Effects of the bounding solid walls are examined numerically for slow flow overregular, square arrays of circular cylinders between two parallel plates. A local magnitudeof the rate of entropy generation is used effectively to determine the flow region affected bythe presence of the solid boundary. Computed axial pressure gradients are compared to thecorresponding solution based on the Darcy-Brinkman equation for porous media in whichthe effective viscosity appears as an additional property to be determined from the flowcharacteristics. Results indicate that, between two limits of the Darcian porous medium andthe viscous flow, the magnitude of μ (the ratio of the effective viscosity to the fluid ˆviscosity) needs to be close to unity in order to satisfy the non-slip boundary conditions atthe bounding walls. Although the study deals with a specific geometric pattern of the porousstructure, it suggests a restriction on the validity of the Darcy-Brinkman equation to modelhigh porosity porous media. The non-slip condition at the bounding solid walls may beaccounted for by introducing a thin porous layer with μ = 1 near the solid walls. ËÂ
A mechanistic model of the respiratory system is proposed to understand differences in quasistatic pressure-volume (p-V) curves of the inflation process in terms of the alveolar recruitment and the elastic distension of the wall tissues. In the model, a total respiratory system consists of a large number of elements, each of which is a subsystem of a cylindrical chamber fitted with a piston attached to a spring. The alveolar recruitment is simulated by allowing a distribution of the critical pressure at which an element opens; while the wall distension is represented by the piston displacement. Relations are derived between parameters in the error-function p-V model equation and properties of the mechanistic model The parameters of the model-based p-V equation are determined for clinical data sets of patients with acute respiratory distress syndrome.
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