Moving Fluid Fronts

The special design of the Latham bowl allows for a specific blood cell separation known as SURGE. This technique makes use of the principle of critical velocity. The Latham bowl is filled until the huffy coat, ie, layer of platelets and white cells, moves in front of the bowl optics. At this point the machine starts to recirculate plasma through the bowl at increasing rates. The smallest particles, ie, platelets, ate the first to leave the bowl. Their high number causes the effluent line to turn foggy. The optical density of the fluid in the effluent line is monitored by the line sensor. A special algorithm then determines when to open and close the appropriate valves, as well as the optimum recirculation rate. 

Convection heat transfer occurs when a fluid (a gas or a liquid) in motion comes into contaa with a solid surface whose temperature diflfers from the moving fluid. For example, on a hot summer day when you sit in front of a fen to cool down, the heat transfer rate that occurs from your warm body to the cooler moving air is by convection. Or when you are cooling a hot food,... 

It is considered that the fluid front moves with the same speed v/, as the fluid particles v(x) at the front do (Stefan condition)... 

The existence of percolating pathways in a system such as a piece of sandstone can be studied experimentally by recording the movement of fluid invading the pore structures. Thus in Figure 9.14 direct measurement of fluid invasion in a piece of sandstone is shown. The movement of the fluid out from the injection point creates a fractal structure which is related to the pore structure of the material. In Figure 9.14(b) data processing generates the numerical estimates of the fractal dimension of the fluid front. In the same way it can be shown that if one drops a drop of liquid onto a porous pharmaceutical tablet the fluid tvill move out to create a fractal front related to the pore structure of the tablet [31]. 

The kinematics of moving fronts and interfaces has been studied in different physical contexts for over two hundred years. Most notable are the studies of free surfaces in ocean hydrodynamics and vortex sheets in free space (e.g., see Lamb, 1945), and more recently, flame propagation dynamics in combustion analyses. The following derivation, which applies to fluid fronts in porous media, is given in Chin (1993a). Let us consider a moving front or interface located anywhere within a three-dimensional Darcy flow (e.g., any surface marked by red dye), and let (()(x,y,z) denote the porosity. Furthermore, denote by u, v, and w the Eulerian speed components, and describe our interface by the surface locus of points... 

Infiltration occurs by the passage of molten metal through open channels in the porous C/C preform. In the simplest case, movement of the fluid front is governed by capillary forces and surface tension. When a liquid wets the channel walls, the pressure drop across the liquid/atmosphere interface forces the liquid to move up the channel. The capillary force is described as follows (Wang et al., 2005) ... 

If the mobility ratio is greater than 1.0, then there will be a tendency for the water to move preferentially through the reservoir, and give rise to an unfavourable displacement front which is described as viscous fingering. If the mobility ratio is less than unity, then one would expect stable displacement, as shown in Figure 8.16. The mobility ratio may be influenced by altering the fluid viscosities, and this is further discussed in Section 8.8, when enhanced oil recovery is introduced. 

If force P is greater than zero, the particle will be in motion relative to the continuous phase at a certain velocity, w. At the beginning of the particle s motion, a resistance force develops in the continuous phase, R, directed at the opposite side of the particle motion. At low particle velocity (relative to the continuous phase), fluid layers running against the particle are moved apart smoothly in front of it and then come together smoothly behind the particle (Figure 14). The fluid layer does not intermix (a system analogous to laminar fluid flow in smoothly bent pipes). The particles of fluid nearest the solid surface will take the same time to pass the body as those at some distance away. 

The absorption is assumed to occur into elements of liquid moving around the bubble from front to rear in accordance with the penetration theory (H13). These elements maintain their identity for a distance into the fluid greater than the effective penetration of dissolving gas during the time required for this journey. The differential equation and initial and boundary conditions for the rate of absorption are then... 

The analysis of fluid-solid reactions is easier when the particle geometry is independent of the extent of reaction. Table 11.6 lists some situations where this assumption is reasonable. However, even when the reaction geometry is fixed, moving boundary problems and sharp reaction fronts are the general rule for fluid-solid reactions. The next few examples explore this point. 

Solution We suppose that the mass transfer and diffusion steps are fast compared with bulk transport by convection. This is the design intent for ion-exchange columns. The reaction front moves through the bed at a speed dependent only on the supply of fluid-phase reactants. Assuming piston... 

Figure 132. Two-dimensional net of knots to simulate a heat storage including knots for the heat transfer fluid and also the environment. For slow flow (left) and fast flow (right) of the heat transfer fluid, the phase front will move differently...

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