass transfer by forced flow. Molecular diffusion occurs much more rapidly than forced flow in most porous catalysts. 

As mentioned at the end of section 4.2.2.2, a one-phase open system cannot support a pressure gradient without experiencing bulk flow. One way around this restriction is to use the chemical potential as the overall driving force.In essence, this driving force combines those of pressure and activity... 

A second example of convective dissolution is the dissolution of a solid floor or roof. Forced convection means that the fluid is moving relative to the solid floor or roof such as magma convection in a magma chamber, or bottom current over ocean sediment. Free convection means that there is no bulk flow or convection, but the interface melt may be gravitationally unstable, leading to its rise or fall. 

The equations for one-dimensional momentum and mass flow are directly analogous to Fourier s Law. A velocity gradient, dv /dy, is the driving force for the bulk flow of momentum, or momentum flux, which we call the shear stress (shear force per unit area), Xyx- This leads to Newton s Law of Viscosity ... 

Let the solvent move such that its velocity is v°(r) if there are no particles present, though v° (r) need not be constant but could, for instance, be produced by bulk flow of the solvent in tubes or around obstacles. Now the particle is located at r - and moves with a velocity r, — v(r ) relative to the solvent velocity, v(r ), when the particle is absent. In a Newtonian liquid, this velocity difference between particle and solvent leads to a force between liquid and particle which is given by... 

The right-hand side of equation 3.60 contains the mass transfer coefficient hD which is used if the driving force is expressed in terms of gas concentrations. Because of the stoichiometric demands imposed by chemical reaction, equimolar counterdiffusion of components may not necessarily occur and the effects of bulk flow must be taken into account (see Volume 1, Chapter 10). 

As pressure is increased above the bubble point pressure, pores of decreasing size have the liquid forced out, and this allows additional bulk flow of the test gas. By measuring and comparing the bulk gas flow rates of both a wetted and a dry filter medium at the same pressure, the percentage of the bulk gas... 

Relative displacement differs for each of the various forces that can be applied its magnitude depends on how different components respond to these forces. Details are provided in Chapter 3. The origin and nature of bulk (flow) displacement will be described in Chapter 4. 

The driving force for drag release from a pump is a pressure difference that causes the bulk flow of a drag, or drug solution, from the device at a controlled rate. This is in contrast to the polymeric controlled release systems described above, where the driving force is due to the concentration difference of the drag between the formulation and the surrounding environment. Pressure differences in an implantable pump can be created by osmotic or mechanical action, as described below. 

Forced Convection. In systems where the flux of A results primarily from forced conveetion, we assume that the diffusion in the direction of the flow (e.g., axial z direetion), is small in comparison with the bulk flow contribution in that direction, [/),... 

Once an appropriate frame of reference is chosen, a two components (A, B) system may be described in terms of the mutual diffusion coefficient (diffusivity of A in B and vice versa). Unfortunately, however, unless A and B molecules are identical in mass and size, mobility of A molecules is different with respect to that of B molecules. Accordingly, the hydrostatic pressure generated by this fact will be compensated by a bulk flow (convective contribution to species transport) of A and B together, i.e., of the whole solution. Consequently, the mutual diffusion coefficient is the combined result of the bulk flow and the molecules random motion. For this reason, an intrinsic diffusion coefficient (Da and Db), accounting only for molecules random motion has been defined. Finally, by using radioactively labeled molecules it is possible to observe the rate of diffusion of one component (let s say A) in a two component system, of uniform chemical composition, comprised of labeled and not labeled A molecules. In this manner, the self-diffusion coefficient (Da) can be defined [54]. Interestingly, it can be demonstrated that both Da and Da are concentration dependent. Indeed, the force/acting on A molecule at point X is [1]... 

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