Flow Control of A+B→C Fronts by Radial Injection

Deciphering immunodiffusion: In silico optimization for faster protein diagnostics

Immunodiffusion tests offer a simple yet powerful method for detecting protein antigens, but their long assay times hinder clinical utility. We unveil the complex interplay of parameters governing this process using finite element simulations. By meticulously validating our model against real-world data, we elucidate how initial concentrations and diffusivities of antigen and antibody shape the intensity, size, and formation time of the precipitin ring. Our key innovation lies in employing phase diagram analysis to map the combined effects of these parameters on assay performance. This framework enables rapid in silico parameter estimation, paving the way for the design of novel immunodiffusion assays with drastically reduced assay times. The presented approach holds immense potential for optimizing protein diagnostics for fast and reliable diagnostics.

Unraveling dispersion and buoyancy dynamics around radial A + B → C reaction fronts: microgravity experiments and numerical simulations

Radial Reaction-Diffusion-Advection (RDA) fronts for A + B → C reactions find wide applications in many natural and technological processes. In liquid solutions, their dynamics can be perturbed by buoyancy-driven convection due to concentration gradients across the front. In this context, we conducted microgravity experiments aboard a sounding rocket, in order to disentangle dispersion and buoyancy effects in such fronts. We studied experimentally the dynamics due to the radial injection of A in B at a constant flow rate, in absence of gravity. We compared the obtained results with numerical simulations using either radial one- (1D) or two-dimensional (2D) models. We showed that gravitational acceleration significantly distorts the RDA dynamics on ground, even if the vertical dimension of the reactor and density gradients are small. We further quantified the importance of such buoyant phenomena. Finally, we showed that 1D numerical models with radial symmetry fail to predict the dynamics of RDA fronts in thicker geometries, while 2D radial models are necessary to accurately describe RDA dynamics where Taylor-Aris dispersion is significant.

The critical mixed transport process in remediation agent radial injection into contaminated aquifer plumes

Accurately depicting the subsurface mixing of radially injected remediation agents with contaminated plumes remains paramount yet challenging for understanding and simulating reactive transport. To address this, the present research employed the mixing dynamics of a potassium permanganate plume injected into a pre-existing contaminated plume. Through combining colour deconvolution and thresholding, we effectively isolated local mixing values within the Gaussian annular narrow mixing zone from the noise of mixed double-plume images. Key findings revealed increasing injection rate promotes plume mixing while adding xanthan gum to increase fluid viscosity moderates interface mixing, reducing mixing zone width by 25.3% and 37.4% for 100 mg/L and 400 mg/L xanthan gum, respectively. Grain size is pivotal, with a 30% increase in mixing areas observed in coarse-grained sands over medium-grained sands. Balancing sufficient mixing and preventing contaminated plume growth is essential for effective remediation. Injection rates below 5 mL/min may suppress contaminated plume expansion, albeit at the possible cost of protracted remediation durations. For the attainment of optimal remediation, it's imperative to harmonize robust mixing processes with the mitigation of contaminated plume expansion - a balance that adding xanthan gum during the initial injection phase seems poised to achieve (xanthan gum optimized the average mixing index (AMI)). These findings provide valuable insights into groundwater plume mixing, supporting effective remediation strategies.

Diffusion in liquid mixtures

The understanding of transport and mixing in fluids in the presence and in the absence of external fields and reactions represents a challenging topic of strategic relevance for space exploration. Indeed, mixing and transport of components in a fluid are especially important during long-term space missions where fuels, food and other materials, needed for the sustainability of long space travels, must be processed under microgravity conditions. So far, the processes of transport and mixing have been investigated mainly at the macroscopic and microscopic scale. Their investigation at the mesoscopic scale is becoming increasingly important for the understanding of mass transfer in confined systems, such as porous media, biological systems and microfluidic systems. Microgravity conditions will provide the opportunity to analyze the effect of external fields and reactions on optimizing mixing and transport in the absence of the convective flows induced by buoyancy on Earth. This would be of great practical applicative relevance to handle complex fluids under microgravity conditions for the processing of materials in space.

Diffusion-controlled annihilation A+B→0: Coalescence, fragmentation, and collapse of nonidentical A-particle islands submerged in the B-particle sea

We present a systematic analysis of diffusion-controlled interaction and collapse of two nonidentical spatially separated d-dimensional A-particle islands in the B-particle sea at propagation of the sharp reaction front A+B→0 at equal species diffusivities. We show that at a sufficiently large initial distance between the centers of islands 2ℓ and a relatively large initial ratio of island-to-sea concentrations, the evolution dynamics of the island-sea-island system demonstrates remarkable universality and, depending on the system dimension, is determined unambiguously by two dimensionless parameters Λ=N_{0}^{+}/N_{Ω} and q=N_{0}^{-}/N_{0}^{+}, where N_{0}^{+} and N_{0}^{-} are the initial particle numbers in the larger and smaller of the islands, respectively, and N_{Ω} is the initial number of sea particles in the volume Ω=(2ℓ)^{d}. We find that at each fixed 0<q≤1, there are threshold values Λ_{★}(q) and Λ_{s}(q)≥Λ_{★}(q) that depend on the dimension and separate the domains of individual death of each of the islands Λ<Λ_{★}(q), coalescence and subsequent fragmentation (division) of a two-centered island Λ_{★}(q)<Λ<Λ_{s}(q), and collapse of a single-centered island formed by coalescence Λ>Λ_{s}(q). We demonstrate that regardless of d, the trajectories of the island centers are determined unambiguously by the parameter q, and we reveal a detailed picture of the evolution of islands and front trajectories with an increase in Λ, focusing on the scaling laws of evolution at the final collapse stage and in the vicinity of starting coalescence and fragmentation points.

Linking mixing and flow topology in porous media: An experimental proof

Transport processes in porous media are controlled by the characteristics of the flow field which are determined by the porous material properties and the boundary conditions of the system. This work provides experimental evidence of the relation between mixing and flow field topology in porous media at the continuum scale. The setup consists of a homogeneously packed quasi-two-dimensional flow-through chamber in which transient flow conditions, dynamically controlled by two external reservoirs, impact the transport of a dissolved tracer. The experiments were performed at two different flow velocities, corresponding to Péclet numbers of 191 and 565, respectively. The model-based interpretation of the experimental results shows that high values of the effective Okubo-Weiss parameter, driven by the changes of the boundary conditions, lead to high rates of increase of the Shannon entropy of the tracer distribution and, thus, to enhanced mixing. The comparison between a hydrodynamic dispersion model and an equivalent pore diffusion model demonstrates that despite the spatial and temporal variability in the hydrodynamic dispersion coefficients, the Shannon entropy remains almost unchanged because it is controlled by the Okubo-Weiss parameter. Overall, our work demonstrates that under highly transient boundary conditions, mixing dynamics in homogeneous porous media can also display complex patterns and is controlled by the flow topology.

A bottom-up approach to construct or deconstruct a fluid instability

Fluid instabilities have been the subject of study for a long time. Despite all the extensive knowledge, they still constitute a serious challenge for many industrial applications. Here, we experimentally consider an interface between two fluids with different viscosities and analyze their relative displacement. We designed the contents of each fluid in such a way that a chemical reaction takes place at the interface and use this reaction to suppress or induce a fingering instability at will. This process describes a road map to control viscous fingering instabilities in more complex systems via interfacial chemical reactions.

Dynamics of A+B→C reaction fronts under radial advection in a Poiseuille flow

A+B→C reaction fronts describe a wide variety of natural and engineered dynamics, according to the specific nature of reactants and product. Recent works have shown that the properties of such reaction fronts depend on the system geometry, by focusing on one-dimensional plug flow radial injection. Here, we extend the theoretical formulation to radial deformation in two-dimensional systems. Specifically, we study the effect of a Poiseuille advective velocity profile on A+B→C fronts when A is injected radially into B at a constant flow rate in a confined axisymmetric system consisting of two parallel impermeable plates separated by a thin gap. We analyze the front dynamics by computing the temporal evolution of the average over the gap of the front position, the maximum production rate, and the front width. We further quantify the effects of the nonuniform flow on the total amount of product, as well as on its radial concentration profile. Through analytical and numerical analyses, we identify three distinct temporal regimes, namely (i) the early-time regime where the front dynamics is independent of the reaction, (ii) the transient regime where the front properties result from the interplay of reaction, diffusion that smooths the concentration gradients and advection, which stretches the spatial distribution of the chemicals, and (iii) the long-time regime where Taylor dispersion occurs and the system becomes equivalent to the one-dimensional plug flow case.

Enhancing the yield of calcium carbonate precipitation by obstacles in laminar flow in a confined geometry

Flow-driven precipitation experiments are performed in model porous media shaped within the confinement of a Hele-Shaw cell. Precipitation pattern formation and the yield of the reaction are investigated when borosilicate glass beads of different sizes are used in a mono-layer arrangement. The trend of the amount of precipitate produced in various porous media is estimated via visual observation. In addition, a new method is elaborated to complement such image analysis based results by titration experiments performed on gel-embedded precipitate patterns. The yield of confined porous systems is compared to experiments carried out in unsegmented reactors. It is found that the obstacles increase the amount of product and preserve its radial spatial distribution. The precipitate pattern is successfully conserved in a slightly cross-linked hydrogel matrix and its microstructure is examined using SEM. The spatial distribution of the precipitate across the cell gap is revealed using X-ray microtomography.

Highly viscous fluid displaced by a chemically controlled reactive interface

Displacement of a viscous fluid by a less viscous one is a challenging problem that usually involves the formation of interfacial digitations propagating into each one of the fluids, mixing them and preventing their normal displacement. We propose in this manuscript a protocol that is implemented via numerical simulation of the corresponding equations to improve the efficiency of the displacement. We consider a chemically active interface between the two chemically active fluids that produce a large viscosity interface that facilitates the process. All the relevant parameters of the mechanism are numerically analyzed aiming to optimize the efficiency of the method.

Oscillatory budding dynamics of a chemical garden within a co-flow of reactants

The oscillatory growth of chemical gardens is studied experimentally in the budding regime using a co-flow of two reactant solutions within a microfluidic reactor. The confined environment of the reactor tames the erratic budding growth and the oscillations leave their imprint with the formation of orderly spaced membranes on the precipitate surface. The average wavelength of the spacing between membranes, the growth velocity of the chemical garden and the oscillations period are measured as a function of the velocity of each reactant. By means of materials characterization techniques, the micro-morphology and the chemical composition of the precipitate are explored. A mathematical model is developed to explain the periodic rupture of droplets delimitated by a shell of precipitate and growing when one reactant is injected into the other. The predictions of this model are in good agreement with the experimental data.

Diffusion-controlled coalescence, fragmentation, and collapse of d-dimensional A-particle islands in the B-particle sea

We present a systematic analysis of diffusion-controlled interaction and collapse of two identical spatially separated d-dimensional A-particle islands in the B-particle sea at propagation of the sharp reaction front A+B→0 at equal species diffusivities. We show that at a sufficiently large initial distance between the centers of islands 2ℓ compared to their characteristic initial size and a relatively large initial ratio of island to sea concentrations, the evolution dynamics of the island-sea-island system is determined unambiguously by the dimensionless parameter Λ=N_{0}/N_{Ω}, where N_{0} is the initial particle number in the island and N_{Ω} is the initial number of sea particles in the volume Ω=(2ℓ)^{d}. It is established that (a) there is a d-dependent critical value Λ_{★} above which island coalescence occurs; (b) regardless of d the centers of each of the islands move toward each other along a universal trajectory merging in a united center at the d-dependent critical value Λ_{s}≥Λ_{★}; (c) in one-dimensional systems Λ_{★}=Λ_{s}, therefore, at Λ<Λ_{★} each of the islands dies individually, whereas at Λ>Λ_{★} coalescence is completed by collapse of a single-centered island in the system center; (d) in two- and three-dimensional systems in the range Λ_{★}<Λ<Λ_{s} coalescence is accompanied by subsequent fragmentation of a two-centered island and is completed by individual collapse of each of the islands. We discuss a detailed picture of coalescence, fragmentation, and collapse of islands focusing on evolution of their shape and on behavior of the relative width of the reaction front at the final collapse stage and in the vicinity of starting coalescence and fragmentation points. We demonstrate that in a wide range of parameters, the front remains sharp up to a narrow vicinity of the coalescence, fragmentation, and collapse points.

Effects of radial injection and solution thickness on the dynamics of confined A + B → C chemical fronts

The reconstructed amount of product n_C as the volume V of KSCN injected radially into Fe(NO₃)₃ increases and comparison to theory.

Confined direct and reverse chemical gardens: Influence of local flow velocity on precipitation patterns

Various cobalt silicate precipitation patterns can be observed when an aqueous solution of cobalt ions gets into contact with a solution of silicate ions upon injection of one solution into the other in the confined geometry of a Hele-Shaw cell. The properties of these precipitation patterns are studied here as a function of the injection flow rate, densities and viscosities of the solutions, and the choice of which solution is injected into the other one. Our results show that the structure of the precipitation pattern depends on the local velocity as well as on the difference in viscosities between the injected and the displaced solutions. Specifically, decreasing the injection flow rate and/or decreasing the density jump while increasing the difference in viscosities between the reactant solutions results in more circular patterns. Moreover, we show that some structures are robustly observed in given ranges of the local flow velocity in the cell. Locally, precipitation can then transition from one type of pattern to another during injection, according to that preferred structure at the given local velocity. We also show that injection of the cobalt solution into the silicate solution results in the so-called direct patterns that are different from the reverse patterns obtained when the silicate solution is injected in the solution of cobalt ions. Our results help in understanding the production of precipitate structures under nonequilibrium flow conditions.

Dynamics of A+B → C reaction fronts under radial advection in three dimensions

The dynamics of A+B→C reaction fronts is studied both analytically and numerically in three-dimensional systems when A is injected radially into B at a constant flow rate. The front dynamics is characterized in terms of the temporal evolution of the reaction front position, r_{f}, of its width, w, of the maximum local production rate, R^{max}, and of the total amount of product generated by the reaction, n_{C}. We show that r_{f}, w, and R^{max} exhibit the same temporal scalings as observed in rectilinear and two-dimensional radial geometries both in the early-time limit controlled by diffusion, and in the longer time reaction-diffusion-advection regime. However, unlike the two-dimensional cases, the three-dimensional problem admits an asymptotic stationary solution for the reactant concentration profiles where n_{C} grows linearly in time. The timescales at which the transition between the regimes arise, as well as the properties of each regime, are determined in terms of the injection flow rate and reactant initial concentration ratio.

Complex dynamics of interacting fronts in a simple A+B→C reaction-diffusion system

Pattern interaction has so far been restricted to systems with relatively complex reaction schemes, such as activator-inhibitor systems, that lead to rich spatio-temporal dynamics. Surprisingly, a simple second-order chemical reaction is capable of generating similar complex phenomena, such as attractive or repulsive interaction modes between the localized reaction zones (or fronts). We illustrate the latter statement both analytically and numerically with two initially separated A+B→C reaction-diffusion fronts when the solution of B is initially confined between two solutions of A. The nature of the front-front interaction changes from an attractive type to a repulsive one above a critical distance separating the two fronts initially. The complexity of the pattern dynamics emerges here due to finite-size effects. A scaling law relating the critical distance d_{c} above which the repulsion occurs and kinetic parameters gives insights into (i) extracting those parameters from experiments for bimolecular reactions and (ii) the control strategy of periodic patterns.

Precipitation patterns driven by gravity current

A precipitation reaction can be driven by a gravity current that spreads on the bottom as a denser fluid is injected into an initially stagnant liquid. Supersaturation and nucleation are restricted to locations where the two liquids come into contact; hence, the flow pattern governs the spatial distribution of the final product. In this numerical study, we quantitatively characterize the flow associated with the gravity current prior to the onset of nucleation and distinguish three zones where the coupling of transport processes with the reaction can take place depending on their time scales. A scaling law associated with the region of Rayleigh-Taylor instability behind the tip of the gravity current is also determined.

Viscous Fingering Induced by a pH-Sensitive Clock Reaction

A pH-changing clock chemical system, also known to induce changes in viscosity, is shown experimentally to induce a viscous fingering instability during the displacement of reactive solutions in a Hele-Shaw cell. Specifically, a low-viscosity solution of formaldehyde is displaced by a more viscous solution of sulfite and of a pH-sensitive poly(acrylic acid) polymer. The pH change triggered by the formaldehyde-sulfite clock reaction in the reactive contact zone between the two solutions affects the polymer and induces a local increase of the viscosity that destabilizes the displacement via a viscous fingering instability. The influence of changes in the chemical parameters on this fingering instability is analyzed using different techniques and the results are compared with numerical simulations.

Influence of microscopic precipitate structures on macroscopic pattern formation in reactive flows in a confined geometry

Thanks to the coupling between chemical precipitation reactions and hydrodynamics, new dynamic phenomena may be obtained and new types of materials can be synthesized.

Influence of mineralization and injection flow rate on flow patterns in three-dimensional porous media

At low flow rates, the precipitate forming at the miscible interface between two reactive solutions guides the evolution of the flow field.