Generalized multirate models for conjugate transfer in heterogeneous materials

We propose a novel macroscopic model for conjugate heat and mass transfer between a mobile region, where advective transport is significant, and a set of immobile regions where diffusive transport is dominant. Applying a spatial averaging operator to the microscopic equations, we obtain a multicontinuum model, where an equation for the average concentration in the mobile region is coupled with a set of equations for the average concentrations in the immobile regions. Subsequently, by mean of spectral decomposition, we derive a set of equations that can be viewed as a generalization of the multirate mass transfer (MRMT) model. This new formulation does not require any assumption on local equilibrium or geometry. We then show that the MRMT can be obtained as the leading order approximation, when the mobile concentration is in local equilibrium. The new generalized multirate transfer model (GMRT) has the advantage of providing a direct method for calculating the model coefficients for immobile regions of arbitrary shapes, through the solution of appropriate microscale cell problems. An important finding is that a simple rescaling or reparametrization of the transfer rate coefficient (and thus, the memory function) is not sufficient to account for the flow field in the mobile region and the resulting nonuniformity of the concentration at the interfaces between mobile and immobile regions

clotFoam: An Open-Source Framework to Simulate Blood Clot Formation Under Flow

Blood clotting involves the coupled processes of platelet aggregation and coagulation. Simulating clotting under flow in complex geometries is challenging due to multiple temporal and spatial scales and high computational cost. clotFoam is an open-source software developed in OpenFOAM that employs a continuum model of platelet advection, diffusion, and aggregation in a dynamic fluid environment and a simplified coagulation model with proteins that advect, diffuse, and react within the fluid and with wall-bound species through reactive boundary conditions. Our framework provides the foundation on which one can build more complex models and perform reliable simulations in almost any computational domain.Comment: Repository: https://github.com/d-montgomery/clotFoa

Macroscopic models for filtration and heterogeneous reactions in porous media

Derivation of macroscopic models for advection-diffusion processes in the presence of dominant heterogeneous (e.g., surface) reactions using homogenisation theory or volume averaging is often deemed unfeasible (Valdés-Parada et al., 2011; Battiato and Tartakovsky, 2011a) due to the strong coupling between scales that characterise such systems. In this work, we show how the upscaling can be carried out by applying and extending the methods presented in Allaire and Raphael (2007), Mauri (1991). The approach relies on the decomposition of the microscale concentration into a reactive component, given by the eigenfunction of the advection-diffusion operator, the associated eigenvalue which represents the macroscopic effective reaction rate, and a non-reactive component. The latter can be then upscaled with a two-scale asymptotic expansion and the final macroscopic equation is obtained for the leading order. The same method can also be used to overcome another classical assumption, namely of non solenoidal velocity fields, such as the case of deposition of charged colloidal particles driven by electrostatic potential forces. The whole upscaling procedure, which consists in solving three cell problems, is implemented for arbitrarily complex two- and three-dimensional periodic structures using the open-source finite volume library OpenFOAM®. We provide details on the implementation and test the methodology for two-dimensional periodic arrays of spheres, and we compare the results against fully resolved numerical simulations, demonstrating the accuracy and generality of the upscaling approach. The effective velocity, dispersion and reaction coefficients are obtained for a wide range of Péclet and surface Damköhler numbers, and for Coulomb-like forces to the grains. Noticeably, all the effective transport parameters are significantly different from the non-reactive (conserved scalar) case, as the heterogeneity introduced by the reaction strongly affects the micro-scale profiles

Electrochemical transport modelling and open-source simulation of pore-scale solid-liquid systems

The modelling of electrokinetic flows is a critical aspect spanning many industrial applications and research fields. This has introduced great demand in flexible numerical solvers to describe these flows. The underlying phenomena is microscopic, non-linear, and often involving multiple domains. Therefore often model assumptions and several numerical approximations are introduced to simplify the solution. In this work we present a multi-domain multi-species electrokinetic flow model including complex interface and bulk reactions. After a dimensional analysis and an overview of some limiting regimes, we present a set of general-purpose finite-volume solvers, based on OpenFOAM(R), capable of describing an arbitrary number of electrochemical species over multiple interacting (solid or fluid) domains. We provide a verification of the computational approach for several cases involving electrokinetic flows, reactions between species, and complex geometries. We first present three one-dimensional verification test-cases for single- and multi-domain cases and then show the capability of the solver to tackle two- and three-dimensional electrically driven flows and ionic transport in random porous structures. The purpose of this work is to lay the foundation of a general-purpose open-source flexible modelling tool for problems in electrochemistry and electrokinetics at different scales

The sensitivity of filtered Two Fluid Models to the underlying resolved simulation setup

Eulerian-Eulerian modelling based on the Kinetic Theory of Granular Flow has proven to be a promising tool for investigating the hydrodynamic and reactive behaviour inside fluidized beds. The primary limitation of this approach is the very fine grid size necessary to fully resolve the transient solid structures that are typical of fluidized bed reactors. It therefore remains impractical to simulate industrial scale fluidized bed reactors using resolved Two Fluid Model (TFM) simulations. For this reason, there is currently widespread interest in developing sub-grid (filtered) models that allow accurate simulations at coarser grids by correcting for the effects of unresolved solid structures. However, little attention has been paid to the importance of the choice of the underlying TFM closures during the derivation of the filtered models. This paper follows a similar approach to an establish filtered TFM (1) to derive sub-grid closures for the interphase momentum exchange , solids viscosity and solids pressure in 2D periodic simulations. These corrections are obtained for different particle-particle restitution coefficients, frictional pressure models and drag models as a function of the particle phase volume fraction and the filter size. This reveals at which values of the markers the individual resolved TFM model choices have significant effects on the final expressions derived for filtered TFMs. Based on these findings suggestions are made regarding the derivation of new filtered TFMs and the use of the existing models. 1. Y. Igci and S. Sundaresan. Constitutive Models for Filtered Two-Fluid Models of Fluidized Gas–Particle Flows. Ind. Eng. Chem. Res., 50: 13190-13201, 2013

Computational framework for complex flow and transport in heterogeneous porous media

We present a flexible scalable open-source computational framework, named SECUReFoam, based on the finite-volume library OpenFOAM®, for flow and transport problems in highly heterogeneous geological media and other porous materials. The framework combines geostatistical pre- and post-processing tools with specialised partial differential equations solvers. Random fields, for permeability and other physical properties, are generated by means of continuous or thresholded Gaussian random fields with various covariance/variogram functions. The generation process is based on an explicit spectral Fourier decomposition of the field which, although more computationally intensive than Fast Fourier Transform methods, allows a more flexible choice of statistical parameters and can be used for general geometries and grids. Flow and transport equations are solved for single-phase and variable density problems, with and without the Boussinesq approximation, and for a wide range of density, viscosity, and dispersion models, including dual-continuum (dual permeability or dual porosity) formulations. The mathematical models are here presented in details and the numerical strategies to deal with heterogeneities, equation coupling, and boundary conditions are discussed and benchmarked for the heterogeneous Henry and Horton–Rogers–Lapwood problems, and other test cases. We show that our framework is capable of dealing with large permeability variances, viscous instabilities, and large-scale three-dimensional transport problems