Morphology control by flow-driven self-organizing precipitation

Pattern selection by material aging: Modeling chemical gardens in two and three dimensions

Chemical gardens are complex, often macroscopic, structures formed by precipitation reactions. Their thin walls compartmentalize the system and adjust in size and shape if the volume of the interior reactant solution is increased by osmosis or active injection. Spatial confinement to a thin layer is known to result in various patterns including self-extending filaments and flower-like patterns organized around a continuous, expanding front. Here, we describe a cellular automaton model for this type of self-organization, in which each lattice site is occupied by one of the two reactants or the precipitate. Reactant injection causes the random replacement of precipitate and generates an expanding near-circular precipitate front. If this process includes an age bias favoring the replacement of fresh precipitate, thin-walled filaments arise and grow-like in the experiments-at the leading tip. In addition, the inclusion of a buoyancy effect allows the model to capture various branched and unbranched chemical garden shapes in two and three dimensions. Our results provide a model of chemical garden structures and highlight the importance of temporal changes in the self-healing membrane material.

Reaction-diffusion phenomena in antagonistic bipolar diffusion fields

Operating natural or artificial chemical systems requires nonequilibrium conditions under which temporal and spatial control of the process is realizable. Open reaction-diffusion systems provide a general way to create such conditions. A key issue is the proper design of reactors in which the nonequilibrium conditions can be maintained. A hydrogel with flow-through channels is a simple, flexible, and easy-to-make device in which chemical reactions are performed in the diffusion field of localized separated sources of reactants. Two reactants separated in two channels create a bipolar antagonistic diffusion field, where the reaction intermediates firmly separate in space. Numerical simulations and corresponding experiments are performed to present this inhomogeneous diffusion field-induced chemical separation in sequential reactions. A remarkable result of this bipolar spatial control is localized wave phenomena in a nonlinear activatory-inhibitory reaction. These findings may help design functioning artificial nonequilibrium systems with the desired spatial separation of chemicals.

Nucleation kinetics of lithium phosphate precipitation

Fourth-order kinetics arises from the consecutive complexation leading to precipitation.

Flow-driven crystal growth of lithium phosphate in microchannels

Flow-driven asymmetric growth of lithium phosphate in the presence of concentration gradients in a microchannel.

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.

Polymorph Selection of ROY by Flow-Driven Crystallization

The selection of polymorphs of the organic compound 5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile, ROY, is studied experimentally in the confined space between two horizontal glass plates when an acetone solution of ROY of variable concentration is injected at a variable flow rate into water. Depending on the local concentration within the radial flow, a polymorph selection is observed such that red prisms are favored close to the injection center while yellow needles are the preferred polymorph close to the edge of the injected ROY domain. At larger flow rates, a buoyancy-driven instability induces stripes at the outer edge of the displacement pattern, in which specific polymorphs are seen to crystallize. Our results evidence the possibility of a selection of ROY polymorph structures in out-of-equilibrium flow conditions.

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.

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.

Osmotic contribution to the flow-driven tube formation of copper–phosphate and copper–silicate chemical gardens

A flow-driven technique allowing osmosis reveals the capacities of gradient-applying methods to form membranes with tailor-made inner and smoother outer surfaces.

Macroscale precipitation kinetics: towards complex precipitate structure design

Producing self-assembled inorganic precipitate micro- and macro-structures with tailored properties may pave the way for new possibilities in, e.g., materials science and the pharmaceutical industry.

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

The dynamics of A+B→C fronts is analyzed theoretically in the presence of passive advection when A is injected radially into B at a constant inlet flow rate Q. We compute the long-time evolution of the front position, r_{f}, of its width, w, and of the local production rate R of the product C at r_{f}. We show that, while advection does not change the well-known scaling exponents of the evolution of corresponding reaction-diffusion fronts, their dynamics is however significantly influenced by the injection. In particular, the total amount of product varies as Q^{-1/2} for a given volume of injected reactant and the front position as Q^{1/2} for a given time, paving the way to a flow control of the amount and spatial distribution of the reaction front product. This control strategy compares well with calcium carbonate precipitation experiments for which the amount of solid product generated in flow conditions at fixed concentrations of reactants and the front position can be tuned by varying the flow rate.

Self-organization in precipitation reactions far from the equilibrium

Far from the thermodynamic equilibrium, many precipitation reactions create complex product structures with fascinating features caused by their unusual origins. Unlike the dissipative patterns in other self-organizing reactions, these features can be permanent, suggesting potential applications in materials science and engineering. We review four distinct classes of precipitation reactions, describe similarities and differences, and discuss related challenges for theoretical studies. These classes are hollow micro- and macrotubes in chemical gardens, polycrystalline silica carbonate aggregates (biomorphs), Liesegang bands, and propagating precipitation-dissolution fronts. In many cases, these systems show intricate structural hierarchies that span from the nanometer scale into the macroscopic world. We summarize recent experimental progress that often involves growth under tightly regulated conditions by means of wet stamping, holographic heating, and controlled electric, magnetic, or pH perturbations. In this research field, progress requires mechanistic insights that cannot be derived from experiments alone. We discuss how mesoscopic aspects of the product structures can be modeled by reaction-transport equations and suggest important targets for future studies that should also include materials features at the nanoscale.

Flow-driven pattern formation in the calcium-oxalate system

The precipitation reaction of calcium oxalate is studied experimentally in the presence of spatial gradients by controlled flow of calcium into oxalate solution. The density difference between the reactants leads to strong convection in the form of a gravity current that drives the spatiotemporal pattern formation. The phase diagram of the system is constructed, the evolving precipitate patterns are analyzed and quantitatively characterized by their diameters and the average height of the gravity flow. The compact structures of calcium oxalate monohydrate produced at low flow rates are replaced by the thermodynamically unstable calcium oxalate dihydrate favored in the presence of a strong gravity current.

Flow-driven control of calcium carbonate precipitation patterns in a confined geometry

Upon injection of an aqueous solution of carbonate into a solution of calcium ions in the confined geometry of a Hele-Shaw cell, various calcium carbonate precipitation patterns are observed.

Flow-driven morphology control in the cobalt–oxalate system

The presence of fluid flow by maintaining the density gradient and controlling the flow rate provides a simple method to modify the microstructure of cobalt oxalate.