Cross-section of the two opposite surfaces with hemispherical pores on the lower surface are shown in Fig.1; each pore has radius r0 and the gap between surfaces equals h0.
Semicircular pore cell geometry
Assuming that the pores are arranged regularly and the distance 2r1 between pores (see Figure 1) is sufficiently large so that the interaction between the pores can be neglected, only one pore with the adjoining part, called the control cell, can be studied. The hydrodynamic lubrication is described by the Reynolds equation, which in its dimensionless form is
X=x/r0,
H=h/h0,
P=p/Λ,
Λ=6μur0/h02.
Here and hereinafter:
P = p/Λ - dimensionless hydrodynamic pressure;
p - dimensional hydrodynamic pressure;
u- dimensional velocity of sliding surface, along coordinate x;
r0 - dimensional pore radii;
r1 – control cell dimension;
h0 - dimensional minimal clearance (gap) between surfaces;
X=x/r0 - dimensionless coordinate;
x - dimensional coordinate;
H – dimensionless local film thickness;
h – dimensional local film thickness;
W=w/(Λr0) - dimensionless load support;
Λ=6μur0/h02;
μ - dimensional dynamic viscosity of lubricating film;
w- dimensional load support along x-direction;
Ψ= r0/ h0 - pore radii to gap value ratio;
ξ = r1/r0 – control cell dimension to pore radii ratio;
max – maximal value;
cav – cavitation threshold.