Flow Transport and Viscous Phenomena

Flow processes constitute a major mechanism of separative transport. Furthermore, the particular nature of flow—its magnitude, cross sectional distribution, origin, and limits—is largely responsible for the level of success in many attempts at separation. 

As noted earlier, flow is a form of bulk displacement in which components entrained in a flowing medium are carried along nonselectively with the medium. Flow displacement thus stands in contrast to the other major transport mechanism—relative displacement—which is selective. 

Flow transport is governed by Eq. 3.22, which expresses the flux density contributed by flow as 

To fully characterize transport, one clearly needs to determine flow velocity v at every point in the system. For simple flow systems (such as open capillary tubes), the v values can be calculated at each point whereas for complex systems (e.g., packed columns), the distribution in us can only be estimated by statistical methods. 

The strength of flow is that it provides the most powerful and versatile mechanism of transport available for separative displacement. The weakness of flow—other than its nonselectivity—is its nonuniformity. For most flow systems, v varies widely from point to point in the flow space. The different us carry component molecules downstream at different rates, thus leading to the broadening of component zones. We must understand the fundamentals of flow in order to control this broadening while still enjoying the significant advantages of flow transport. 

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As discussed in Section 2.6, vorticity is a measure of the angular rotation rate of a fluid. Generally speaking, vorticity is produced by forces that cause rotation of the flow. Most often, those forces are caused by viscous shearing action. As viscous fluid flows over solid walls, for example, the shearing forces caused by a no-slip condition at the wall is an important source of vorticity. The following analysis shows how vorticity is transported throughout a flow field by convective and viscous phenomena. 

Before looking at how Gaussian peaks arise from these transport equations we will devote our attention, by way of the next chapter, to the details of another form of transport, flow transport, and some related viscous phenomena. 

As noted above, as the size difference between the solvent and solute become progressively smaller, viscous flow rapidly becomes less important, and molecular interactions become dominant factors. In this limit, molecular solution (or sorption) and diffusion phenomena control the relative transport rates of the solute and solvent. This transition region is an area of ongoing discussion regarding what is a pore and what is not a pore ... 

In terms of organization, the text has two main parts. The first six chapters constitute generic background material applicable to a wide range of separation methods. This part includes the theoretical foundations of separations, which are rooted in transport, flow, and equilibrium phenomena. It incorporates concepts that are broadly relevant to separations diffusion, capillary and packed bed flow, viscous phenomena, Gaussian zone formation, random walk processes, criteria of band broadening and resolution, steady-state zones, the statistics of overlapping peaks, two-dimensional separations, and so on. 

Gas Transport. Initially, in a vessel containing air at atmospheric pressure, mass motion takes place when temperature differences exist and especially when a valve is opened to a gas pump. Initial tiow in practical systems has been discussed (29), as have Monte Carlo methods to treat shockwave, turbulent, and viscous flow phenomena under transient and steady-state conditions (5). 

All transport processes (viscous flow, diffusion, conduction of electricity) involve ionic movements and ionic drift in a preferred direction they must therefore be interrelated. A relationship between the phenomena of diffusion and viscosity is contained in the Stokes-Einstein equation (4.179). 

This inaccuracy stems from their calculation of molecular transport effects, such as viscous dissipation and thermal conduction, from bulk flow quantities, such as mean flow velocity and temperature. This approximation of microscale phenomena with macroscale information fails as the characteristic length of the (gaseous) flow gradients approaches the average distance travelled by molecules between collisions - the mean path. The ratio of these quantities is referred to as Knudsen number. 

It is probably true to say that in a heat exchanger involving turbulent flow, these mechanisms are overshadowed in the bulk flow by the more prominent effects of the fluid flow forces and turbulence, i.e. eddy transport and inertia. Within the viscous sub-layer however, it is likely that all these mechanisms can have an influence on the deposition process together with the phenomena that may be associated with the viscous sub-layer, i.e. instabilities including turbulent bursts (lift forces and fluid downsweeps) and surface drag. 

In this chapter we formulate the thermodynamic and stochastic theory of the simple transport phenomena diffusion, thermal conduction and viscous ffow (1) to present results parallel to those listed in points 1-7, Sect. 8.1, for chemical kinetics. We still assume local equilibrium with respect to translational and internal degrees of freedom. We do not assume conditions close to chemical or hydrodynamic equilibrium. For chemical reactions and diffusion the macroscopic equations for a given reaction mechanism provide sufficient detail, the fluxes in the forward and reverse direction, to write a birth-death master equation with a stationary solution given in terms of For thermal conduction and viscous flow we derive the excess work and then find Fokker-Planck equations with stationary solutions given in terms of that excess work. 

A difficulty might face the worker who wishes to apply Cohen and Turnbull s theory to transport phenomena in molten salts not only near the glass transition temperature but also above the normal melting point (see Section 5.6.2.2). Experimental evidence shows that the heat of activation of diffusion and of conductance for viscous flows is related to the normal melting point of the substance concerned... 

Momentum, thermal and mass transports are three basic physical phenomena of any fluid flow. In a CVD process, when the precursor gases enter a high temperature reaction chamber from room temperature, the aforementioned three transports occur under certain velocity, temperature and concentration gradients. The common underlying physical laws for these three transports are all based on a molecule s thermal motion. Three specific underlying laws which describe the three transports are Newton s viscous law, Fourier law and Fick s law respectively. For a simple one-dimensional system, these laws can be expressed by [14]... 

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