Mass Transfer Characteristics of Haemofiltration Modules—Experiments and Modeling

Reliable mathematical models are important tools for design/optimization of haemo-filtration modules. For a specific module, such a model requires knowledge of fluid- mechanical and mass transfer parameters, which have to be determined through experimental data representative of the usual countercurrent operation. Attempting to determine all these parameters, through measured/external flow-rates and pressures, combined with the inherent inaccuracies of pressure measurements, creates an ill-posed problem (as recently shown). The novel systematic methodology followed herein, demonstrated for Newtonian fluids, involves specially designed experiments, allowing first the independent reliable determination of fluid-mechanical parameters. In this paper, the method is further developed, to determine the complete mass transfer module-characteristics; i.e., the mass transfer problem is modelled/solved, employing the already fully-described flow field. Furthermore, the model is validated using new/detailed experimental data on concentration profiles of a typical solute (urea) in counter-current flow. A single intrinsic-parameter value (i.e., the unknown effective solute-diffusivity in the membrane) satisfactorily fits all data. Significant insights are also obtained regarding the relative contributions of convective and diffusive mass-transfer. This study completes the method for reliable module simulation in Newtonian-liquid flow and provides the basis for extension to plasma/blood haemofiltration, where account should be also taken of oncotic-pressure and membrane-fouling effects.

SPECIAL SPLINE APPROXIMATION FOR THE SOLUTION OF THE NON-STATIONARY 3-D MASS TRANSFER PROBLEM

In this paper we consider the conservative averaging method (CAM) with special spline approximation for solving the non-stationary 3-D mass transfer problem. The special hyperbolic type spline, which interpolates the middle integral values of piece-wise smooth function is used. With the help of these splines the initial-boundary value problem (IBVP) of mathematical physics in 3-D domain with respect to one coordinate is reduced to problems for system of equations in 2-D domain. This procedure allows reduce also the 2-D problem to a 1-D problem and thus the solution of the approximated problem can be obtained analytically. The accuracy of the approximated solution for the special 1-D IBVP is compared with the exact solution of the studied problem obtained with the Fourier series method. The numerical solution is compared with the spline solution. The above-mentioned method has extensive physical applications, related to mass and heat transfer problems in 3-D domains.

Supporting quadric method for collimated beams

We consider the problem of calculating a refractive element with two surfaces, forming a flat front and a given distribution of illumination. The supporting quadrics method is formulated for calculating a given optical element and it is shown that this method coincides with the gradient method for some functional related to the problem of the Monge-Kantorovich mass transfer problem. This enables adaptive selection of the step in the supporting quadric method. At the end of the article a design example is given.

Investigation of variable viscosity and thermal conductivity on MHD mass transfer flow problem over a moving non-isothermal vertical plate

In this paper we investigate numerically the influence of variable viscosity and thermal conductivity on MHD convective flow of heat and mass transfer problem over a moving non-isothermal vertical plate. The viscosity of the fluid and thermal conductivity are presumed to be the inverse linear functions of temperature. With the help of similarity substitution, the flow governing equations and boundary conditions are transformed into non-dimensional ordinary differential equations. The boundary value problem so obtained is then solved using MATLAB bvp4c solver. The effects of various parameters viz. magnetic parameter, viscosity parameter, thermal conductivity parameter, stratification parameter and Schmidt number on velocity, temperature and concentration are obtained numerically and presented trough graphs. Also the coefficient of skin-friction, Nusselt number and Sherwood number are computed and displayed in tabular form. The effects of the viscosity parameter and thermal conductivity parameter in particular are prominent. This study has applications in a number of technological processes such as metal and polymer extrusion.

Challenges in Modeling Pheromone Capture by Pectinate Antennae

Synopsis Insect pectinate antennae are very complex objects and studying how they capture pheromone is a challenging mass transfer problem. A few works have already been dedicated to this issue and we review their strengths and weaknesses. In all cases, a common approach is used: the antenna is split between its macro- and microstructure. Fluid dynamics aspects are solved at the highest level of the whole antenna first, that is, the macrostructure. Then, mass transfer is estimated at the scale of a single sensillum, that is, the microstructure. Another common characteristic is the modeling of sensilla by cylinders positioned transversal to the flow. Increasing efforts in faithfully modeling the geometry of the pectinate antenna and their orientation to the air flow are required to understand the major advantageous capture properties of these complex organs. Such a model would compare pectinate antennae to cylindrical ones and may help to understand why such forms of antennae evolved so many times among Lepidoptera and other insect orders.

The two reflector design problem for forming a flat wavefront from a point source as an optimal mass transfer problem

The article deals with a problem of calculating two reflecting surfaces that form a given irradiance distribution with a flat wavefront, provided that a point source of light is used. A notion of a weak solution for the said problem is formulated and the equivalence of this problem and the Monge–Kantorovich mass transfer is proven.