Controls that expedite first passage times in disordered systems

First passage time statistics in disordered systems exhibiting scale invariance are studied widely. In particular, long trapping times in energy or entropic traps are fat-tailed distributed, which slow the overall transport process. We study the statistical properties of the first passage time of biased processes in different models, and employ the big jump principle that shows the dominance of the maximum trapping time on the first passage time. Inspired by the restart paradigm, we demonstrate that the removal of this maximum significantly expedites transport. As the disorder increases, the system enters a phase where the removal shows a dramatic effect. Our results show how we may speed up transport in strongly disordered systems exploiting scale invariance. In contrast to the disordered systems studied here, the removal principle has essentially no effect in homogeneous systems; this indicates that improving the conductance of a poorly conducting system is, theoretically, relatively easy as compared to a homogeneous system

Process-Dependent Solute Transport in Porous Media

From Springer Nature via Jisc Publications RouterHistory: received 2021-01-18, accepted 2021-07-09, registration 2021-07-13, pub-print 2021-10, online 2021-10-01, pub-electronic 2021-10-01Publication status: PublishedFunder: ISF; Grant(s): 485/16Funder: University of Manchester; Grant(s): NAFunder: British Council; Grant(s): NAAbstract: Solute transport under single-phase flow conditions in porous micromodels was studied using high-resolution optical imaging. Experiments examined loading (injection of ink-water solution into a clear water-filled micromodel) and unloading (injection of clear water into an ink-water filled micromodel). Statistically homogeneous and fine-coarse porous micromodels patterns were used. It is shown that the transport time scale during unloading is larger than that under loading, even in a micromodel with a homogeneous structure, so that larger values of the dispersion coefficient were obtained for transport during unloading. The difference between the dispersion values for unloading and loading cases decreased with an increase in the flow rate. This implies that diffusion is the key factor controlling the degree of difference between loading and unloading transport time scales, in the cases considered here. Moreover, the patterned heterogeneity micromodel, containing distinct sections of fine and coarse porous media, increased the difference between the transport time scales during loading and unloading processes. These results raise the question of whether this discrepancy in transport time scales for the same hydrodynamic conditions is observable at larger length and time scales

A continuous time random walk (CTRW) integro-differential equation with chemical interaction

A nonlocal-in-time integro-differential equation is introduced that accounts for close coupling between transport and chemical reaction terms. The structure of the equation contains these terms in a single convolution with a memory function M (t), which includes the source of non-Fickian (anomalous) behavior, within the framework of a continuous time random walk (CTRW). The interaction is non-linear and second-order, relevant for a bimolecular reaction A + B → C. The interaction term ΓPA (s, t) PB (s, t) is symmetric in the concentrations of A and B (i.e. PA and PB); thus the source terms in the equations for A, B and C are similar, but with a change in sign for that of C. Here, the chemical rate coefficient, Γ, is constant. The fully coupled equations are solved numerically using a finite element method (FEM) with a judicious representation of M (t) that eschews the need for the entire time history, instead using only values at the former time step. To begin to validate the equations, the FEM solution is compared, in lieu of experimental data, to a particle tracking method (CTRW-PT); the results from the two approaches, particularly for the C profiles, are in agreement. The FEM solution, for a range of initial and boundary conditions, can provide a good model for reactive transport in disordered media

Reactive Transport with Fluid–Solid Interactions in Dual-Porosity Media

We study pore-scale dynamics of reactive transport in heterogeneous, dual-porosity media, wherein a reactant in the invading fluid interacts chemically with the surface of the permeable grains, leading to the irreversible reaction Aaq + Bs → Caq. A microfluidic porous medium was synthesized, consisting of a single layer of hydrogel pillars (grains), chemically modified to contain immobilized enzymes on the grain surfaces. Fluorescence microscopy was used to monitor the spatiotemporal evolution of the reaction product Caq at different flow rates (Péclet values) and to characterize the impact on its transport. The experimental setup enables delineation of three key features of the temporal evolution of the reaction product within the domain: (i) the characteristic time until the rate of Caq production reaches steady state, (ii) the magnitude of the reaction rate at steady state, and (iii) the rate at which Caq is flushed from the system. These features, individually, are found to be sensitive to the value of the Péclet number, because of the relative impact of diffusion (vs advection) on the production and spatiotemporal evolution of Caq within the system. As the Péclet number increases, the production of Caq is reduced and the transport becomes more localized within the vicinity of the grains. The dual-porosity feature causes the residence time of the transported species to increase, by forming stagnant zones and diffusive-dominant regions within the flow field, thus enhancing the reaction potential of the system. Using complementary numerical simulations, we explore these effects for a wider range of Péclet and Damköhler numbers and propose nonlinear scaling laws for the key features of the temporal evolution of Caq

Global warming accelerates soil heterotrophic respiration

Carbon efflux from soils is the largest terrestrial carbon source to the atmosphere, yet it is still one of the most uncertain fluxes in the Earth’s carbon budget. A dominant component of this flux is heterotrophic respiration, influenced by several environmental factors, most notably soil temperature and moisture. Here, we develop a mechanistic model from micro to global scale to explore how changes in soil water content and temperature affect soil heterotrophic respiration. Simulations, laboratory measurements, and field observations validate the new approach. Estimates from the model show that heterotrophic respiration has been increasing since the 1980s at a rate of about 2% per decade globally. Using future projections of surface temperature and soil moisture, the model predicts a global increase of about 40% in heterotrophic respiration by the end of the century under the worst-case emission scenario, where the Arctic region is expected to experience a more than two-fold increase, driven primarily by declining soil moisture rather than temperature increase.ISSN:2041-172

Global warming accelerates soil heterotrophic respiration

Abstract Carbon efflux from soils is the largest terrestrial carbon source to the atmosphere, yet it is still one of the most uncertain fluxes in the Earth’s carbon budget. A dominant component of this flux is heterotrophic respiration, influenced by several environmental factors, most notably soil temperature and moisture. Here, we develop a mechanistic model from micro to global scale to explore how changes in soil water content and temperature affect soil heterotrophic respiration. Simulations, laboratory measurements, and field observations validate the new approach. Estimates from the model show that heterotrophic respiration has been increasing since the 1980s at a rate of about 2% per decade globally. Using future projections of surface temperature and soil moisture, the model predicts a global increase of about 40% in heterotrophic respiration by the end of the century under the worst-case emission scenario, where the Arctic region is expected to experience a more than two-fold increase, driven primarily by declining soil moisture rather than temperature increase

Process-Dependent Solute Transport in Porous Media

Solute transport under single-phase flow conditions in porous micromodels was studied using high-resolution optical imaging. Experiments examined loading (injection of ink-water solution into a clear water-filled micromodel) and unloading (injection of clear water into an ink-water filled micromodel). Statistically homogeneous and fine-coarse porous micromodels patterns were used. It is shown that the transport time scale during unloading is larger than that under loading, even in a micromodel with a homogeneous structure, so that larger values of the dispersion coefficient were obtained for transport during unloading. The difference between the dispersion values for unloading and loading cases decreased with an increase in the flow rate. This implies that diffusion is the key factor controlling the degree of difference between loading and unloading transport time scales, in the cases considered here. Moreover, the patterned heterogeneity micromodel, containing distinct sections of fine and coarse porous media, increased the difference between the transport time scales during loading and unloading processes. These results raise the question of whether this discrepancy in transport time scales for the same hydrodynamic conditions is observable at larger length and time scales.ISSN:0169-3913ISSN:1573-163