| 1. |
- Stewart, I. W., et al.
(författare)
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Boundary layers in pressure-driven flow in smectic a liquid crystals
- 2015
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 75:4, s. 1817-1851
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Tidskriftsartikel (refereegranskat)abstract
- This article examines the steady flow of a smectic A liquid crystal sample that is initially aligned in a classical "bookshelf" geometry confined between parallel plates and is then subjected to a lateral pressure gradient which is perpendicular to the initial local smectic layer arrangement. The nonlinear dynamic equations are derived. These equations can be linearized and solved exactly to reveal two characteristic length scales that can be identified in terms of the material parameters and reflect the boundary layer behavior of the velocity and the director and smectic layer normal orientations. The asymptotic properties of the nonlinear equations are then investigated to find that these length scales apparently manifest themselves in various aspects of the solutions to the nonlinear steady state equations, especially in the separation between the orientations of the director and smectic layer normal. Non-Newtonian plug-like flow occurs and the solutions for the director profile and smectic layer normal share features identified elsewhere in static liquid crystal configurations. Comparisons with numerical solutions of the nonlinear equations are also made.
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| 2. |
- Vynnycky, Michael, et al.
(författare)
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An asymptotic model for gas-solid flow in a countercurrent moving bed reactor
- 2023
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Ingår i: SIAM Journal on Applied Mathematics. - : Society for Industrial & Applied Mathematics (SIAM). - 0036-1399 .- 1095-712X. ; 83:2, s. 882-908
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Tidskriftsartikel (refereegranskat)abstract
- Asymptotic methods are employed to analyze earlier two-phase steady-state Euler-Euler models that were originally intended as simplified representations for gas-solid flow in an ironmaking blast furnace; more generally, however, they can be thought of as models for two-phase flow in countercurrent moving bed reactors. A scaling analysis, based around the fact that the solid velocity is typically several orders of magnitude smaller than the gas velocity, indicates that the effects of viscosity and inertia are basically negligible compared with those of gravity and interphase momentum transfer. The resulting reduced model yields quasi-analytical expressions for the solid fraction and the gas velocity, with the former being directly related to the shapes of the reactor and any stagnant zone that may form as a consequence of solids or granular materials being able to withstand substantial amounts of shear; in ironmaking blast furnaces, this occurs near the bottom of the reactor, and the zone is commonly known as the deadman. On the other hand, the solid velocity can be found via a numerical solution of Laplace’s equation; nevertheless, the solution is different to that obtained from earlier potential flow models in blast furnace modeling. Most significantly, the current model would form the basis of a computationally efficient approach for modeling transient heat and mass transfer with chemical reactions in a countercurrent moving bed reactor.
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| 3. |
- Vynnycky, Michael, et al.
(författare)
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THE VANADIUM REDOX FLOW BATTERY : AN ASYMPTOTIC PERSPECTIVE
- 2019
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Ingår i: SIAM Journal on Applied Mathematics. - : SIAM PUBLICATIONS. - 0036-1399 .- 1095-712X. ; 79:4, s. 1147-1172
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Tidskriftsartikel (refereegranskat)abstract
- Asymptotic methods are used to analyze a time-dependent two-dimensional (2D) model for the operation of a vanadium redox flow battery-an energy storage technology that has attracted much attention recently. The model takes into account mass, momentum, and charge conservation involving a total of seven ionic species in two porous electrodes that are separated by a proton exchange membrane and attached to external recirculating tanks. In particular, we demonstrate a self-consistent asymptotic reduction of the original model. From this, we identify the presence of concentration boundary layers in each porous electrode at its interface with the membrane, and are able to explain the linear evolution in time of the inlet concentrations of the reacting ionic species-an assumption used in earlier models but never justified. The results of the asymptotic model, which ultimately requires only the numerical solution of four coupled nonlinear ordinary differential equations, are found to compare favorably with those of the original 2D transient problem, which involves 11 coupled nonlinear partial differential equations and two algebraic relations. The solution of the fully reduced asymptotic model is found to require around 300 times less computational time than that of the original model.
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