Of fluid diffusion

Fig. 5 Diffusion of molecules cein be restricted in closed spaces, such as cells. Diffusion might also be hindered by obstacles that result in tortuous pathways. Exchange between compartments also slows down molecular displacements. Left panel shows a model of the movement of fluids (diffusion and bulk flow) with three compartments of heeilthy brain tissues. Bulk flow is seen in vascular compartment while the diffusion happens in the interstitial spaces and cell compartments. Right panel shows the changes in diffusion of water as a result of edema. Molecular displacement between compartments increases as a result of BBB breakdown in vasogenic edema. Tortuosity will decrease as intracellular space is reduced...

A useful criterion for a novel reaction, barring the possibility of the direct calculation of diffusion rates, depends upon the increase of fluid diffusion coefficients with linear velocity of the fluid. For a reaction of any order, with a film-diffusion limitation, the fraction of reactant converted (i.e., pass conversion) will increase with linear velocity, other things (notably contact time) being equal. This requires homogeneity of flow and similarity of temperature distribution if these cannot be guaranteed, as in a complex exothermal reaction, only a complete examination will suffice. The results of a check for film diffusion in the testing of a vanadium catalyst are given in Fig. 1 and are discussed below. 

Due to the low permeability of shales, the coefficient of thermal diffusivity is at least a few orders of magnitude greater than the coefficient of fluid diffusivity. Hence, heat transfer in the formation will be dominated by diffusion, and convective transfer by fluid flow may be ignored. Since the coefficient of thermal expansion of pore fluid is much larger (in the order of 100 times) than the coefficient of rock solid, temperature change will result in a change in pore pressure. 

Owing to the fibrous structure of the sclera, the dynamics of fluid diffusion within the tissue eould be approximated by free diffusion wifli flie approximate solution of diffusion equation [19,21,120]. 

Here f denotes the fraction of molecules diffusely scattered at the surface and I is the mean free path. If distance is measured on a scale whose unit is comparable with the dimensions of the flow channel and is some suitable characteristic fluid velocity, such as the center-line velocity, then dv/dx v and f <<1. Provided a significant proportion of incident molecules are scattered diffusely at the wall, so that f is not too small, it then follows from (4.8) that G l, and hence from (4.7) that V v° at the wall. Consequently a good approximation to the correct boundary condition is obtained by setting v = 0 at the wall. ... 

Other Models for Mass Transfer. In contrast to the film theory, other approaches assume that transfer of material does not occur by steady-state diffusion. Rather there are large fluid motions which constantiy bring fresh masses of bulk material into direct contact with the interface. According to the penetration theory (33), diffusion proceeds from the interface into the particular element of fluid in contact with the interface. This is an unsteady state, transient process where the rate decreases with time. After a while, the element is replaced by a fresh one brought to the interface by the relative movements of gas and Uquid, and the process is repeated. In order to evaluate a constant average contact time T for the individual fluid elements is assumed (33). This leads to relations such as... 

As velocity continues to rise, the thicknesses of the laminar sublayer and buffer layers decrease, almost in inverse proportion to the velocity. The shear stress becomes almost proportional to the momentum flux (pk ) and is only a modest function of fluid viscosity. Heat and mass transfer (qv) to the wall, which formerly were limited by diffusion throughout the pipe, now are limited mostly by the thin layers at the wall. Both the heat- and mass-transfer rates are increased by the onset of turbulence and continue to rise almost in proportion to the velocity. 

Circulation of fluid is promoted by surface tension gradients but inhibited by viscosity, which slows the flow, and by molecular diffusion, which tends to even out the concentration differences. The onset of instabibty is described by a critical Marangoni number (Mo), an analogue of the Rayleigh... 

The creation terms embody the changes in momentum arising from external forces in accordance with Newton s second law (F = ma). The body forces arise from gravitational, electrostatic, and magnetic fields. The surface forces are the shear and normal forces acting on the fluid diffusion of momentum, as manifested in viscosity, is included in these terms. In practice the vector equation is usually resolved into its Cartesian components and the normal stresses are set equal to the pressures over those surfaces through which fluid is flowing. 

Supercritical Mixtures Dehenedetti-Reid showed that conven-tionaf correlations based on the Stokes-Einstein relation (for hquid phase) tend to overpredict diffusivities in the supercritical state. Nevertheless, they observed that the Stokes-Einstein group D g l/T was constant. Thus, although no general correlation ap es, only one data point is necessaiy to examine variations of fluid viscosity and/or temperature effects. They explored certain combinations of aromatic solids in SFg and COg. 

Experimental confirmations of the relative independence of kc with respecl to total pressure have been widely reported. Deviations do occur at extreme conditions. For example, Bretsznajder (Pi ediction of Ti anspoii and Othei Physical Piopeiiies of fluids, Pergamon Press, Oxford, 1971, p. 343) discusses the effects of pressure on the D bPt product and presents experimental data on the self-diffusion of CO9 which show tnat the D-p product begins to decrease at a pressure of... 

Mixing of fluids is a discipline of fluid mechanics. Fluid motion is used to accelerate the otherwise slow processes of diffusion and conduction to bring about uniformity of concentration and temperature, blend materials, facihtate chemical reactions, bring about intimate contact of multiple phases, and so on. As the subject is too broad to cover fully, only a brier introduction and some references for further information are given here. 

Pore dijfusion in fluid-filled pores. These pores are sufficiently large that the adsorbing moleciile escapes the force field of the adsorbent surface. Thus, this process is often referred to as macropore dijfusion. The driving force for such a diffusion process can be approximated by the gradient in mole fraction or, if the molar concentration is constant, by the gradient in concentration of the diffusing species within the pores. 

Pore Diffusion When flmd transport through a network of fluid-filled pores inside the particles provides access for solute adsorption sites, the diffusion fliix can be expressed in terms of a pore diffusion coefficient D as ... 

SoUd Diffusion In the case of pore diffusion discussed above, transport occurs within the fluid phase contained inside the particle here the solute concentration is generally similar in magnitude to the external fluid concentration. A solute molecule transported by pore diffusion may attach to the sorbent and detach many times along its... 

Stokes diameter is defined as the diameter of a sphere having the same density and the same velocity as the particle in a fluid of the same density and viscosity settling under laminar flow conditions. Correction for deviation from Stokes law may be necessary at the large end of the size range. Sedimentation methods are limited to sizes above a [Lm due to the onset of thermal diffusion (Brownian motion) at smaller sizes. 

Nielsen, P. V., and Ake T. A. Moller. 1988. Measurements on buoyant jet flows from a ceiling-mounted slot diffuser. In The. 3rd Seminar on Applications of Fluid Mechanics in E,in,-irotimeru tal Protection-88. Selesian Technical University, Gliwice, Poland. 

For laminar flow - flow in whieh the layers of fluid are stratified aeross whieh there is no mixing apart from that due to moleeular diffusion - Stokes Law (Stokes, 1851) applies. Firstly, however, it is neeessary to define an index of the flow to indieate whether it is laminar or turbulent. This is done through the... 

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