On the Choking of the Flow of Piezoviscous Liquids

Experimental evidence for choking of a piezoviscous fluid in a capillary tube is presented. It is shown that under a nearly isothermal condition, it is possible for the flow to experience choking whereby increasing the inlet pressure ceases to affect the flow rate. The occurrence of this phenomenon can be predicted by noting a singularity in the flowrate equation in a capillary tube under typical conditions encountered in injection molding (cf. Denn, 1981). Further examination of the general equations governing the shear flow of laminar, incompressible, linearly viscous (Newtonian) liquids under high pressures reveals a singularity in the solution for the pressure gradient. This apparently unreported phenomenon is shown to occur in liquids whose viscosity, μ, increases exponentially with pressure, p, as μ = μ₀e^αp, where α denotes the pressure-viscosity coefficient. For a two-dimensional configuration with the shearing action taking place in the x direction and with p = p(x, y), the singularity is shown to take place when: $τyx=±(1/α)1+α2τxxτyy$⁠, at which case both δp/δx and δp/δy →∞. The occurrence of such a singularity in the pressure gradient may have an important physical implication in lubrication flows particularly in concentrated contacts such as elastohydrodynamic lubrication of rolling element bearings and gears.