Hydrodynamic behavior at the triple line of spreading liquids and the divergence problem

A basic problem in spreading of a Newtonian liquid is the hydrodynamic description of the viscous energy dissipation near the moving contact line. With a sharp wedge profile, the braking force becomes infinite (divergence problem), implying that a drop is unable to spread on a solid surface, due to an infinite braking force. Introducing a "cutoff" length currently solves the problem, generating a finite value for the braking force. We propose an original approach to solve the divergence problem at a moving solid/liquid/ vapor triple line, exhibiting a fully explicit derivation for the viscous energy dissipation expression. It consists of observing that the rheological behavior of the liquid is modified near the triple line due to high shear rate. Above a critical value of the shear rate, near the triple line and near the solid surface, the liquid becomes shear-thinning, so that there is no divergence of the energy dissipation and viscous braking force. This description of the viscous braking phenomenon in liquid spreading is well supported by experiments of silicone oil spreading on glass substrates.