Characterization of Effective Diffusion within Viscoelastic Fluids with Elastic Instabilities

We considered effective diffusion, characterized by magnitudes of effective diffusion coefficients, in order to quantify mass transport due to the onset and development of elastic instabilities. Effective diffusion coefficient magnitudes were determined using different analytic approaches, as they were applied to tracked visualizations of fluorescein dye front variations, as circumferential advection was imposed upon a flow environment produced using a rotating Couette flow arrangement. Effective diffusion coefficient results were provided for a range of flow shear rates, which were produced using different Couette flow rotation speeds and two different flow environment fluid depths. To visualize the flow behavior within the rotating Couette flow environment, minute amounts of fluorescein dye were injected into the center of the flow container using a syringe pump. This dye was then redistributed within the flow by radial diffusion only when no disk rotation was used, and by radial diffusion and by circumferential advection when disk rotation was present. Associated effective diffusion coefficient values, for the latter arrangement, were compared to coefficients values with no disk rotation, which were due to molecular diffusion alone, in order to quantify enhancements due to elastic instabilities. Experiments were conducted using viscoelastic fluids, which were based on a 65% sucrose solution, with different polymer concentrations ranging from 0 ppm to 300 ppm. Associated Reynolds numbers based on the fluid depth and radially averaged maximum flow velocity ranged from 0.00 to 0.5. The resulting effective diffusion coefficient values for different flow shear rates and polymer concentrations quantified the onset of elastic instabilities, as well as significant and dramatic changes to local mass transport magnitudes, which are associated with the further development of elastic instabilities.

Influence of Diffusion through a Porous Film under Electrode Surface in Chronoamperometry Problems

In the presented work on chronoamperometry, the Cottrell model has been generalized by taking into account a thin porosity layer covering the surface of the electrode and Tafel kinetics of an electrode reaction. The effective diffusion coefficient inside a porosity layer is calculated by Bruggeman’s law. It is shown that in the quasi-stationary approximation of diffusion inside a thin porous layer, the chronoamperometry problem can be solved analytically. The obtained solution has been compared with the results of direct numerical simulations and a good agreement is shown. Limiting cases of the solution related to low and high porosity are considered.

Mathematical Modelling of Infra-Red Evaporation Characteristics of Wheat Straw Black Liquor

Infrared (IR) evaporation characteristics of Weak Soda Black Liquor (WSBL) were determined at five different temperatures of 80, 90, 100, 110 and 120oC. The effect of constant temperature on evaporation rate and moisture content (on a dry basis) of 1.5 gm approx. WSBL tests were contemplated and required a careful time frame of IR dissipation to vanish the dampness content at a different consistent temperature. The dissipation rate expanded with expanding infrared temperature. Therefore, different numerical models, such as Page and Logarithmic, Henderson, Pabis and Lewis, were utilised to fit the experimental data properly. A Gaussian model equation was developed for evaporation rate and moisture fraction of black liquor. The probable empirical parameters, along with the relating of reduced chi-square (X2), Residual Sum of Square (RSS), and coefficients of determination (adjusted R2) from non-linear regression analysis of all the numerical model equations, were examined. In addition, the effect of evaporation temperature on the water removal rate, the effective diffusion coefficient and activation energy were also estimated. The effective diffusion coefficient ranges from 2.67 × 10–10 m2/s to 10.4 × 10–10 m2/s, and the activation energy was 39.19 kJ/mol. The statistical indicators (chi-square and determination coefficient) showed that the Decay model equation and Gaussian equation are the most suitable models for describing the evaporation process of WSBL.

Impact of water vapor diffusion and latent heat on the effective thermal conductivity of snow

Heat transport in snowpacks is understood to occur through the two processes of heat conduction and latent heat transport carried by water vapor, which are generally treated as decoupled from one another. This paper investigates the coupling between both these processes in snow, with an emphasis on the impacts of the kinetics of the sublimation and deposition of water vapor onto ice. In the case when kinetics is fast, latent heat exchanges at ice surfaces modify their temperature and therefore the thermal gradient within ice crystals and the heat conduction through the entire microstructure. Furthermore, in this case, the effective thermal conductivity of snow can be expressed by a purely conductive term complemented by a term directly proportional to the effective diffusion coefficient of water vapor in snow, which illustrates the inextricable coupling between heat conduction and water vapor transport. Numerical simulations on measured three-dimensional snow microstructures reveal that the effective thermal conductivity of snow can be significantly larger, by up to about 50 % for low-density snow, than if water vapor transport is neglected. A comparison of our numerical simulations with literature data suggests that the fast kinetics hypothesis could be a reasonable assumption for modeling heat and mass transport in snow. Lastly, we demonstrate that under the fast kinetics hypothesis the effective diffusion coefficient of water vapor is related to the effective thermal conductivity by a simple linear relationship. Under such a condition, the effective diffusion coefficient of water vapor is expected to lie in the narrow 100 % to about 80 % range of the value of the diffusion coefficient of water vapor in air for most seasonal snows. This may greatly facilitate the parameterization of water vapor diffusion of snow in models.

Comparison of Sr Transport in Compacted Homoionous Na and Ca Bentonite Using a Planar Source Method Evaluated at Ideal and Non-Ideal Boundary Condition

With the aim to determine the influence of dominant interlayer cation on the sorption and diffusion properties of bentonite, diffusion experiments with Sr on the compacted homoionous Ca- and Na-forms of Czech natural Mg/Ca bentonite using the planar source method were performed. The bentonite was compacted to 1400 kg·m−3, and diffusion experiments lasted 1, 3 or 5 days. Two methods of apparent diffusion coefficient Da determination based on the analytical solution of diffusion equation for ideal boundary conditions in a linear form were compared and applied. The determined Da value for Ca-bentonite was 1.36 times higher than that for Na-bentonite sample. Values of Kd were determined in independent batch sorption experiments and were extrapolated for the conditions of compacted bentonite. In spite of this treatment, the use of Kd values determined by batch sorption experiments on a loose material for the determination of effective diffusion coefficient De values from planar source diffusion experiments proved to be inconsistent with the standard Fickian description of diffusion taking into account only the pore diffusion in compacted bentonite. Discrepancies between Kd and De values were measured in independent experiments, and those that resulted from the evaluation of planar source diffusion experiments could be well explained by the phenomenon of surface diffusion. The obtained values of surface diffusion coefficients Ds were similar for both studied systems, and the predicted value of total effective diffusion coefficient De(tot) describing Sr transport in the Na-bentonite was four times higher than in the Ca-bentonite.