Effect of fluid inertia on probe-tack adhesion

One way of determining the adhesive strength of liquids is provided by a probe-tack test, which involves measuring the force required to pull apart two parallel flat plates separated by a thin fluid film. The large majority of existing theoretical and experimental work on probe-tack adhesion use very viscous fluids and considers relatively low lifting plate velocities, so that effects due to fluid inertia can be neglected. However, the employment of low-viscosity fluids and the increase in operating speeds of modern lifting apparatus can modify this scenario. By dealing with a proper gap averaging of the Navier-Stokes equation, we obtain a modified Darcy-law-like description of the problem and derive an adhesion force which incorporates the effects of fluid inertia, fluid viscosity (for Newtonian and power law fluids), and the contribution of the compliance and inertia of the probe-tack apparatus. Our results indicate that fluid inertia may have a significant influence on the adhesion force profiles, inducing a considerable increase in the force peaks and producing oscillations in the force-displacement curves as the plate-plate separation is increased. The combined role of inertial and non-Newtonian fluid behaviors on the adhesion force response is also investigated.