Coupled Transport Problem Research Articles

Droplet absorption and spreading into thin layers of polymer hydrogels

From biological tissues to microactuators and absorption of solvents into layers of paint, macroscopically non-porous materials with the capacity to swell when in contact with a solvent are ubiquitous. In these systems, owing to strong solid–fluid interactions, chemically driven flows can yield large geometric changes. We study experimentally and theoretically the canonical problem of the swelling of a thin hydrogel layer by a single water drop. Using a bespoke experimental set-up, we observe fast absorption leading to a radially spreading axisymmetric blister. We use a fully three-dimensional linear poroelastic framework with nonlinear kinematic equations to obtain governing equations, which we then reduce with thin-layer scalings to a one-dimensional nonlinear diffusion equation for the evolution of the blister geometry. In the limits of large and small deformations, the evolution of the blister characteristic height and radius are self-similar, following power laws in time. Our experimental measurements show that the evolution of the blister is broadly within the theoretical predictions in the large and small deformation regimes. In the general intermediate deformation regime, the measurements are well captured by our reduced one-dimensional diffusion model, which does not require the sophisticated and computationally expensive numerical approaches necessary for the original two-dimensional nonlinear coupled transport problem. By adapting modelling techniques from the fluid dynamics of thin porous elastic layers to a polymer swelling problem, our modelling framework extends the range of polymer swelling problems that can be treated with semi-analytical methods. Moreover, our detailed experimental data can serve as a test case for future nonlinear poroelastic frameworks of swelling polymer materials.

A face-centred finite volume approach for coupled transport phenomena and fluid flow

We present a particular derivation of the face-centred finite volume (FCFV) method and study its performance in non-linear, coupled transport problems commonly encountered in geoscientific and geotechnical applications. The FCFV method is derived from the hybridisable discontinuous Galerkin formulation, using a constant degree of approximation for the discretization of the unknowns defined on the mesh faces (edges in two dimensions). The piecewise constant degrees of freedom are determined in a global problem over the mesh skeleton. Then, the solution and its gradient are recovered at the cells centroid in a set of element-by-element independent postprocesses, both exhibiting linear convergence. The formulation of the transient advection-diffusion-reaction equation is presented in detail and the numerical analysis under challenging advective/diffusive regimes is studied. Finally, we use several numerical examples to illustrate the advantages and limitations of the FCFV method to solve problems of geoscientific and geotechnical relevance governed by the non-linear coupling between advection-diffusion-reactive transport and Stokes flow. Our results show that the FCFV method is an attractive and highly competitive alternative to other commonly used methods.

Transient flows in active porous media.

Stimuli-responsive materials that modify their shape in response to changes in environmental conditions-such as solute concentration, temperature, pH, and stress-are widespread in nature and technology. Applications include micro- and nanoporous materials used in filtration and flow control. The physiochemical mechanisms that induce internal volume modifications have been widely studied. The coupling between induced volume changes and solute transport through porous materials, however, is not well understood. Here, we consider advective and diffusive transport through a small channel linking two large reservoirs. A section of stimulus-responsive material regulates the channel permeability, which is a function of the local solute concentration. We derive an exact solution to the coupled transport problem and demonstrate the existence of a flow regime in which the steady state is reached via a damped oscillation around the equilibrium concentration value. Finally, the feasibility of an experimental observation of the phenomena is discussed.

Discrete and continuum links to a nonlinear coupled transport problem of interacting populations

We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind are inspired by the dynamics of pedestrian flows in open spaces and are intimately connected to cross-diffusion and thermo-diffusion problems holding a variational structure. The tools we use include a suitable structure of the relative entropy controlling TV-norms, the construction of Lyapunov functionals and particular closed-form solutions to nonlinear transport equations, a hydrodynamics limiting procedure due to Philipowski, as well as the construction of numerical approximates to both the continuum limit problem in 2D and to the original interacting particle systems.

Assessment of differential evolution for multi-objective optimization in a natural convection problem solved by a local meshless method

ABSTRACTThe performance of Differential Evolution for Multi-objective Optimization (DEMO) in a nonlinear coupled transport problem, solved by a Meshless Local Strong form Method (MLSM), is assessed from different points of view. First, the behaviour of the optimization algorithm is tested for different scenarios, ranging from optimization of trivial diffusive transport to more complex nonlinear natural convection problems. Second, a hybrid parallel implementation of both the optimization and simulation codes, is introduced to optimize execution time, since such simulation-based optimization might require a vast amount of computational power. The goal of optimization is partially to cover the differentially heated cavity with non-permeable obstacles so as maximally to obstruct the flow with minimal possible coverage. Different scenarios are taken into account to analyse the optimization performance. The results are presented in terms of temperature contour plots, velocity profiles, analysis of heat losses, Pareto fronts of optimal solutions, convergence of optimal solutions, and sensitivity analysis of the optimizer and parallel execution performance.

Bremsstrahlung contribution to the X‐ray spectrum in coupled photon–electron transport

Secondary electrons produced by Compton scattering and photoelectric effect contribute to the photon field through conversion mechanisms like bremsstrahlung and inner‐shell impact ionization (ISII). Because electrons interact continuously, the solution of the coupled transport problem is complex and time consuming. For this reason, photon transport codes frequently neglect the effects due to secondary electrons. Both of these contributions have been computed by means of the ad hoc code KERNEL that uses the Monte Carlo code PENELOPE specific for coupled transport. The correction on the intensity of the characteristic lines due to ISII was treated in a recent paper of our group. This paper adds the continuous contribution to the radiation field due to bremsstrahlung by secondary electrons. The bremsstrahlung emission is studied in terms of angle, space, and energy. The continuous contribution is stored in a data library for selected photon source energies in the interval 1–150 keV and for all the elements Z = 1–92. For intermediate source energies, the single element contribution is obtained by interpolating the data library. An example is presented on how to use the data library to include bremsstrahlung in the simulation of a synchrotron experiment. Copyright © 2015 John Wiley & Sons, Ltd.

A parameter-free dynamic alternative to hyper-viscosity for coupled transport equations: Application to the simulation of 3D squall lines using spectral elements

The stabilization of high order spectral elements to solve the transport equations for tracers in the atmosphere remains an active topic of research among atmospheric modelers. This paper builds on our previous work on variational multiscale stabilization (VMS) and discontinuity capturing (DC) (Marras et al. (2012) [7]) and shows the applicability of VMS+DC to realistic atmospheric problems that involve physics coupling with phase change in the simulation of 3D deep convection. We show that the VMS+DC approach is a robust technique that can damp the high order modes characterizing the spectral element solution of complex coupled transport problems. The method has important properties that techniques of more common use often lack: 1) it is free of a user-defined parameter, 2) it is anisotropic in that it only acts along the flow direction, 3) it is numerically consistent, and 4) it can improve the monotonicity of high-order spectral elements. The proposed method is assessed by comparing the results against those obtained with a fourth-order hyper-viscosity programmed in the same code. The main conclusion that arises is that tuning can be fully avoided without loss of accuracy if the dissipative scheme is properly designed. Finally, the cost of parallel communication is that of a second order operator which means that fewer communications are required by VMS+DC than by a hyper-viscosity method; fewer communications translate into a faster and more scalable code, which is of vital importance as we approach the exascale range of computing.

Multiscale Simulation of Electro-Chemo-Mechanical Coupling Behavior of PEN Structure under SOFC Operation

Numerical simulations are performed to characterize the micro- and macro-scale aspects of the electro-chemo-mechanical coupling behavior of a positive-electrolyte-negative (PEN) structure under SOFC operation. The mathematical homogenization method is applied to evaluate the macroscopic material properties of porous electrodes by performing the corresponding microscopic analyses. In particular, the potential transfer conditions at pore surfaces and triple-phase boundaries are homogenized to be source terms in the macroscopic electron-ion coupled transport problem. A case study is conducted to identify the major source of generation and evolution of cracks running through a disc-shaped cell. In this context, we are concerned especially with the effects of the radius of the cell, the thickness of an electrolyte and the profile of temperature's in-plane distribution on the macroscopic tensile circumferential stress distributions.

Amplified Electrokinetic Response by Concentration Polarization near Nanofluidic Channel

Ion concentration polarization is the fundamental transport phenomenon that occurs near ion-selective membranes, but this important membrane phenomenon has been poorly understood due to theoretical and experimental challenges. Here, we report the first direct measurements of detailed flow and electric potential profiles within and near the depletion region. This work is an important step toward a full characterization of this coupled transport problem. Using microfabricated electrodes integrated with the microfluidic device, we measured and confirmed that the electric field inside an ion depletion region is amplified more than 30-fold compared to outside of the depletion zone due to the highly nonuniform ion concentration distribution along the microchannel. As a result, the electrokinetic motion of both fluid (electroosmosis) and particle (electrophoresis) was significantly amplified. The detailed flow profile within the depletion zone was also measured for the first time by optically tracking photobleached neutral dye molecules. We further showed that the amplified electrokinetic flows generated in this device may be used as a field-controlled, microfluidic fluid pump and switch.

Analysis of coupled electron and mass transport in the gas diffusion layer of a PEM fuel cell

A numerical investigation of the coupled electrical conduction and mass diffusion in the cathodic GDL of a PEMFC is performed using 2D simulations. The current density on the GDL/catalyst layer interface, which constitutes one of the boundary conditions for the GDL domain and reflects the activation overpotential in the catalyst layer and the ohmic loss in the membrane, is solved iteratively using a novel numerical algorithm. A parametric study is performed to investigate the effects on current density distribution of various operating conditions such as oxygen concentration and membrane resistance, and of design factors such as GDL geometry, anisotropic transport properties, and deformation under the land area due to compression. The results show that the current density distribution under the land area can be dominated by either electron transport or mass transport, depending on the operating regime. The analysis of the in-plane current density gradients shows the contributions due to electrical conduction, oxygen diffusion and membrane resistance in an explicit form. The analysis also provides guidance for the scaling of the coupled transport problem.

A new unified a posteriori error estimator for adaptive finite element analysis of coupled transport problems

In this study, a new error estimator for coupled transport equations has been developed and successfully implemented. The error norm, based on the definition of the energy norm for the system of coupled equations, is evaluated and used in the process of error estimation and calculation of the sizes of the elements in the adapted mesh. A new adaptive strategy for transient problems was also implemented. The performance of the proposed methodology is evaluated by applying it to selected examples. The results showed that the proposed error estimator is suitable for this type of analysis. The adaptive strategy utilized has proved to be efficient, avoiding unnecessary remeshings.

Effect of Viscosity on Membrane Fluxes in Cross-Flow Ultrafiltration

Abstract For practical applications of ultrafiltration (UF), an estimation of membrane fluxes under various operational conditions is very important. This study analyzed concentration polarization (CP) as a coupled transport problem with concentration-dependent solute viscosity. Besides the effects of variable viscosity, the model includes the effects of solute osmotic pressure, solute rejection at the membrane surface, and the axial pressure drop. This provides a fundamental understanding of the effects of various operating parameters on concentration polarization and transmembrane flux. A finite-difference solution of the transport equations is presented to model the concentration polarization in a thin-channel UF system. Simulation results for ultrafiltration of Dextran T-70 show that concentration-dependent solute viscosity adversely affects the transmembrane flux and needs to be carefully considered in modeling concentration polarization in membrane filtration.

Critical assessment of the operator-splitting technique in solving the advection-dispersion-reaction equation: 2. Monod kinetics and coupled transport

In the first manuscript of this two-part series, the behavior of the inherent time-lag error in the operator-splitting technique has been discussed. However, the discussion has been limited to the advection-dispersion-reaction equation with first-order kinetics. In this manuscript, the discussion is extended to address the applicability of the operator-splitting technique in solving the advection-dispersion-reaction equation with Monod kinetics. The discussion also considers the two-species coupled transport problem. The results of the analysis show that the behavior of the time-lag error causing a mass balance error is rather similar to those observed with first-order kinetics. The time-lag error directly depends on the reaction rate, and hence, affects the oxygen equation due to the high rate of oxygen consumption. Also, the alternate operator-splitting scheme shows a greater accuracy compared to the normal operator-splitting technique. Upon observing such similarities, a concept of equivalent first-order reaction rate is derived. The equivalent reaction rate has been found to be extremely useful for predicting the time-lag error of the single- and two-species mass transport with Monod kinetics using the result of the first-order reaction problems obtained in the first manuscript.

Quasi-steady-state strategy for numerical simulation of geothermal circulation in hot dry rock fractures

The solving of non-steady-state, non-linear, coupled transport problems often requires an immense amount of numerical calculations. Therefore, alternative computation strategies that provide reasonable accuracy are proposed to keep the numerical calculations within acceptable bounds. If transient effects are negligible and/or their time dependence is known, the model equations can be solved directly for any time. It should be possible to reduce drastically the number of calculations for such quasi-steady-state problems because results can be obtained immediately for the time of interest without carrying out the entire non-steady-state computations. Success of this strategy depends on how far one can guarantee numerical stability, especially if non-linear effects become dominant.