Falling Film on a Vertical Wall

In a variety of apparatus and chemical reactors, liquid films or rivulets are flowing around pipes, walls, or packing elements (packed colunuis, cooling towers, liquid film coolers). Things are very easy in the case of a laminar film ruiuiing on a vertical wall, see Fig. 3.1-10. 

Only viscosity and gravity forces are acting on a film element with the thickness dy. A force balance (Nusselt 1916) leads to the equation 

With the already presented equation valid for the shear stress for Newtonian liquids, the last equation can be written as 

There are two boundary conditions. On the wall the velocity is zero  

If the liquid film is flowing between this wall and a stagnant gas without shear stress on the film, the slope of the velocity profile at the film-gas boundary is zero  

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