A theoretical model of foam as a consolidating continuum is proposed. The general model is applied to foam in a gravity settler. It is predicted that liquid drainage from foam in a gravity settler begins with a slow drainage stage. Next, a stage with faster drainage occurs where the drainage rate doubles compared to the initial stage. The experiments conducted within the framework of this work confirmed the theoretical predictions and allowed measurements of foam characteristics. Foams of three different concentrations of Pantene Pro-V Classic Care Solutions shampoo were studied, as well as the addition of polyethylene oxide (PEO) in one case. The shampoo's main foaming components are sodium lauryl sulfate and sodium laureth sulfate. It is shown to what extent foam drainage is slowed down by using higher shampoo concentrations and how it is further decreased by adding polymer (PEO).
Gravitational drainage from thin vertical surfactant solution films and gravitational drainage in a settler column are used to study the behavior of foams based on two-surfactant mixtures. Namely, solutions of the anionic sodium dodecyl sulfate (SDS) and nonionic superspreader SILWET L-77, and their mixtures at different mixing ratios, are studied. It is shown, for the first time, that solutions having a longer lifetime in the vertical film drainage process also possess a higher foamability. An additional and unexpected unique result is that when using a mixed surfactant system, the foamability can be much greater than the foamabilities of the individual components.
This work aims to study flows within a wedge at the inclination angles in the 5°-20°range. Flow within a wedge occurs when a Carbopol solution is pulled horizontally by a moving conveyer belt through the wedge apex opening at different speeds. The upper side of the wedge is fixed at the exit by a pivot joint about which it could rotate. At the wedge entrance, a force gauge is placed so that it is pushing at the upper side of the wedge to keep it at a predetermined position (and thus at a predetermined inclination angle). The gauge measures the restraining force required to counteract the pressure buildup on the flowing Carbopol solution side and to keep the upper side of the wedge at its position. Visualization through the transparent vertical sides of the wedge was used to track seeding particles inside the solution to reconstruct the velocity profile and in particular to reveal plug flow regions characteristic of the yield stress liquids.
In this work the flow of 1.5% Carbopol-940 solution was studied as it was transported through a wedge-like system at different angles, entrance heights, exit heights, and velocities. The high-speed video recordings of the flow were processed by tracking air bubbles entrapped in the solution. This data was used to find the velocity field of the solution beneath the wedge. Also, the force imposed by the solution on the inclined top plate of the wedge was measured. The theoretical description in the framework of the lubrication approximation for Newtonian fluids was used for comparison to the experimental results. It was found that Herschel-Bulkley fluids exhibit qualitatively similar behavior to the Newtonian fluid, such as the reverse flow near the top of the wedge. Overall, this work proves that the lubrication approximation can be effectively used to characterize the flow field of non-Newtonian Herschel-Bulkley fluids at the wedge angles at least up to 20 degrees.
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