Falling films laminar flow

Labuntsov (LI), 1956 Heat transfer to falling films (laminar flow) effects of convective heat transfer and inertia forces (neglected in Nusselt theory) considered experimentally and theoretically. 

Laminar Flow For films falling down vertical flat surfaces, as shown in Fig. 6-52, or vertical tubes with small film thickness compared to tube radius, laminar flow conditions prevail for Reynolds numbers less than about 2,000, where the Reynolds number is given by... 

Experimental measurements of the wall shear stress exerted by a falling liquid film have been reported for the cases of film flow outside a vertical tube (B14) and in a channel of variable slope (F7). In both cases the experimental results in the zone of smooth laminar flow were in agreement... 

The superficial vapor velocity is Wpz, e is the void fraction of the packing, and 0 is the angle of the channel with respect to the horizontal. The effective liquid velocity is based on the relationship for laminar flow in a falling film... 

The effective liquid velocity is besed ou the falling film relationship for laminar flow ... 

In order to overcome the coupling of power dissipation and mass transfer, we need to consider a different mechanism for gas-liquid contacting. If we turn to laminar flow, an external structure should be used to create or maintain the surface area. For example, in a falling-film reactor the gas /liquid interfacial area is roughly equal to the wall area. In capillaries at moderate velocities, the predominant flow pattern is called Taylor [29] flow, see Fig. 6.3. In Taylor flow, the gas bubbles are too large to retain their spherical shape and are stretched to fit inside the channel. Surface tension pushes the bubble towards the channel wall, and only a thin film remains between the bubble and the wall. 

However, the absence of any parameter related to the channel size limits the application of the model to different two-phase systems. Van Baten and Krishna (2004) and Irandoust and Andersson (1989) included in their models the contributions of both bubble caps and film (Eq. 2.2.34). Van Baten and Krishna (2004) evaluated the contribution of the caps according to the Higbie penetration theory (Eq. 2.2.35), whilst the transfer through the film was obtained based on mass transfer in a falling film in laminar flow (Eqs. 2.2.36 and 2.2.37). 

Intensification of liquid mass transfer can also be achieved by structuring the channels of falling film plates in the form of staggered grooves in herring bone arrangements (Figure 7.14b) [52, 53] as presented in Section 4.4.1. This kind of chaotic mixers are very efficient at low Reynolds numbers and allow, in addition, to narrow the residence time distribution of laminar flow (Section 3.6.2). 

We now use an approach similar to that used for laminar flow inside a pipe for the case of flow of a fluid as a film in laminar flow down a vertical surface. Falling films have been used to study various phenomena in mass transfer, coatings on surfaces, and so on. The control volume for the falling film is shown in Fig. 2.9-3a, where the shell of fluid considered is Ax thick and has a length of L in the vertical z direction. This region is sufficiently far from the entrance and exit regions so that the flow is not affected by these regions. This means the velocity u.(x) does not depend on position z. 

Diffusion into a falling film (see Figure 7.6)[8]. Consider the diffusion of a solute A into a moving liquid film B. The liquid is in laminar flow. Assuming that (1) the film moves with a flat velocity profile vo, (2) the film may be... 

A wetted wall tower is a piece of process equipment that uses a liquid film of S meters thickness in laminar flow in the axial (Z direction). Find the velocity profile in the falling film. 

Figure 3.4 shows a liquid falling in a thin film in laminar flow down a vertical flat surface while being exposed to a gas A, which dissolves in the liquid. The liquid contains a uniform concentration c o of fop. At the liquid... 

Asbjdmsen (A6), 1961 Residence times in falling water films determined by a pulsed tracer technique. Mean residence time 2-7% greater than calculated from laminar film flow theory. 

Consider the sorption of a dye. A, into a falling thin polymer film as shown in Figure 4.6. Assume that the flow of the film is fully developed and laminar, the process is at steady-state conditions, the solubility of the dye in the polymer is low, and no chemical reaction is present. Calculate the dye concentration profile in the polymer film as a function of time. 

---