ABSTRACT
The case of two planar circular surfaces of radius R approaching each other with velocity V along their symmetric axis in a fluid with viscosity JJ and density 8 is illustrated in Figure 18.1. It is assumed that one of the surfaces is stationary and the other in relative motion. If the cylindrical coordinates (r, rp, z) are used, the ~quations and the ~terms contained in all the equations described in Table 3.3 in Chapter 3 are
identically satisfied due to the axial symmetry of the film. Therefore, the reduced coordinate system (r, z) is sufficient. The governing equations in the reduced coordinate system give
Continuity equation:
(18.1)
r-component of the Navier-Stokes equations:
Ot r Or z Oz Or Or r Or & 2 (18.2)
z-component of the Navier-Stokes equations:
(18.3)
2R K
Figure 18.1 A liquid film between two parallel surfaces with radius R and with relative approach velocity V.
