III-7
Air Entrainment at Low Viscosities
Alexandra Indeikina, Igor Veretennikov and Hsueh-Chia Chang
University of Notre Dame
Abstract
We examine experimentally and theoretically the breakdown of a straight contact line on a roller which rotates into a liquid. At a critical dimensionless speed (capillary number Ca
c), V-shaped air pockets appear along the contact line and this process precedes the industrially important air entrainment phenomenon. a corn syrup/water mixture with relatively low viscosities (0.3-0.7 Poise) is used as a test fluid. Our flow visualization experiments indicate that the liquid interfacial velocity at the nearly-critical air cusp accelerates rapidly towards the contact line (by two orders of magnitude) over the short length of the cusp (a few capillary lengths). Moreover, Cac is found to be insensitive to agitation in the liquid phase but extremely sensitive to obstacles placed above the cusp in the gas phase.With further increasing of the speed, developed air triangles grow and become unstable. Our observation of time evolution of air pockets which lead to air entrainment indicate that the rearrangements of air flow precede changes in the shape of gas/liquid interface, and subsequent receding (or advancing) of the triple contact line follows these rearrangements. We have also found that air bubbles can detach form the thickest part of the air packet, and not necessary by tip pinching.
The above observations suggest that the evolution of air flow with changes in the shape of the air-liquid interface, is of paramount importance in the stability of the two-dimensional air cusp and the entire air entrainment phenomenon. Air is dragged into the cusp by both the solid roller and the liquid phase. This in-flow builds up a stagnation point near the tip of the air cusp and its high pressure ejects air in the middle of the cusp in a split-flow gas-flow configuration. The stagnation pressure is specified by both the capillary force introduced by the cusp curvature and by the centrifugal normal stress of the curved interfacial momentum boundary layer on the liquid side of the cusp.
Both the injection drag forces and the length of the cusp increase with increasing roller speed. The build-up of stagnation pressure, however, saturates as the cusp flattens. Consequently, at a critical Ca, the steady flow balance breaks down. The required pressure gradient for ejection becomes impossible in two dimensions-a larger curvature gradient is needed to push the air out of the longer flat cusp. Hence, the third dimension should be invoked, and formation of triangular air pockets along the contact line is initiated. Capillary force at the air-liquid interface of the vertex of the triangle can provide a very small radius of curvature and again create sufficient pressure gradient for ejection.
We support this physical mechanism for air entrainment via matched asymptotics. Momentum boundary layers on all interfaces are connected to each other and to inviscid outer solutions. The matching at the contact line requires a molecular model for the gas viscosity when the air cusp width approaches the mean-free path of gas molecules. A predicted Ca
c from the theory will be compared to experimental data.