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Should Tortuosity Still Be Used In Upscaling?, Francisco J. Valdes-Parada, Mark L. Porter, Brian D. Wood
Should Tortuosity Still Be Used In Upscaling?, Francisco J. Valdes-Parada, Mark L. Porter, Brian D. Wood
Francisco J. Valdes-Parada
The concept of tortuosity is an integral part of models that describe trans- port in multiscale systems. Traditionally, tortuosity is de#12;ned as the ratio of an e#11;ective path length to the shortest path length in a representative sample of the porous medium microstructure. While the latter can be unambiguously speci#12;ed, the same is not true for the e#11;ective path length, since it changes from one type of transport to another. Consequently, it is possible to have di#11;erent tortuosity values for di#11;erent transport processes taking place in the same system. In order to avoid running into unclear interpretations, we pro- pose …
Computation Of Jump Coefficients For Momentum Transfer Between A Porous Medium And A Fluid Using A Closed Generalized Transfer Equation, Francisco J. Valdes-Parada, José Alvarez-Ramirez, Benoît Goyeau, J. Alberto Ochoa-Tapia
Computation Of Jump Coefficients For Momentum Transfer Between A Porous Medium And A Fluid Using A Closed Generalized Transfer Equation, Francisco J. Valdes-Parada, José Alvarez-Ramirez, Benoît Goyeau, J. Alberto Ochoa-Tapia
Francisco J. Valdes-Parada
The momentum transfer between a homogeneous fluid and a porous medium in a system analogous to the one used by Beavers and Joseph (J Fluid Mech 30:197–207, 1967) is studied using volume averaging techniques. In this article, we present a closed generalized momentum transport equation (GTE) that is valid everywhere and is expressed in terms of position-dependent effective transport coefficients, which are computed from the solution of associated closure problems previously reported. A combination of the velocity profiles from the GTE in the definition of the excess terms that define the jump coefficients allows their computation using numerical techniques. The …
Jump Condition For Diffusive And Convective Mass Transfer Between A Porous Medium And A Fluid Involving Adsorption And Chemical Reaction, Francisco J. Valdes-Parada, Jose Alvarez-Ramirez, Benoît Goyeau, J. Alberto Ochoa-Tapia
Jump Condition For Diffusive And Convective Mass Transfer Between A Porous Medium And A Fluid Involving Adsorption And Chemical Reaction, Francisco J. Valdes-Parada, Jose Alvarez-Ramirez, Benoît Goyeau, J. Alberto Ochoa-Tapia
Francisco J. Valdes-Parada
In this paper, mass transfer at the fluid–porous medium boundaries is studied.The problem considers both diffusive and convective transport, along with adsorption and reaction effects in the porous medium. The result is a mass flux jump condition that is expressed in terms of effective transport coefficients. Such coefficients (a total dispersion tensor and effective reaction and adsorption coefficients) may be computed from the solution of the corresponding closure problem here stated and solved as a function of the Péclet number (Pe), the porosity and a local Thiele modulus. For the case of negligible convective transport (i.e., Pe << 1), the closure problem reduces to the one recently solved by the authors for diffusion and reaction between a fluid and a microporous medium.
Linear Stability Of A Volatile Liquid Film Flowing Over A Locally Heated Surface, N Tiwari, Jm Davis
Linear Stability Of A Volatile Liquid Film Flowing Over A Locally Heated Surface, N Tiwari, Jm Davis
Jeffrey M. Davis
The dynamics and linear stability of a volatile liquid film flowing over a locally heated surface are investigated. The temperature gradient at the leading edge of the heater induces a gradient in surface tension that leads to the formation of a pronounced capillary ridge. Lubrication theory is used to develop a model for the film evolution that contains three key dimensionless groups: a Marangoni parameter (M), an evaporation number (E), and a measure of the vapor pressure driving force for evaporation (K), which behaves as an inverse Biot number. The two-dimensional, steady solutions for the local film thickness are computed …
Nonmodal And Nonlinear Dynamics Of A Volatile Liquid Film Flowing Over A Locally Heated Surface, N Tiwari, Jm Davis
Nonmodal And Nonlinear Dynamics Of A Volatile Liquid Film Flowing Over A Locally Heated Surface, N Tiwari, Jm Davis
Jeffrey M. Davis
The stability of a thin, volatile liquid film falling under the influence of gravity over a locally heated, vertical plate is analyzed in the noninertial regime using a model based on long-wave theory. The model is formulated to account for evaporation that is either governed by thermodynamic considerations at the interface in the one-sided limit or limited by the rate of mass transfer of the vapor from the interface. The temperature gradient near the upstream edge of the heater induces a gradient in surface tension that opposes the gravity-driven flow, and a pronounced thermocapillary ridge develops in the streamwise direction. …