Fluid laminar film layer

Mass and heat transfer to the walls in turbulent flows is a complex mixture of molecular transport and transport by turbulent eddies. The generally assumed analogy between mass and heat transfer by assuming Sh = Nu, is not valid for turbulent flows [26]. Simulations and measurements have shown that there is a laminar film close to the surface where most of the mass transfer resistance for high Sc liquids is located. This fUm is located below y+ = 1 and for low Sc fluids, and for heat transfer the whole boundary layer is important [27]. 

There have been many studies of the effect of boundary films on mass and heat transfer to single pellets and in packed beds, including the work of Ranz and Marshall 27 and Dwivedi and Upadhey(28). Other theories of mass and heat transfer are discussed in Volume 1, Chapter 10, although only the steady-state film-theory is considered here. It is assumed that the difference in concentration and temperature between the bulk fluid and the external surface of a pellet is confined to a narrow laminar boundary-layer in which the possibility of accumulation of adsorbate or of heat is neglected. 

Figure 2.4b shows, conceptually, the velocity distribution in steady turbulent flow through a straight round tube. The velocity at the tube wall is zero, and the fluid near the wall moves in laminar flow, even though the flow of the main body of fluid is turbulent. The thin layer near the wall in which the flow is laminar is called the laminar sublayer or laminar film, while the main body of fluid where turbulence always prevails is called the turbulent core. The intermediate zone between the laminar sublayer and the turbulent core is called the buffer layer, where the motion of fluid may be either laminar or turbulent at a given instant. With a relatively long tube, the above statement holds for most of the tube length, except for... 

Figure 4.2 Fluid flow velocity through the channel of a membrane module is nonuniform, being fastest in the middle and essentially zero adjacent to the membrane. In the film model of concentration polarization, concentration gradients formed due to transport through the membrane are assumed to be confined to the laminar boundary layer...

The thin fluid layer in the immediate neighborhood of the solid surface is called the fluid film [32]. In this connection, there are instances where the fluid film is referred to as the laminar film, the boundary layer or the viscous sublayer. 

In a laminar flow, the fluid moves in smooth layers or films. There is relatively little mixing and, consequently, the velocity gradients are small and the shear stresses are low. The thickness of the laminar boundary layer increases with the distance from the start of the boundary layer and decreases with Re. For the laminar boundary layer, the average width of the diffusion layer, 8, is approximately Re 1/2, but it is Re 1 / 5 for a turbulent flow. 

A theory which incorporates some of the principles of both the two-film theory and the penetration theory has been proposed by TOOR and Marchello The whole of the resistance to transfer is regarded as lying within a laminar film at the interface, as in the two-film theory, but the mass transfer is regarded as an unsteady state process. It is assumed that fresh surface is formed at intervals from fluid which is brought from the bulk of the fluid to the interface by the action of the eddy currents. Mass transfer then takes place as in the penetration theory, except that the resistance is confined to the finite film, and material which traverses the film is immediately completely mixed with the bulk of the fluid. For short times of exposure, when none of the diffusing material has reached the far side of the layer, the process is identical to that postulated in the penetration theory. For prolonged periods of exposure when a steady concentration gradient has developed, conditions are similar to those considered in the two-film theory. 

As pointed out previously, this laminar boundary layer on smooth plates holds up to a Reynolds number of about 5 x 10". In using the results above, the fluid properties are usually evaluated at the film temperature 7 = (7 + T )j2. 

First let us examine mass transport through this film under isothermal conditions by employing the continuity equations for mass (a mass balance) and for momentum (an energy balance). In this stagnant film, which can correspond to the laminar boundary layer that develops when a fluid passes over a flat surface, there is no motion of the fluid, hence the latter equation is irrelevant. The continuity equation for mass describes the spacial dependence of concentration in terms of the velocities parallel, u, and perpendicular, V, to the surface ... 

The convective heat transfer coefficient (h) is dependent upon the physical properties of the fluid and the physical situation. Typically, the convective heat transfer coefficient for laminar flow is relatively low compared to the convective heat transfer coefficient for turbulent flow. This is due to turbulent flow having a thinner stagnant fluid film layer on the heat transfer surface. Values of h have been measured and tabulated for the commonly encountered fluids and flow situations occurring during heat transfer by convection. 

External Fluid Film Resistance. A particle immersed ia a fluid is always surrounded by a laminar fluid film or boundary layer through which an adsorbiag or desorbiag molecule must diffuse. The thickness of this layer, and therefore the mass transfer resistance, depends on the hydrodynamic conditions. Mass transfer ia packed beds and other common contacting devices has been widely studied. The rate data are normally expressed ia terms of a simple linear rate expression of the form... 

For turbulent flow of a fluid past a solid, it has long been known that, in the immediate neighborhood of the surface, there exists a relatively quiet zone of fluid, commonly called the Him. As one approaches the wall from the body of the flowing fluid, the flow tends to become less turbulent and develops into laminar flow immediately adjacent to the wall. The film consists of that portion of the flow which is essentially in laminar motion (the laminar sublayer) and through which heat is transferred by molecular conduction. The resistance of the laminar layer to heat flow will vaiy according to its thickness and can range from 95 percent of the total resistance for some fluids to about I percent for other fluids (liquid metals). The turbulent core and the buffer layer between the laminar sublayer and turbulent core each offer a resistance to beat transfer which is a function of the turbulence and the thermal properties of the flowing fluid. The relative temperature difference across each of the layers is dependent upon their resistance to heat flow. 

In this approach, it is assumed that turbulence dies out at the interface and that a laminar layer exists in each of the two fluids. Outside the laminar layer, turbulent eddies supplement the action caused by the random movement of the molecules, and the resistance to transfer becomes progressively smaller. For equimolecular counterdiffusion the concentration gradient is therefore linear close to the interface, and gradually becomes less at greater distances as shown in Figure 10.5 by the full lines ABC and DEF. The basis of the theory is the assumption that the zones in which the resistance to transfer lies can be replaced by two hypothetical layers, one on each side of the interface, in which the transfer is entirely by molecular diffusion. The concentration gradient is therefore linear in each of these layers and zero outside. The broken lines AGC and DHF indicate the hypothetical concentration distributions, and the thicknesses of the two films arc L and L2. Equilibrium is assumed to exist at the interface and therefore the relative positions of the points C and D are determined by the equilibrium relation between the phases. In Figure 10.5, the scales are not necessarily the same on the two sides of the interface. 

HARRIOTT 25 suggested that, as a result of the effects of interfaeial tension, the layers of fluid in the immediate vicinity of the interface would frequently be unaffected by the mixing process postulated in the penetration theory. There would then be a thin laminar layer unaffected by the mixing process and offering a constant resistance to mass transfer. The overall resistance may be calculated in a manner similar to that used in the previous section where the total resistance to transfer was made up of two components—a Him resistance in one phase and a penetration model resistance in the other. It is necessary in equation 10.132 to put the Henry s law constant equal to unity and the diffusivity Df in the film equal to that in the remainder of the fluid D. The driving force is then CAi — CAo in place of C Ao — JPCAo, and the mass transfer rate at time t is given for a film thickness L by ... 

The mass transfer coefficient (3C with SI units of m/s or m3/(sm2) is defined using these equations. It is a measure of the volumetric flow transferred per area. The concentration difference Aca defines the mass transfer coefficient. A useful choice of the decisive concentration difference for mass transfer has to be made. A good example of this is for mass transfer in a liquid film, see Fig. 1.41 where the concentration difference cA0 — cM between the wall and the surface of the film would be a a suitable choice. The mass transfer coefficient is generally dependent on the type of flow, whether it is laminar or turbulent, the physical properties of the material, the geometry of the system and also fairly often the concentration difference Aca. When a fluid flows over a quiescent surface, with which a substance will be exchanged, a thin layer develops close to the surface. In this layer the flow velocity is small and drops to zero at the surface. Therefore close to the surface the convective part of mass transfer is very low and the diffusive part, which is often decisive in mass transfer, dominates. 

Either side of the phase boundary two stationary laminar fluid layers (films) are formed with thicknesses (5g and dt, through which the gas can only pass by diffusion. 

Reverse osmosis is a cross-flow process and, as in any dynamic hydraulic process, the fluid adjacent to the membrane moves slower than the main stream. While the main stream flow may be turbulent, the layer next to the membrane surface is laminar. This thin, laminar flow film is called the boundary layer. When water permeates through the membrane, nearly all of the salt remains behind in the boundary layer next to the membrane. The salt must then diffuse across the boundary layer and back into the bulk stream. This results in a boundary layer with a salt concentration which is more concentrated than the bulk stream. The effect has been termed concentration polarization, and it is defined by the following equation ... 

Laminar Free Convection. Sparrow and Gregg [33] were the first to use the boundary layer method to study laminar, gravity-driven film condensation on a vertical plate. They improved upon the approximate analysis of Nusselt by including fluid acceleration and energy convection terms in the momentum and energy equations, respectively. Their numerical results can be expressed as ... 

When fluid flows at a 90° angle across a tube, it creates turbulence, which is called vortex shedding. The swirls created when a river flows across a tree stump is a common example. The swirls destroy the film resistance to heat transfer created by laminar layers of fluid surrounding the tube. My experience indicates that a shell-side cross-flow velocity of 3 to 5 ft/s is sufficient to obtain this benefit. 

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