Squeeze force of a Maxwell fluid between circular smooth surfaces with simple harmonic motion

Abstract

The force and mechanical power required to maintain the simple harmonic motion (SHM) of the upper circular surface squeezing a viscoelastic fluid film is analyzed. The amplitude of the displacement of the upper surface is very small compared to the gap width as a function of time. The smoothness of the upper and lower surfaces is characterized by the slip model with two constant parameters, a slip length and a critical surface shear stress. The nonlinear convection terms in the momentum equation are neglected since the viscous forces dominate the inertial forces. The acceleration and deceleration terms are retained since the upper plate oscillates harmonically and the velocity in the fluid is strictly periodic. An exact solution of the governing equations is found as a function of the Deborah number, the Womersley number, the slip length, and the critical surface shear stress. A circular region without slip condition, bounded by a time-dependent radius, appears when the shear stress of the fluid does not exceed a critical surface shear stress. In addition, an annular region with slip up to the radius of the disk appears when the critical surface shear stress is exceeded. Our results show that viscoelastic and hydrophobic effects together with the Womersley number and a critical surface stress cause changes in the amplitude and phase lag of the waveform of the time-dependent radius and the force acting on the wall surface to maintain the SHM of the upper disk.