The Stefan column was designed in the 19
th
Century to estimate binary gas diffusivities by placing a pure volatile liquid at the bottom overlaid with a stagnant gas. A steady gas sweep at the top ...removed the diffused species. Previous validation, by other research groups, of the Maxwell-Stefan multicomponent mass transport equations in the Stefan column prompted a study to test an azeotropic binary liquid as the source of both gaseous species, maintaining the composition at the liquid-gas interface constant. Azeotropic acetone (A)-n-hexane (B) mixtures were placed in a vertical glass pipette in preparation for an isothermal evaporation-diffusion experiment in atmospheric air (C). The pure solvents were also tested separately. The experimental interfacial descent, the solvents' diffusivities in air, and their molar fluxes were provided as input to the Maxwell-Stefan equations to obtain the binary gas diffusivity D
AB,exp
, which is unavailable in the literature. The pure solvent diffusivities in air showed good agreement with the Chapman-Enskog kinetic theory for low-density gases, but the experimental gas diffusivity of acetone in n-hexane exceeded consistently the theoretical predictions by at least two orders of magnitude. A possible explanation for this unexpected result is the high affinity between the solvent molecules in the liquid state, which undoubtedly affects their gas transport behavior. Further studies are necessary to elucidate this finding. This is the first attempt to use a liquid azeotrope in a Stefan column. By combining this approach with the Maxwell-Stefan transport equations, the gas diffusivity of acetone in n-hexane was obtained.
A modeling framework is developed to perform two- and three-dimensional simulations of ice accretion over solid bodies in a wet air flow. The PoliMIce (Politecnico di Milano Ice accretion software) ...library provides a general interface allowing different aerodynamic and ice accretion software to communicate. The built-in ice accretion engine moves from the well-known Myers approach and it includes state-of-the-art ice formation models. The ice accretion engine implements a fully three-dimensional representation of the two-phase flow over the solid body, accounting for both rime and glaze ice formation. As an improvement over the reference model, a parabolic temperature profile is assumed to guarantee the consistency with respect to the wall boundary conditions. Moreover, the mass balance is generalized to conserve the liquid fraction at the interface between the glaze and the rime ice types. Numerical simulations are presented regarding in-flight ice accretion over two-dimensional airfoils and three-dimensional straight- and swept-wings. The CFD open-source software OpenFOAM was used to compute the aerodynamic field and the droplet trajectories. Simulation results compare fairly well with available experiments on ice accretion.
The characteristics of Stefan blowing effects in a magneto-hydrodynamic flow of a Casson fluid past a stretching sheet are investigated. The effects of radiation, heat source/sink, Newtonian heating, ...Arrhenius activation energy and binary chemical reaction are considered for heat and mass transfer analysis. The homotopy analysis method (HAM) was utilised to solve the transformed non-dimensionalized equations analytically. The impact of various physical parameters affecting the flow are investigated. Further, the relationship of various parameters on the skin friction and rate of heat and mass transfer was explored using correlation and probable error. A sensitivity analysis was carried out based on the Response Surface Methodology to analyse the effect of Stefan blowing parameter, magnetic parameter and stretching/shrinking parameter on the reduced Nusselt number and reduced Sherwood number. A constant positive sensitivity for the reduced Nusselt number towards the Stefan blowing parameter for all levels of magnetic parameter and stretching/shrinking parameter was found. Further, the reduced Sherwood number indicated a negative sensitivity towards the Stefan blowing parameter.
•CFD-DEM simulation of particle drying processes.•Immersed boundary method for handling complex geometries.•Stefan flow has no effect on simulation results.•Development of particle drying model for ...discrete simulation.
A great deal of industrial processes involves drying processes that removes water from the surface and interior of particles, where knowing the flow behavior, mass and heat transfer is crucial for proper design and optimization of industrial dryers. This work developed a CFD-DEM method for the simulation of particle drying processes, where the immersed boundary method (IBM) was used to handle the no-slip boundary condition of gas phase at the wall of complex geometries. The model was validated by comparing the numerical results to the experimental data of particle moisture and gas (particle) temperature in the dense bubbling bed and dilute pneumatic conveying bed, respectively. Compared with the experimental results, the maximum relative errors of outlet gas temperature, particle temperature and water content in the pneumatic conveying bed are 2.2%,2.2% and 7.9%, respectively. It was also found that considering the effect of Stefan flow on the drag correction did not affect the studied particle drying processes. Present study proved that CFD-DEM-IBM method is powerful for simulating the fluid flow, mass and heat transfer in gas-fluidized beds.
Display omitted
•Transport in membranes containing distinct pores was analyzed using Maxwell-Stefan theory.•Diffusive cross-coupling can lead to a shift in rejection of 20 %•Viscous flow has an ...important contribution to the total flux.•Thermodynamic non-ideal behavior can lead to large variations in solute rejection.
Ceramic membranes are highly promising for application in organic solvent nanofiltration (OSN). Unfortunately, the governing molecular transport mechanisms are not yet fully understood. To study the importance of different transport mechanisms, we analyze transport through these membranes using Maxwell-Stefan theory. We show that the total flux is dominated by the viscous contribution, when using Poiseuille’s law. Cross-coupling of the order of magnitude observed in liquids, leads to changes in retention of up to 20%. Finally, it was shown that non-ideal thermodynamics in the external liquid phase can explain changes from positive to negative retention when using the same solute in different solvents. This work opens perspectives to choose simpler mass transfer models for process modelling, as well as provides physical insight into which mass transfer mechanisms are important in OSN with ceramic membranes.
The Maxwell–Stefan equations are a system of nonlinear partial differential equations that describe the diffusion of multiple chemical species in a container. These equations are of particular ...interest for their applications to biology and chemical engineering. The nonlinearity and coupled nature of the equations involving many variables rule out analytical solutions, so numerical methods are often used. In the literature the system is inverted to write fluxes as functions of the species gradient before any numerical method is applied. In this paper it is shown that employing a mixed finite element method makes the inversion unnecessary, allowing the numerical solution of Maxwell–Stefan equations in their primitive form. A mixed variational formulation is derived in the general n-ary case. A priori error estimates between the finite element and exact solutions are obtained. The order of convergence of the method is then verified and compared with standard methods using a manufactured solution. Finally, the solution is computed for a test case from the literature involving the diffusion of three species and compared to solutions from other methods.
Display omitted
•Binary and ternary gas diffusion is investigated in situ with FTIR Spectroscopy.•The binary diffusion of CH4/CO2, CH4/C2H6, CH4/C3H8 and C2H6/C3H8 is studied.•Ternary gas diffusion ...of CH4/CO2/C3H8 is measured at 0.1 MPa and 308.15 K.•The Maxwell – Stefan theory of multicomponent diffusion is effectively applied.•Osmotic, reverse and barrier diffusion are observed and predicted.
The unsteady diffusion of the ternary gas mixture CH4(α) – CO2(β) – C3H8(γ) is measured with FTIR Spectroscopy in the transmission mode at 308.15 K, 0.1 MPa and equilibrium compositions xα,∞=0.333 and xβ,∞=0.363. A parallel is drawn between the experimental approach and the classical Two-Bulb method. The geometry of the setup is calibrated by measuring the equimolar counter-diffusion of C3H8/CO2 at 308.15 K and 0.1 MPa. Then, analogous experiments are conducted for the gas pairs CH4/CO2, CH4/C2H6, CH4/C3H8 and C2H6/C3H8 to measure their mutual diffusivity. Last, the ternary diffusion of CH4(α) – CO2(β) – C3H8(γ) is measured and modelled with the Maxwell – Stefan theory of multicomponent equimolar diffusion for ideal gas mixtures. Osmotic, reverse and barrier diffusion are observed and predicted for methane before reaching equilibrium.
Flow around a solid sphere finds utility in numerous single- and two-phase engineering applications, such as sport balls, combustion systems, silt conveyance in waterways, hydraulic conveying, ...pneumatic equipment, food and chemical manufacturing. Therefore, this paper aims to examine the Casson nanofluids flow and heat transfer over a solid sphere that is saturated in an isotropic porous material in the presence of Stefan blowing and slip conditions. The forced situation is due to the presence of a stagnation point while the surface of the sphere is subjected to thermal slip conditions. Besides, various significant impacts are taken into account such as Lorentz force, thermal radiation, heat source/sink, and activation energy. The solution technique is based on non-similar transformations and implicit finite difference method with the Blottner algorithm. It is remarkable that, for all values of the activation parameter, the growth of Stefan number reduces the gradients of the velocity, temperature, and nanoparticle concentration. Also, the presence of the thermal slip factor reduces the temperature distributions. Additionaly, an increase in either the Casson parameter or Darcy number enhances the flow while both temperature and concentration are diminishing. Furthermore, there is an improvement in values of the Nusselt number up to 50.57 % when the magnetic parameter is varied from 0 to 6.
In the paper, we solve two Stefan problems. The first problem recovers an unknown moving boundary by specifying the Cauchy boundary conditions on a fixed left-end. The second problem finds a ...time-dependent heat flux on the left-end, such that a desired moving boundary can be achieved. Then, we solve an inverse Cauchy-Stefan problem, using the over-specified Cauchy boundary conditions on a given moving boundary to recover the solution. Resorting on a homogenization function method, we recast these problems into the ones having homogeneous boundary and initial conditions. Consequently, the approximate solution is obtained by solving a linear system obtained from the collocation method in a reduced domain. For the first Stefan problem the moving boundary can be determined accurately, after solving a nonlinear equation at each discretized time. For the second Stefan problem, we can obtain the required boundary heat flux without needing of iteration. Numerical examples, including non-smooth ones, confirm that the novel methods are simple and robust against large noise. Moreover, the Stefan and inverse Cauchy-Stefan problems are solved without initial conditions.
PDF
