Micropolar squeeze films between rough rectangular plates

In this paper, the lubrication theory for squeezing with micropolar fluids in smooth surfaces has been advanced to analyze the effects arising from roughness considerations using the stochastic approach. This theory is subsequently applied to the problem of squeezing between rough rectangular plates. It is observed that the roughness effects are more pronounced for micropolar fluids as compared to the Newtonian fluids.Nomenclature a x-dimension of rectangular plate - A area of rectangular plate - b z-dimension of rectangular plate - B non-dimensional roughness parameter, c/h_n (for load capacity), c/h_n1 (for squeeze time) - c maximum asperity deviation from nominal film height - E expectancy operator - f(N, l, h) defined by equation (4) - F(N, L, H) defined by equation (31) - F₁(N, L, B) defined by equation (29) - F₂(N, L, B) defined by equation (30) - F₃(N, L, H_n, B) defined by equation (34) - F₄(N, L, H_n, B) defined by equation (35) - g probability density distribution function - h film height, h=h_n+h_s - h_n nominal film height - h_s deviation of film height from nominal level - h_n1 initial (nominal) film height - H, H_n, H_s non-dimensional forms of h, h_n, h_s respectively - l characteristic material length, (/4)^1/2 - L length ratio, h_n/l (for load capacity), h_n1/l (for squeeze time) - n integer - N coupling number, (/(2+))^1/2 - p pressure - q_x, q_z flow components in x- and z-directions, respectively - t time - T non-dimensional time - w load capacity - W non-dimensional load capacity - x, z cartesian coordinates - angular coordinate - Newtonian viscosity - , micropolar viscosity coefficients - aspect ratio, b/a - standard deviation - /h_n - random variable - defined by equation (19) - defined in equation (28) - defined in equation (33)