Theoretical Treatments of Film Flow

From the brief discussion above it is apparent that the flow of viscous liquids in the form of thin films is usually accompanied by various phenomena, such as waves at the free surface. These waves greatly complicate any attempt to give a general theoretical treatment of the film flow problem Keulegan (Kl4) considers that certain types of wavy motion are the most complex phenomena that exist in fluid motion. However, by making various simplifying assumptions it is possible to derive a number of relationships which are of great utility, since they describe the limits to which the flow behavior should tend as the assumptions are approached in practice. 

In the present section the general equations are set up, and the main results of the various treatments of smooth laminar flow, wavy flow, turbulent flow, and flow of films with an adjoining gas stream will be reviewed briefly. 

The most general equations for the laminar flow of a viscous incompressible fluid of constant physical properties are the Navier-Stokes equations. In terms of the rectangular coordinates x, y, z, these may be written  

Since only gravity fields will be considered here, the negative derivatives of S2 are merely equal to the components of g in the respective directions. 

For flow on flat plates, the following coordinate convention will be used, except where otherwise noted the x-axis is directed along the plate surface in the direction of the greatest slope, the 2-axis is directed across the plate, and the y-axis is taken perpendicular to the plate. 

---

Beda (B3), 1961 Minimum residence time in agreement with Brauer s (B14) effective surface velocity results up to Nbm = 400. Distribution function agrees with theory in presence of surfactants. Theoretical treatment of film flow of liquid permeating through porous wall, with heat transfer. 

---