Solute transport within porous biofilms: diffusion or dispersion?

Many microorganisms live within surface-associated consortia, termed biofilms, that can form intricate porous structures interspersed with a network of fluid channels. In such systems, transport phenomena, including flow and advection, regulate various aspects of cell behaviour by controllling nutrient supply, evacuation of waste products and permeation of antimicrobial agents. This study presents multiscale analysis of solute transport in these porous biofilms. We start our analysis with a channel-scale description of mass transport and use the method of volume averaging to derive a set of homogenized equations at the biofilmscale. We show that solute transport may be described via two coupled partial differential equations for the averaged concentrations, or telegrapher’s equations. These models are particularly relevant for chemical species, such as some antimicrobial agents, that penetrate cell clusters very slowly. In most cases, especially for nutrients, solute penetration is faster, and transport can be described via an advection-dispersion equation. In this simpler case, the effective diffusion is characterised by a second-order tensor whose components depend on: (1) the topology of the channels’ network; (2) the solute’s diffusion coefficients in the fluid and the cell clusters; (3) hydrodynamic dispersion effects; and (4) an additional dispersion term intrinsic to the two-phase configuration. Although solute transport in biofilms is commonly thought to be diffusion-dominated, this analysis shows that dispersion effects may significantly contribute to transport

Convergence of the Generalized Volume Averaging Method on a Convection-Diffusion Problem: A Spectral Perspective

A mixed formulation is proposed and analyzed mathematically for coupled convection-diffusion in heterogeneous medias. Transfer in solid parts driven by pure diffusion is coupled with convection-diffusion transfer in fluid parts. This study is carried out for translation-invariant geometries (general infinite cylinders) and unidirectional flows. This formulation brings to the fore a new convection-diffusion operator, the properties of which are mathematically studied: its symmetry is first shown using a suitable scalar product. It is proved to be self-adjoint with compact resolvent on a simple Hilbert space. Its spectrum is characterized as being composed of a double set of eigenvalues: one converging towards −∞ and the other towards +∞, thus resulting in a nonsectorial operator. The decomposition of the convection-diffusion problem into a generalized eigenvalue problem permits the reduction of the original three-dimensional problem into a two-dimensional one. Despite the operator being nonsectorial, a complete solution on the infinite cylinder, associated to a step change of the wall temperature at the origin, is exhibited with the help of the operator’s two sets of eigenvalues/eigenfunctions. On the computational point of view, a mixed variational formulation is naturally associated to the eigenvalue problem. Numerical illustrations are provided for axisymmetrical situations, the convergence of which is found to be consistent with the numerical discretization

Modelling In-situ Upgrading of Heavy Oil Using Operator Splitting Methods

Heavy oil and oil sands are important hydrocarbon resources that account for over 10 trillion barrels (Meyer et al., 2007), nearly three times the conventional oil in place in the world. There are huge, wellknown resources of heavy oil, extra-heavy oil, and bitumen in Canada, Venezuela, Russia, the USA and many other countries. The oil sands of Alberta alone contain over two trillion barrels of oil. In Canada, approximately 20% of oil production is from heavy oil and oil sand resources

Modelling Heat and Mass Transfer in Porous Material during Pyrolysis using Operator Splitting and Dimensionless Analysis

Dimensionless analysis isused to improve the computational performance when using operator splitting methods to model the heat and mass transfer during pyrolysis. The specific examples investigated are thermal decomposition of polymer composite when used as heat shields during space-craft re-entry or for rocket nozzle’s protection, and the In-Situ Upgrading (ISU) of solid oil shale by subsurface pyrolysis to form liquid oil and gas. ISU is a very challenging process to model numerically because a large number of components need to be modelled using a system of equations that are both highly non-linear and strongly coupled. Inspectional Analysis is used to determine the minimum number of dimensionless groups that can be used to describe the process. This set of dimensionless numbers is then reduced to those that are key to describing the system behaviour. This is achieved byperforming a sensitivity study using Experimental Design torank the numbers in terms of their impact on system behaviour. The numbers are then sub-divided into those of primary importance, secondary importance and those which are insignificant based on the t-value of their effect, which is compared to the Bonferroni corrected t-limit and Lenth’s margin of error. Finally we use the sub-set of the most significant numbers to improve the stability and performance when numerically modelling this process. A range of operator splitting techniques is evaluated including the Sequential Split Operator (SSO), the Iterative Split Operator (ISO) and theAlternating Split Operator (ASO

Scaling heat and mass flow through porous media during pyrolysis.

The modelling of heat and mass flow through porous media in the presence of pyrolysis is complex because various physical and chemical phenomena need to be represented. In addition to the transport of heat by conduction and convection, and the change of properties with varying pressure and temperature, these processes involve transport of mass by convection, evaporation, condensation and pyrolysis chemical reactions. Examples of such processes include pyrolysis of wood, thermal decomposition of polymer composite and in situ upgrading of heavy oil and oil shale. The behaviours of these systems are difficult to predict as relatively small changes in the material composition can significantly change the thermophysical properties. Scaling reduces the number of parameters in the problem statement and quantifies the relative importance of the various dimensional parameters such as permeability, thermal conduction and reaction constants. This paper uses inspectional analysis to determine the minimum number of dimensionless scaling groups that describe the decomposition of a solid porous material into a gas in one dimension. Experimental design is then used to rank these scaling groups in terms of their importance in describing the outcome of two example processes: the thermal decomposition of heat shields formed from polymer composites and the in situ upgrading of heavy oils and oil shales. A sensitivity analysis is used to divide these groups into three sets (primary, secondary and insignificant), thus identifying the combinations of solid and fluid properties that have the most impact on the performance of the different processes

Improvement of Neuroenergetics by Hypertonic Lactate Therapy in Patients with Traumatic Brain Injury Is Dependent on Baseline Cerebral Lactate/Pyruvate Ratio.

Energy dysfunction is associated with worse prognosis after traumatic brain injury (TBI). Recent data suggest that hypertonic sodium lactate infusion (HL) improves energy metabolism after TBI. Here, we specifically examined whether the efficacy of HL (3h infusion, 30-40 μmol/kg/min) in improving brain energetics (using cerebral microdialysis [CMD] glucose as a main therapeutic end-point) was dependent on baseline cerebral metabolic state (assessed by CMD lactate/pyruvate ratio [LPR]) and cerebral blood flow (CBF, measured with perfusion computed tomography [PCT]). Using a prospective cohort of 24 severe TBI patients, we found CMD glucose increase during HL was significant only in the subgroup of patients with elevated CMD LPR >25 (n = 13; +0.13 [95% confidence interval (CI) 0.08-0.19] mmol/L, p < 0.001; vs. +0.04 [-0.05-0.13] in those with normal LPR, p = 0.33, mixed-effects model). In contrast, CMD glucose increase was independent from baseline CBF (coefficient +0.13 [0.04-0.21] mmol/L when global CBF was <32.5 mL/100 g/min vs. +0.09 [0.04-0.14] mmol/L at normal CBF, both p < 0.005) and systemic glucose. Our data suggest that improvement of brain energetics upon HL seems predominantly dependent on baseline cerebral metabolic state and support the concept that CMD LPR - rather than CBF - could be used as a diagnostic indication for systemic lactate supplementation following TBI

Hydrodynamic dispersion within porous biofilms

Many microorganisms live within surface-associated consortia, termed biofilms, that can form intricate porous structures interspersed with a network of fluid channels. In such systems, transport phenomena, including flow and advection, regulate various aspects of cell behavior by controlling nutrient supply, evacuation of waste products, and permeation of antimicrobial agents. This study presents multiscale analysis of solute transport in these porous biofilms. We start our analysis with a channel-scale description of mass transport and use the method of volume averaging to derive a set of homogenized equations at the biofilm-scale in the case where the width of the channels is significantly smaller than the thickness of the biofilm. We show that solute transport may be described via two coupled partial differential equations or telegrapher's equations for the averaged concentrations. These models are particularly relevant for chemicals, such as some antimicrobial agents, that penetrate cell clusters very slowly. In most cases, especially for nutrients, solute penetration is faster, and transport can be described via an advection-dispersion equation. In this simpler case, the effective diffusion is characterized by a second-order tensor whose components depend on (1) the topology of the channels' network; (2) the solute's diffusion coefficients in the fluid and the cell clusters; (3) hydrodynamic dispersion effects; and (4) an additional dispersion term intrinsic to the two-phase configuration. Although solute transport in biofilms is commonly thought to be diffusion dominated, this analysis shows that hydrodynamic dispersion effects may significantly contribute to transport

Association of Trace Element Levels with Outcomes in Critically Ill COVID-19 Patients.

The primary objective of this study was to compare the plasma levels of copper, selenium, and zinc between critically ill COVID-19 patients and less severe COVID-19 patients. The secondary objective was to investigate the association of these trace element levels with adverse outcomes, including the duration of mechanical ventilation, occurrence of septic shock, and mortality in critically ill COVID-19 patients. All COVID-19 patients admitted to the ICU of the Geneva University Hospitals between 9 March 2020 and 19 May 2020 were included in the study. Plasma levels of copper, selenium and zinc were measured on admission to the ICU and compared with levels measured in COVID-19 patients hospitalized on the ward and in non-hospitalized COVID-19 patients. To analyze the association of trace elements with clinical outcomes, multivariate linear and logistic regressions were performed. Patients in the ICU had significantly lower levels of selenium and zinc and higher levels of copper compared to COVID-19 patients hospitalized on the ward and in non-hospitalized COVID-19 patients. In ICU patients, lower zinc levels tended to be associated with more septic shock and increased mortality compared to those with higher zinc levels (p = 0.07 for both). Having lower copper or selenium levels was associated with a longer time under mechanical ventilation (p = 0.01 and 0.04, respectively). These associations remained significant in multivariate analyses (p = 0.03 for copper and p = 0.04 for selenium). These data support the need for interventional studies to assess the potential benefit of zinc, copper and selenium supplementation in severe COVID-19 patients

Homogenization via formal multiscale asymptotics and volume averaging: How do the two techniques compare?

A wide variety of techniques have been developed to homogenize transport equations in multiscale and multiphase systems. This has yielded a rich and diverse field, but has also resulted in the emergence of isolated scientific communities and disconnected bodies of literature. Here, our goal is to bridge the gap between formal multiscale asymptotics and the volume averaging theory. We illustrate the methodologies via a simple example application describing a parabolic transport problem and, in so doing, compare their respective advantages/disadvantages from a practical point of view. This paper is also intended as a pedagogical guide and may be viewed as a tutorial for graduate students as we provide historical context, detail subtle points with great care, and reference many fundamental works