Yield stress measurements of aqueous foams in the dry limit

This paper reports measurements of yield stress of aqueous foams approaching the dry foam limit using a pendulum device. Traditionally, the vane rheometer has been used to measure the yield stress in liquids that exhibit wall slip. However, using the simple and inexpensive pendulum technique, shear rates many orders of magnitudes lower can be achieved. The pendulum was used to observe the change in yield stress for the foam as the gas fraction and bubble size increased. The local gas fraction in the foam was found by measuring the sonic velocity, and the bubble size was determined photographically. Strong support is found for the existence of a true yield stress in aqueous foams at the dry foam limit. Yield stress results, once scaled by σ/⟨R⟩, agree well with data from previous studies

Entropy Stable Finite Volume Approximations for Ideal Magnetohydrodynamics

This article serves as a summary outlining the mathematical entropy analysis of the ideal magnetohydrodynamic (MHD) equations. We select the ideal MHD equations as they are particularly useful for mathematically modeling a wide variety of magnetized fluids. In order to be self-contained we first motivate the physical properties of a magnetic fluid and how it should behave under the laws of thermodynamics. Next, we introduce a mathematical model built from hyperbolic partial differential equations (PDEs) that translate physical laws into mathematical equations. After an overview of the continuous analysis, we thoroughly describe the derivation of a numerical approximation of the ideal MHD system that remains consistent to the continuous thermodynamic principles. The derivation of the method and the theorems contained within serve as the bulk of the review article. We demonstrate that the derived numerical approximation retains the correct entropic properties of the continuous model and show its applicability to a variety of standard numerical test cases for MHD schemes. We close with our conclusions and a brief discussion on future work in the area of entropy consistent numerical methods and the modeling of plasmas

Prediction of pressure losses in pipe flow of aqueous foams

This paper presents a model for predicting pressure losses in foams of various expansions and pressures, in pipes of any given diameter, once the foam behavior has been characterized at a single expansion and pressure. The model incorporates a modified form of the power-law viscosity model of foam, which is obtained through the method of volume equalization. Since apparent wall slip contributes significantly to pipe flow of foam, the wall slip also needs to be characterized to enable predictions of pressure losses. The couplings between foam flow and wall slip characteristics are investigated, and two models are presented to predict slip velocities for slow and fast flow rates. Experimentally we find that uslip ∝ ∈-3/2, where ∈ denotes the foam expansion ratio at the experimental pressure. Predicted results are compared with experimental observations, with good agreement

Rheology of fire-fighting foams

This paper examines the rheological properties of compressed-air foams and contains velocity profiles of foams flowing through straight horizontal tubes. It is shown that a master equation can be derived from the experimental data to account for a range of expansion ratios and pressures normally encountered during pumping of polyhedral-in-structure fire-fighting foams. The experimental data come from a Poiseuille-flow rheometer consisting of three stainless steel tubes 6.95, 9.9, 15.8 mm in diameter, with foam generated by mixing a pressurised solution of Class A foam with compressed air. Results are corrected for wall slip following the method of Oldroyd-Jastrzebski, which implies the dependence of slip coefficients on the curvature of the tube wall. The experimental results demonstrate the applicability of the volume equalisation method to the more expanded, polyhedral (ε>5) and transition, bubbly-to-polyhedral (5⩾ε⩾4) foams. (The method of volume equalisation was introduced by Valkó and Economides to correlate the viscosity of low expansion foams (ε<4), characterised by spherical bubbles.) The present results indicate that all data points align themselves along two master curves, depending on whether the foam consists of bubbles or polyhedral cells

Free drainage in aqueous foams: Model and experimental study

Free drainage in compressed-air foams were studied experimentally and theoretically. The time evolution of liquid holdup profiles in a 0.2-m-high by 0.29-m-diameter foam column was determined at various heights by measuring sonic velocity. A new experimental technique was devised to measure the true drainage rate of surfactant solution leaving the foam column. A drainage model was outlined to predict the discharge rate and evolution of the liquid-fraction profile in aqueous foams. The model led to the formulation of a nonlinear partial differential equation in which the liquid fraction was used explicitly as a dependent variable. The model was applied with one adjustable parameter to simulate drainage in foams made from fluorocarbon surfactants containing mobile plateau border and film walls. The liquid-fraction profiles, drainage rates, and final equilibrium liquid profiles depended strongly on the surface mobility of plateau border and film walls; the bubble size; and therefore on the coarsening history in the foam under study. Over longer time periods this model needs to be coupled with inter-bubble gas diffusion to account for coarsening-induced drainage. Free drainage in compressed-air foams were studied experimentally and theoretically. The time evolution of liquid holdup profiles in a 0.2-m-high by 0.29-m-diameter foam column was determined at various heights by measuring sonic velocity. A new experimental technique was devised to measure the true drainage rate of surfactant solution leaving the foam column. A drainage model was outlined to predict the discharge rate and evolution of the liquid-fraction profile in aqueous foams. The model led to the formulation of a nonlinear partial differential equation in which the liquid fraction was used explicitly as a dependent variable. The model was applied with one adjustable parameter to simulate drainage in foams made from fluorocarbon surfactants containing mobile plateau border and film walls. The liquid-fraction profiles, drainage rates, and final equilibrium liquid profiles depended strongly on the surface mobility of plateau border and film walls; the bubble size; and therefore on the coarsening history in the foam under study. Over longer time periods this model needs to be coupled with inter-bubble gas diffusion to account for coarsening-induced drainage

The steady shear of three-dimensional wet polydisperse foams

In this paper, steady shear results are presented from simulations of three-dimensional, polydisperse, wet foams. The simulations use the bubble dynamics model to obtain steady shear results over a wide range of gas fractions, shear rates, and for two normal bubble size distributions. Bingham plastic behaviour is observed in all foams with gas volume fraction above the critical packing fraction of randomly packed hard spheres. Time averaged stress results are seen to be independent of the bubble size distribution. The predicted yield stress behaviour compares favourably with experimental yield stress measurements by previous authors. Shear may increase or decrease the level of topological disorder of foam depending on the foam polydispersity. The present data indicate that shear-induced topological ordering occurs because of insufficient time available for bubbles to pack efficiently in a sheared foam. (C) 2000 Elsevier Science B.V. All rights reserved

Performance of aged aqueous foams for mitigation of thermal radiation

This paper investigates the effect of aging on the performance of aqueous foams as absorbers of thermal radiation. It employs a previously developed engineering method to evaluate the performance of fire-fighting foams exposed to high fluxes of thermal radiation (5-40 kW/m 2). A radiator cone from the ISO 5660 cone calorimeter is utilized to generate a uniform heat flux of thermal radiation on a 50 mm thick aqueous foam layer. A comparison of the effect of thermal radiation on freshly-made and aged foam in terms of the drainage, evaporation and foam-decay characteristics is carried out. Class B fire-fighting foams in the expansion range 5-30 are studied. The experimental data for the aged foam reflect real-life situations. A performance cost index developed previously by the authors, is applied to quantify the overall stability of aged fire-fighting foams exposed to fluxes of thermal radiation. The index demonstrates the superior performance of fresh foams in comparison to aged foams and shows that the low expansion foam (E = 5) displays the worst performance to price ratio

A comparative study of drainage characteristics in AFFF and FFFP compressed-air fire-fighting foams

Drainage measurements are commonly used for assessing the quality, water-retention ability and stability of aqueous foams used in fire-fighting applications. A new experimental technique is proposed in this paper, for measuring the drainage rate of liquid from compressed-air fire-fighting foams. The procedure outlined here provides advancement in precision over that prescribed by the standard for low expansion foams (NFPA 11, Standard for evaluating low expansion foams, NFPA, Quincy, MA, 1998). A comparative analysis of drainage characteristics in two commonly used Class B fire-fighting foams was undertaken, from theoretical and experimental perspectives: (i) aqueous film forming foam and (ii) film forming fluoroprotein foam. It is demonstrated that even though both the foam solutions exhibited similar fundamental physical properties, the disparities in surface rheological properties cause the resulting foams to have remarkably distinct drainage and coarsening characteristics. In addition, a drainage model is outlined, which allows the explicit prediction of the time evolution of liquid holdup profiles and drainage rates in fire-fighting foams. The existing drainage model is extended to simulate fire-fighting foams made from protein based and synthetically produced surfactants