Flow factor for molecularly thin fluid films in one-dimensional flow due to fluid discontinuity

Abstract

This article studies the flow of molecularly thin fluid films confined between and entrained by two contact surfaces in one dimension problem based on a simplified momentum transfer model between fluid molecules. The fluid discontinuity across the fluid film thickness is taken into account. The total fluid mass flow through the contact is directly derived based on this model. According to this obtained flow, the flow factor is introduced into the conventional calculation of this flow, which ignores the fluid discontinuity across the fluid film thickness, to make the flow correction. The calculation of this flow by using the present flow factor would be more accurate. It is also found that in the present molecularly thin film hydrodynamic lubrication, the influence of the fluid discontinuity across the fluid film thickness on the total fluid mass flow through the contact is determined by the operational parameter K which is defined as K = ∂ p / ∂ x h 2 / [ 6 η bulk ( 1 − ξ ) ( u a + u b ) ] . Here, the value of the operational parameter K depends on the fluid film pressure gradient ∂ p/∂ x, the fluid film thickness h, the bulk viscosity η bulk of the fluid, the contact–fluid interfacial slip rate ξ and the speeds u a and u b of the upper and lower contact surfaces. In the present molecularly thin film hydrodynamic lubrication, when the value of the operational parameter K is high, i.e., over 0.1, the influence of the fluid discontinuity across the fluid film thickness on the total fluid mass flow through the contact is significant. When the value of the operational parameter K is low, i.e., close to zero, this influence is negligible. It is found that the fluid film shear stresses at both the upper and lower contact surfaces are reduced by the effect of the fluid discontinuity across the fluid film thickness in the present molecularly thin film hydrodynamic lubrication and this reduction can be significant.