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We develop a new mathematical model for cross filtration in a dialyzer, taking into account the membrane fouling caused by progressive protein deposition. We focus on a single fiber and, starting from the basic laws of fluid dynamics and exploiting the smallness of the aspect ratio of fibers, we obtain significant simplifications of the flow equations. We end up with a hyperbolic system that describes the temporal evolution (specifically the decrease) of the filtering efficiency caused by the albumin deposit. Such an effect is then described quantitatively by means of numerical simulations. [ABSTRACT FROM AUTHOR]

This paper investigates the hydrodynamic behavior of gas-solid two-phase flow in the annular space of an air drilling well under different arrangements by using three-dimensional approach. Two-fluid model is used to solve the governing equations in the Eulerian-Eulerian framework. Effect of eccentricity and drill pipe rotation on the pressure drop, volume fraction and velocity profile are examined. The results are compared with available data in the literature and good agreement is found. The results show that the presence of solid particles in the annulus change the air velocity profile significantly and create two off-center peaks velocity close to the walls instead of one peak velocity in the middle. Eccentricity of drill pipe makes more accumulation of the cuttings in the smaller space of the annulus. Increasing the eccentricity increases pressure drop due to impact of particles with annulus wall and also particles collision with each other. Rotation of the drill pipe shifts maximum air velocity location toward smaller space of the annulus which results more uniform cutting distributions in the annulus and improvement in their transportations. Pressure drop in the annulus increases as eccentricity and rotation of drill pipe increase. [ABSTRACT FROM AUTHOR]