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

This article analyzes the oscillatory squeeze flow (OSF) of a viscoelastic Maxwell fluid confined between two parallel disks, focusing on the effects of partial slip at the fluid–solid interface characterized by a slip length and a critical surface shear stress. By combining a dynamic slip model derived from the Maxwell fluid constitutive equations with the static slip model of Spikes and Granick, the study derives exact solutions for velocity, pressure, and force as functions of key dimensionless parameters: the Deborah number (De), the Womersley number (α), the Navier slip length (λ_N), and the critical surface shear stress (τ_c0). The analysis reveals that when the fluid shear stress exceeds τ_c0, slip occurs in an annular region on the disk surfaces, while a no-slip condition prevails within a time-dependent inner radius; this interplay affects the amplitude and phase lag of both the slip region and the mechanical force required to maintain harmonic motion. Results show that viscoelasticity and hydrophobic slip reduce the force and power needed to sustain oscillations, with the Womersley number influencing phase behavior and the elongational viscosity of the fluid. These findings have implications for applications involving squeeze films in polymer processing, lubrication, and rheometry where slip and viscoelastic effects are significant.