Dilute species transport in generalized Newtonian fluids (GNFs) is typically described using explanatory empirical approaches assuming a traditional Fickian form, which is an approach that lacks predictive ability for systems and conditions not specifically investigated. Dilute species transport was investigated for a wide range of Cross and Carreau fluids flowing through a set of monodisperse and polydisperse sphere pack porous media. Both microscale and macroscale simulations were performed to demonstrate that GNF fluid flow can be predicted based upon Newtonian characterization of the media and rheological characterization of the fluid. Dilute species transport was shown to have a Fickian limit with dispersivity dependent on the porous media, fluid properties, and the flow rate in a nonlinear fashion. Dimensionless analysis and symbolic regression was used to deduce an explanatory and predictive function to describe dispersivity in terms of relevant system properties, enabling prediction of dilute species transport for GNFs flowing through porous media that does not require any non-Newtonian experiments or parameter estimation.

Molecular-scale simulations of pressure-driven transport through polyamide domains were performed. Analysis revealed the importance of non-equilibrium molecular distributions and the existence of connected pathways from feed to permeate at all times. Individual pathways were found to be ephemeral with an observed upper bound persistence time of 1.75 ns.

Transport during flow of generalized Newtonian fluids (GNFs) appears often in systems that can be treated in a simplified form as either cylindrical tubes or slit openings between parallel plates. Based on the pioneering work of Taylor, analytical solutions for transport in these simplified systems were derived generally. This includes analytical solutions for advection dominated transport, as well as a computation of the enhanced molecular diffusion coefficient in low Peclet number systems. These generally derived solutions were developed without assuming any specific fluid rheology and can predict transport when only a steady velocity field is known. The newly derived general solutions for species transport were applied to Cross and Carreau model fluids using a semi-analytical solution for velocity of these fluids. The semi-analytical solutions derived herein were compared to microscale simulations and showed agreement with the numerical error of those simulations. Because of the general nature of the transport solutions derived herein, these solutions can be applied to other non-Newtonian fluids, such as viscoelastic or viscoplastic fluids, as a straightforward extension of this work.

Molecular-scale simulations of pressure-driven transport through polyamide nanogaps (5–100 Å) were performed to investigate fundamental transport mechanisms. Results show that transport in nanogaps ≤ 10 Å is always subdiffusive, but superdiffusive transport was observed in nanogaps ≥ 20 Å. Near typical operating pressures for applications (Δp = 100 atm), only the 100 Å nanogap exhibited superdiffusive behavior. Since openings in common membrane materials are typically <20 Å, results indicate that subdiffusive to diffusive transport dominates for typical applications, such as reverse osmosis.

Porous medium researchers and practitioners usually rely on macroscale models to represent systems of concern. While macroscale models have often been formulated phenomenologically, the thermodynamically constrained averaging theory (TCAT) provides a means to rigorously derive closed macroscale models for a wide variety of systems. However, the TCAT approach can appear overwhelmingly complicated, the entry point for use unclear, and the advantages not self-evident. In response to these perceived shortcomings, we demonstrate several aspects of TCAT macroscale model formulations for single-fluid flow in a porous medium. Specifically, we illustrate an essentially exact macroscale model derived from a rigorous connection across scales, show how an entropy inequality can be used to derive an approximate macroscale form for the Stokes-flow regime, and examine models in the transition flow regime. A special emphasis is placed upon leveraging available results, and other application opportunities are summarized.

Comments are provided on the recent paper by Ebadi et al. (2024) which demonstrates that the formulated model that was solved contains misconceptions or errors that render the work unsuitable for describing the evolution of interfacial areas in two -fluid porous medium systems. The need for kinematic equations is described and components of a theoretically consistent approach are summarized.

The traditional equations for describing open channel flow have appeared in the literature for decades and are so ingrained that they might seem to be statements of settled science. Careful derivations that detail assumptions and approximations relied upon in the formulation are mostly absent. We derive mass, momentum, and energy equations by averaging their small-scale counterparts and formulate forms that are Galilean invariant as required by continuum mechanics. Averaging is over a time increment and a spatial region in a single step, clarifying the need for closure relations. The derivation leads to the Boussinesq tensor and Coriolis vector as rigorous generalizations of the Boussinesq and Coriolis coefficients typically proposed. Examples are provided for the computation of these coefficients from published data. The approach employed here can be extended to systems such as pipe flow or shallow water equations, and the Galilean invariant forms are also suitable for entropy generation analyses.

Carreau fluids occur routinely in porous medium systems for a range of applications, and the dependence of the viscosity for such fluids on the rate of strain tensor poses challenges to modeling at an averaged macroscale. Traditional approaches for macroscale modeling such flows have relied upon experimental observations of flows for generalized Newtonian fluids (GNFs) and a phenomenological approach referred to herein as the shift factor. A recently developed approach based upon averaging conservation and thermodynamic equations from the microscale for Cross model GNFs is extended to the case of Carreau fluids and shown to predict the flow through both isotropic and anisotropic media accurately without the need for GNF-flow experiments. The model is formulated in terms of rheological properties, a standard Newtonian resistance tensor, and a length-scale tensor, which does require estimation. An approach based upon measures of the morphology and topology of the pore space is developed to approximate this length-scale tensor. Thus, this work provides the missing components needed to predict Carreau GNF macroscale flow with only rheological information for the fluid and analysis of the pore morphology and topology independent of any fluid flow experiments. Accuracy of predictions based upon this approach is quantified, and extension to other GNFs is straightforward.

Magnetic beads have been widely and successfully used for target enrichment in life science assays. There exists a large variety of commercially available magnetic beads functionalized for specific target capture, as well as options that enable simple surface modifications for custom applications. While magnetic beads are ideal for use in the macrofluidic context of typical laboratory workflows, their performance drops in microfluidic contexts, such as consumables for point-of-care diagnostics. A primary cause is the diffusion-limited analyte transport in these low Reynolds number environments. A new method, BeadPak, uses magnetically actuatable microposts to enhance analyte transport, improving yield of the desired targets. Critical parameters were defined for the operation of this technology and its performance characterized in canonical life-science assays. BeadPak achieved up to 1000× faster capture than a microfluidic chamber relying on diffusion alone, enabled a significant specimen concentration via volume reduction, and demonstrated compatibility with a range of biological specimens. The results shown in this work can be extended to other systems that utilize magnetic beads for target capture, concentration, and/or purification.

The authors assess the current status of scholarly publishing and reach the conclusion that the current situation is both in a state of flux and not sustainable. While such an assessment is becoming increasingly well understood, a solution to the problems seemingly does not exist. What even embodies an improvement to the current state of scholarly publishing depends on one's perspective. The authors approach the problem from the perspective of the main producers and consumers of scholarly knowledge-academic and governmental research institutions. From this perspective, they define a set of objectives for scholarly publishing and dissemination of published works, and they assess the challenges with current approaches to meeting these objectives for commercial publishers, professional organization publishers, and academic press publishers. Based on this analysis, the authors propose a new model for academic publishing that might help achieve the stated objectives. The academic research community alliance model suggested is based on the scholarly community taking on the responsibilities of peer review, article production, and knowledge dissemination while acting in an altruistic way of doing so. The proposed approach is described in detail, and both challenges and potential solutions to the impediments to implementing this model are explored. Finally, the authors report on initial efforts to build support for the proposed model, which suggests that meaningful progress on this difficult problem is possible.

Understanding the dynamics of wet granular materials is important for a range of applications, including levee safety, beach erosion, and scour around hydraulic structures. Several continuum models have been proposed recently to model the relevant processes for these applications at computationally tractable resolutions, which were derived using mixture theory approaches for granular and aerated flows. The thermodynamically constrained averaging theory is used to formulate a framework for three-phase flow models involving mechanistic conservation and balance principles for a set of entities consisting of phases, interfaces, and a common curve. The derived entropy inequality provides a basis for formulating permissibility conditions on closure relations. An example is provided showing how the entropy inequality derived in this work can be used to examine the closure relations in existing models. Results from this example show that this existing model violates entropy permissibility conditions. Several possible extensions and uses of this foundational work are summarized.

Introduction: Evidence suggests that gender may influence many aspects of type 2 diabetes (T2DM) self-management (SM) and we posit that limited English language–proficient Latinx immigrants face additional challenges. Methods: Instruments and semi-structured interviews were used to examine gender differences on health literacy, diabetes knowledge, health-promoting behaviors, diabetes, eating and exercise self-efficacy (SE), and T2DM SM practices among a cohort of limited English language–proficient Latinx immigrants. Statistical and qualitative analysis procedures were performed comparing males and females. Results: Thirty persons participated. Males tended to be older, have higher educational achievement, and more financial security than females. Physiologic measures tended worse among female participants. Health literacy and exercise SE scores were similar, but females scored lower on Eating and Diabetes SE. Forty-seven percent ( n= 9) of the women reported a history of gestational diabetes mellitus and a majority of men ( n = 7) cited difficulty with excessive alcohol. Consumption: Males appeared to receive more SM support compared to females. Females more frequently noted how family obligations and a lack of support impeded their SM. Work environments negatively influenced SM practices. Conclusion: Men and women have unique SM challenges and as such require individualized strategies and support to improve T2DM management.

Arsenic (As), chromium (Cr), and vanadium (V) are naturally occurring, redox-active elements that can become human health hazards when they are released from aquifer substrates into groundwater that may be used as domestic or irrigation source. As such, there is a need to develop incisive conceptual and quantitative models of the geochemistry and transport of potentially hazardous elements to assess risk and facilitate interventions. However, understanding the complexity and heterogeneous subsurface environment requires knowledge of solid-phase minerals, hydrologic movement, aerobic and anaerobic environments, microbial interactions, and complicated chemical kinetics. Here, we examine the relevant geochemical and hydrological information about the release and transport of potentially hazardous geogenic contaminants, specifically As, Cr, and V, as well as the potential challenges in developing a robust understanding of their behavior in the subsurface. We explore the development of geochemical models, illustrate how they can be utilized, and describe the gaps in knowledge that exist in translating subsurface conditions into numerical models, as well as provide an outlook on future research needs and developments.

Sharp-front problems arising from equations that tend toward a hyperbolic limit occur routinely in modeling transport phenomena in porous medium systems. Numerical methods to approximate hyperbolic conservation equations are mature for finite volume methods. However, irregularly shaped domains make finite element methods (FEMs) an attractive approach for many subsurface problems. For conforming FEM approaches, sharp fronts continue to pose a computational challenge. We build on recent work to develop and evaluate an entropy viscosity approach. Recent theoretical advancements have resulted in the formulation of entropy inequality equations for many porous medium problems, which we use to compute a physically-based entropy production rate for both linear and nonlinear species transport problems. The entropy production rate is in turn used to add dissipation to the approximation of the hyperbolic operator using an entropy-viscosity formulation. We demonstrate how existing, problem-specific theoretical results can be leveraged in a generic and efficient numerical method to create problem-specific dissipation functions.

The growth and treatment of tumors is an important problem to society that involves the manifestation of cellular phenomena at length scales on the order of centimeters. Continuum mechanical approaches are being increasingly used to model tumors at the largest length scales of concern. The issue of how to best connect such descriptions to smaller-scale descriptions remains open. We formulate a framework to derive macroscale models of tumor behavior using the thermodynamically constrained averaging theory (TCAT), which provides a firm connection with the microscale and constraints on permissible forms of closure relations. We build on developments in the porous medium mechanics literature to formulate fundamental entropy inequality expressions for a general class of three-phase, compositional models at the macroscale. We use the general framework derived to formulate two classes of models, a two-phase model and a three-phase model. The general TCAT framework derived forms the basis for a wide range of potential models of varying sophistication, which can be derived, approximated, and applied to understand not only tumor growth but also the effectiveness of various treatment modalities.

The molecular-scale morphology and topology of polyamide composite membranes determine the performance characteristics of these materials. However, molecular-scale simulations are computationally expensive and morphological and topological characterization of molecular structures are not well developed. Molecular dynamics simulation and analysis methods for the polymerization, hydration, and quantification of polyamide membrane structures were developed and compared to elucidate efficient approaches for producing and analyzing the polyamide structure. Polymerization simulations that omitted the reaction-phase solvent did not change the observed hydration, pore-size distribution, or water permeability, while improving the simulation efficiency. Pre-insertion of water into the aggregate pores (radius ≈ 4 Å) of dry domains enabled shorter hydration simulations and improved simulation scaling, without altering pore structure, properties, or performance. Medial axis and Minkowski functional methods were implemented to identify permeation pathways and quantify the polyamide morphology and topology, respectively. Better agreement between simulations and experimentally observed systems was accomplished by increasing the domain size rather than increasing the number of ensemble realizations of smaller systems. The largest domain hydrated was an order of magnitude larger by volume than the largest domain previously reported. This work identifies methods that can enable more efficient and meaningful fundamental modeling of membrane materials.

Single-fluid-phase porous medium systems are typically modeled at an averaged length scale termed the macroscale, and Darcy's law is typically relied upon as an approximation of the momentum equation under Stokes flow conditions. Standard approaches for modeling macroscale single-fluid-phase flow of generalized Newtonian fluids (GNFs) extend the standard Newtonian model based upon Darcy's law using an effective viscosity and assuming that the intrinsic permeability is invariant with respect to fluid properties. This approach results in a need to perform an experiment for a non-Newtonian fluid, the introduction of effective parameters that are not tied to known microscale physics, and uncertainty regarding the dependencies of the fitted empirical parameter on system properties. We use the thermodynamically constrained averaging theory (TCAT) to examine the formulation and closure of a macroscale model for GNF flow that is consistent with microscale conservation principles and the second law of thermodynamics. A direct connection between microscale and macroscale quantities is used to formulate an expression for interphase momentum transfer for GNF flow in porous medium systems. Darcy's law is shown to approximate momentum transfer from the fluid phase to the solid phase. Momentum transfer is found to depend on the viscosity at the solid surface, which is only invariant for Newtonian flow. TCAT is used to derive a macroscale equation for the hydraulic resistance based on accessible fluid and solid properties. This hydraulic resistance may be used in the same way that hydraulic conductivity is typically used to model flow at the macroscale, and it includes parameters that can be calculated a priori, without the need to carry out microscale simulations, or experiments, for any GNF. The TCAT approach is validated for four model isotropic and anisotropic media and five Cross-model fluids. The traditional shift factor and effective viscosity are related to the newly derived TCAT model, shedding new light on this common empirical approach. The results from this work form a basis for the modeling of GNF flow in porous medium systems under Stokes flow, which is predictive given the rheological properties of the GNF and the resistance observed for Newtonian flow.

This paper presents a spatially and temporally adaptive boundary condition to specify the volumetric flux for lattice Boltzmann methods. The approach differs from standard velocity boundary conditions because it allows the velocity to vary over the boundary region provided that the total flux through the boundary satisfies a prescribed constraint, which is a typical scenario for laboratory experimental studies. This condition allows the boundary pressure to adjust dynamically to yield a specified boundary flow rate as a means to avoid unphysical mismatch between the boundary velocity and the interior flow field that can arise when a constant velocity boundary condition is applied. The method is validated for simulation of one- and two-fluid flow in complex materials, with conditions determined to match typical experiments used to study flow in porous media.