Precipitation-induced filament pattern of injected fluid controlled by a structured cell

Mixing of two fluids can lead to the formation of a precipitate. If one of the fluids is injected into a confined space filled with the other, then a created precipitate disrupts the flow locally and forms complex spatiotemporal patterns. The relevance of controlling these patterns has been highlighted in the engineering and geological contexts. Here, we show that such injection patterns can be controlled consistently by injection rate and obstacles. Our experimental results revealed filament patterns for high-injection and low-reaction rates, and the injection rate can control the number of active filaments. Furthermore, appropriately spaced obstacles in the cells can straighten the motion of the advancing tip of the filament. A mathematical model based on a moving boundary adopting the effect of precipitation reproduced the phase diagram and the straight motion of filaments in structured cells. Our study clarifies the impact of the nonlinear permeability response on the precipitate density and that of the obstacles in the surrounding medium on the motion of the injected fluid with precipitation.

Light-modulated colour transformation in highly intertwined vertically growing silver tungstate tubes

Achieving control over growth kinetics in chemical garden architectures is challenging due to the nonequilibrium conditions. In this study, we demonstrate the vertical growth of silver tungstate chemical garden tubes under both illuminated and dark conditions, a phenomenon not observed in a comparable silver-based system, specifically silver silicate, under light exposure. Physicochemical factors, viz. thermo chemical radius of the tungstate anion, its density-buoyancy relation, the osmotic pressure gradient, and the hydration enthalpy, contributed to the tube appearance in silver tungstate even in light. Tubes grown in light illumination were greyish black, while dark-grown tubes were creamy white, and both tubes appeared twisted and highly intertwined. The colour of the as obtained silver tungstate tubes could be transformed via exposure to light. In the presence of a strong oxidizing agent, the growing tubes retain the original creamy white colour even under illumination. Colour transformation in chemical garden tubes has not yet been observed, and this report could lead the way.

Synthesis and composition modification of precipitate tubes in a confined flow reactor

Precipitation reactions coupled to various transport phenomena, such as flow or diffusion, lead to the formation of different spatial gradients which can be influenced by tuning the experimental parameters (e.g., reactant concentration, flow rate, reactor geometry, etc.). Thereby it gives us the opportunity to change the micro and macrostructure of the products. Herein, we investigate the precipitate tube formation in a flow-driven system applying a horizontal confined geometry for individual and composite alkaline earth metal (Mg(II), Ca(II), Sr(II), and Ba(II))-carbonate systems. First we attempted to achieve tube-like structures in each reactive system by increasing the reactant concentrations. It is found that the precipitate tubes are not present in the magnesium-carbonate system even at extremely high concentrations. Therefore, we doped the magnesium solution with other alkaline earth metal ions, which resulted in the desired precipitate patterns. Besides the macroscopic characteristics, the microstructure of the crystals (morphology, crystal phase, size, and composition) could also be modified by combining the ions and varying their concentration ratio. In addition, by varying the relative concentration of the alkaline earth metal cations, separated and composite crystals could also be produced as different extrema. These were spatially isolated due to the reactor geometry, and thus the products, which contain the metal ions either homogeneously or individually, can be easily separated from each other.

Comparative Evaluation of Chemical Garden Growth Techniques

Chemical gardens are an exciting area of self-organized precipitation structures that form nano- and micro-sized structures in different shapes. This field has attracted great interest from researchers due to the specific characteristics and potential applications of these structures. Today, research on chemical gardens has provided deeper information regarding the formation mechanisms of these structures, and several techniques have been developed for chemical garden growth. However, they all show different growth patterns and lead to the formation of structures with a variety of morphological, chemical, or physical properties. This study aimed to evaluate the effects of different production techniques on chemical garden growth, taking into consideration the growth patterns, morphology, microstructure, and chemical composition. The chemical garden structures obtained in seed and injection experiments, two common methods, showed highly similar surface structures, void formation, and chemical composition. The membrane growth method has a small number of applications; thus, it was comprehensively evaluated to add new insights to the existing limited data. It produced the most stable and standard structures in a flat sheet-like shape and showed different morphologies than those observed in other two methods. Overall, this study presented significant results about the effect of growth techniques on chemical garden structures and similar systems.

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.

Shape Evolution of Precipitate Membranes in Flow Systems

Chemical gardens are macroscopic structures that form when a salt seed is submerged in an alkaline solution. Their thin precipitate membranes separate the reactant partners and slow down the approach toward equilibrium. During this stage, a gradual thickening occurs, which is driven by steep cross-membrane gradients and governed by selective ion transport. We study these growth dynamics in microfluidic channels for the case of Ni(OH)₂ membranes. Fast flowing reactant solutions create thickening membranes of a nearly constant width along the channel, whereas slow flows produce wedge-shaped structures that fail to grow along their downstream end. The overall dynamics and shapes are caused by the competition of reactant consumption and transport replenishment. They are reproduced quantitatively by a two-variable reaction-diffusion-advection model which provides kinetic insights into the growth of precipitate membranes.

Downward fingering accompanies upward tube growth in a chemical garden grown in a vertical confined geometry

Chemical gardens are self-assembled structures of mineral precipitates enabled by semi-permeable membranes. To explore the effects of gravity on the formation of chemical gardens, we have studied chemical gardens grown from cobalt chloride pellets and aqueous sodium silicate solution in a vertical Hele-Shaw cell. Through photography, we have observed and quantitatively analysed upward growing tubes and downward growing fingers. The latter were not seen in previous experimental studies involving similar physicochemical systems in 3-dimensional or horizontal confined geometry. To better understand the results, further studies of flow patterns, buoyancy forces, and growth dynamics under schlieren optics have been carried out, together with characterisation of the precipitates with scanning electron microscopy and X-ray diffractometry. In addition to an ascending flow and the resulting precipitation of tubular filaments, a previously not reported descending flow has been observed which, under some conditions, is accompanied by precipitation of solid fingering structures. We conclude that the physics of both the ascending and descending flows are shaped by buoyancy, together with osmosis and chemical reaction. The existence of the descending flow might highlight a limitation in current experimental methods for growing chemical gardens under gravity, where seeds are typically not suspended in the middle of the solution and are confined by the bottom of the vessel.

Archimedean Spirals Form at Low Flow Rates in Confined Chemical Gardens

We describe and study the formation of confined chemical garden patterns. At low flow rates of injection of cobalt chloride solution into a Hele-Shaw cell filled with sodium silicate, the precipitate forms with a thin filament wrapping around an expanding "candy floss" structure. The result is the formation of an Archimedean spiral structure. We model the growth of the structure mathematically. We estimate the effective density of the precipitate and calculate the membrane permeability. We set the results within the context of recent experimental and modeling work on confined chemical garden filaments.

Hydrodynamic Fingering Induced by Gel Film Formation in Miscible Fluid Systems: An Experimental and Mathematical Study

Hydrodynamic fingering induced by gel formation shares common features with growing biofilms, bacterial colonies, and the instability of a confined chemical garden. Fluid displacement with gel formation is also essential in various engineering applications, including CO2 leakage remediation from storage reservoirs and enhanced oil recovery. We conducted Hele-Shaw cell displacement experiments for a miscible fluid system using skim milk and aqueous citric acid solution. This study aimed to investigate the effects of gel film formation on the fingering instability of a miscible fluid system and develop a mathematical model of the sequential growth of gel film formation at the fingertip. We found that the gel film formation thickens with time, resulting in instability at the interface. A distinctive fingering pattern, resembling tentacles, appears where miscibility is suppressed, and the growth of the finger is localized at the fingertip. The finger width remains constant with increasing flow rate, whereas the number of fingers increases linearly before the fingers merge. The gap width significantly limits the finger width. Finally, a mathematical model of sequential film thickness growth for a bubble-like fingertip structure was developed. This model is based upon the interplay between the diffusion of citric acid through the existing gel film formation and elongation of the fingertip. The model provides an understanding of the fundamental mechanism of the growth of the bubble-like fingertip.

Filament dynamics in vertical confined chemical gardens

When confined to a Hele-Shaw cell, chemical gardens can grow as filaments, narrow structures with an erratic and tortuous trajectory. In this work, the methodology applied to studies with horizontal Hele-Shaw cells is adapted to a vertical configuration, thus introducing the effect of buoyancy into the system. The motion of a single filament tip is modeled by taking into account its internal pressure and the variation of the concentration of precipitate that constitutes the chemical garden membrane. While the model shows good agreement with the results, it also suggests that the concentration of the host solution of sodium silicate also plays a role in the growth of the structures despite being in stoichiometric excess.

Formation and growth of lithium phosphate chemical gardens

We show that a chemical garden can be developed from an alkaline metal precipitate using a flow-driven setup. By injecting sodium phosphate solution into lithium chloride solution from below, a liquid jet appears, on which a precipitate grows forming a structure resembling a hydrothermal vent. The precipitate column continuously builds upward until a maximum height is reached. The vertical growth then significantly slows down while the tube diameter still increases. The analysis of the growth profiles has revealed a linear dependence of volume growth rate on the injection rate, hence yielding a universal growth profile. The expansion in diameter, localized at the tip of the structure, scales with a power law suggesting that the phenomenon is controlled by both diffusion and convection.

Controlled self-assembly of chemical gardens enables fabrication of heterogeneous chemobrionic materials

Chemical gardens are an example of a chemobrionic system that typically result in abiotic macro-, micro- and nano- material architectures, with formation driven by complex out-of-equilibrium reaction mechanisms. From a technological perspective, controlling chemobrionic processes may hold great promise for the creation of novel, compositionally diverse and ultimately, useful materials and devices. In this work, we engineer an innovative custom-built liquid exchange unit that enables us to control the formation of tubular chemical garden structures grown from the interface between calcium loaded hydrogel and phosphate solution. We show that systematic displacement of phosphate solution with water (H₂O) can halt self-assembly, precisely control tube height and purify structures in situ. Furthermore, we demonstrate the fabrication of a heterogeneous chemobrionic composite material composed of aligned, high-aspect ratio calcium phosphate channels running through an otherwise dense matrix of poly(2-hydroxyethyl methacrylate) (pHEMA). Given that the principles we derive can be broadly applied to potentially control various chemobrionic systems, this work paves the way for fabricating multifunctional materials that may hold great potential in a variety of application areas, such as regenerative medicine, catalysis and microfluidics.

Anomalous patterns of Saffman-Taylor fingering instability during a metastable phase separation

Phase separation is important in biology, biochemistry, industry, and other areas and is divided into two types: a spinodal decomposition type and a nucleation and growth type. The spinodal decomposition type phase separation occurs under the thermodynamically unstable conditions, and the nucleation and growth type phase separation occurs under thermodynamically metastable conditions. On the other hand, when a less viscous fluid displaces a more viscous one in porous media, the interface of the two fluids becomes hydrodynamically unstable and forms a finger-like pattern. The coupling of the hydrodynamic instability with the thermodynamic instability has been studied. It is reported that the hydrodynamic instability under thermodynamically unstable conditions, where spinodal decomposition type phase separation occurs, creates multiple moving droplets with a radius of 3-4 mm because of the spontaneous convection induced by the Korteweg force, which is driven by a compositional gradient during phase separation. However, the hydrodynamic instability under metastable conditions, where the phase separation of nucleation and growth type occurs, is still unrevealed. In this study, we applied fingering instability (hydrodynamic instability) under the metastable conditions, where the patterns are changed from fingering or droplets to anomalous patterns such as tip-widening or needle-like (top-pointed) fingering patterns when the initial concentration is metastable, which is considered near a binodal curve. These patterns are ubiquitous in nature, similar to dendrite crystals (snowflakes) or our body's cells. Thus, the patterns created can be controlled through hydrodynamic conditions such as the injection flow and thermodynamic conditions such as spinodal decomposition (thermodynamically unstable conditions) and metastable conditions.

Filament dynamics in planar chemical gardens

Filaments in a planar chemical garden grow following tortuous, erratic paths. We show from statistical mechanics that this scaling results from a self-organized dispersion mechanism. Effective diffusivities as high as 10-5 m2 s-1 are measured in 2D laboratory experiments. This efficient transport is four orders of magnitude larger than molecular diffusion in a liquid, and ensures widespread contact and exchange between fluids in the chemical-garden structure and its surrounding environment.

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.

The impact of reaction rate on the formation of flow-driven confined precipitate patterns

The evolution of different confined precipitation patterns is determined by the ratio of the chemical and hydrodynamic time scales.

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.

Earth's earliest and deepest purported fossils may be iron-mineralized chemical gardens

Recognizing fossil microorganisms is essential to the study of life's origin and evolution and to the ongoing search for life on Mars. Purported fossil microbes in ancient rocks include common assemblages of iron-mineral filaments and tubes. Recently, such assemblages have been interpreted to represent Earth's oldest body fossils, Earth's oldest fossil fungi, and Earth's best analogues for fossils that might form in the basaltic Martian subsurface. Many of these putative fossils exhibit hollow circular cross-sections, lifelike (non-crystallographic, constant-thickness, and bifurcate) branching, anastomosis, nestedness within ‘sheaths’, and other features interpreted as strong evidence for a biological origin, since no abiotic process consistent with the composition of the filaments has been shown to produce these specific lifelike features either in nature or in the laboratory. Here, I show experimentally that abiotic chemical gardening can mimic such purported fossils in both morphology and composition. In particular, chemical gardens meet morphological criteria previously proposed to establish biogenicity, while also producing the precursors to the iron minerals most commonly constitutive of filaments in the rock record. Chemical gardening is likely to occur in nature. Such microstructures should therefore not be assumed to represent fossil microbes without independent corroborating evidence.

Magnetic-Field-Manipulated Growth of Flow-Driven Precipitate Membrane Tubes

Chemobrionics is an emerging scientific field focusing on the coupling of chemical reactions and different forms of motion, that is, transport processes. Numerous phenomena appearing in various gradient fields, for example, pH, concentration, temperature, and so on, are thoroughly investigated to mimic living systems in which spatial separation plays a major role in proper functioning. In this context, chemical garden experiments have received increased attention because they inherently involve membrane formation and various transport processes. In this work, a noninvasive external magnetic field was applied to gain control over the directionality of membrane structures obtained by injecting one reactant solution into the other in a three-dimensional domain. The geometry of the resulted patterns was quantitatively characterized as a function of the injection rate and the magnitude of magnetic induction. The magnetic field was proven to influence the microstructure of precipitate tubes by diminishing spatial defects.

High-speed tracking of fast chemical precipitations

Heterogeneous reactions taking place in the aqueous phase bear significant importance both in applied and fundamental research. Among others, producing solid catalysts, crystallizing biomorphs or pharmaceutically relevant polymorphs, and yielding bottom-up synthesised precipitate structures are prominent examples. To achieve a better control on product properties, reaction kinetics and mechanisms must be taken into account especially in dynamic systems where transport processes are coupled to chemistry. Since the characteristic time scale of numerous precipitation reactions falls below 1 s within the relevant concentration range, unique experimental protocols are needed. Herein we present a high-speed camera supported experimental procedure capable of determining such characteristic time scales in the range of 10 ms to 1 s. The method is validated both experimentally and by performing 3D hydrodynamic 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.

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.

Filament dynamics in confined chemical gardens and in filiform corrosion

Once rescaled by the preferred wavenumber ω* of the curvature power spectrum, both filiform corrosion and chemical garden filaments display similar dynamics.

Flow instabilities due to the interfacial formation of surfactant-fatty acid material in a Hele-Shaw cell

We present an experimental study of pattern formation during the penetration of an aqueous surfactant solution into a liquid fatty acid in a Hele-Shaw cell. When a solution of the cationic surfactant cetylpyridinium chloride is injected into oleic acid, a wide variety of fingering patterns are observed as a function of surfactant concentration and flow rate, which are strikingly different than the classic Saffman-Taylor (ST) instability. We observe evidence of interfacial material forming between the two liquids, causing these instabilities. Moreover, the number of fingers decreases with increasing flow rate Q, while the average finger width increases with Q, both trends opposite to the ST case. Bulk rheology on related mixtures indicates a gel-like state. Comparison of experiments using other oils indicates the importance of pH and the carboxylic head group in the formation of the surfactant-fatty acid material.

Realtime Observation of Diffusing Elements in a Chemical Garden

The chemical garden, which has been known as the plant-growth-like diffusion of chemicals since the 17th century, has regained much attention in recent years. Significant progress in research not only promoted the understanding of the phenomenon itself but also suggested a prospective method of synthesizing new materials via the chemical garden route. It is extremely important to introduce new characterization techniques to provide more insights into chemical diffusion and element redistribution during the reaction process. The present article describes some successful applications of the realtime X-ray fluorescence (XRF) movie technique to observe each diffusing element. The protagonist of the movie is a chemical garden reaction growing from a seed of calcium salt and ferrous salt mixtures. Through observation by an XRF movie, it has been found that the growth rate and diffusion behavior of calcium and iron are very different. This results in a macroscopic diversity of the element composition in the finally precipitated chemical garden structures. The present research not only reconfirms the potential of fabricating gradient composites through the self-organized chemical garden approach but also demonstrates the attractive achievements of XRF movies. It has been demonstrated that the XRF movie is an indispensable realtime characterization technique for the study of chemical garden reactions or even other related diffusions.

Camphor-Engine-Driven Micro-Boat Guides Evolution of Chemical Gardens

A micro-boat self-propelled by a camphor engine, carrying seed crystals of FeCl₃, promoted the evolution of chemical gardens when placed on the surface of aqueous solutions of potassium hexacyanoferrate. Inverse chemical gardens (growing from the top downward) were observed. The growth of the “inverse” chemical gardens was slowed down with an increase in the concentration of the potassium hexacyanoferrate. Heliciform precipitates were formed under the self-propulsion of the micro-boat. A phenomenological model, satisfactorily describing the self-locomotion of the camphor-driven micro-boat, is introduced and checked.

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.

Chemo-hydrodynamic patterns in porous media

Chemical reactions can interplay with hydrodynamic flows to generate chemo-hydrodynamic instabilities affecting the spatio-temporal evolution of the concentration of the chemicals. We review here such instabilities for porous media flows. We describe the influence of chemical reactions on viscous fingering, buoyancy-driven fingering in miscible systems, convective dissolution as well as precipitation patterns. Implications for environmental systems are discussed.This article is part of the themed issue 'Energy and the subsurface'.

Fluid-flow-templated self-assembly of calcium carbonate tubes in the laboratory and in biomineralization: The tubules of the watering-pot shells, Clavagelloidea

We show with laboratory experiments that self-assembled mineral tube formation involving precipitation around a templating jet of fluid - a mechanism well-known in the physical sciences from the tubular growth of so-called chemical gardens - functions with carbonates, and we analyse the microstructures and compositions of the precipitates. We propose that there should exist biological examples of fluid-flow-templated tubes formed from carbonates. We present observational and theoretical modelling evidence that the complex structure of biomineral calcium carbonate tubules that forms the 'rose' of the watering-pot shells, Clavagelloidea, may be an instance of this mechanism in biomineralization. We suggest that this is an example of self-organization and self-assembly processes in biomineralization, and that such a mechanism is of interest for the production of tubes as a synthetic biomaterial.

STATEMENT OF SIGNIFICANCE

The work discussed in the manuscript concerns the self-assembly of calcium carbonate micro-tubes and nano-tubes under conditions of fluid flow together with chemical reaction. We present the results of laboratory experiments on tube self-assembly together with theoretical calculations. We show how nature may already be making use of this process in molluscan biomineralization of the so-called watering-pot shells, and we propose that we may be able to take advantage of the formation mechanism to produce synthetic biocompatible micro- and nano-tubes.

Wavy membranes and the growth rate of a planar chemical garden: Enhanced diffusion and bioenergetics

To model ion transport across protocell membranes in Hadean hydrothermal vents, we consider both theoretically and experimentally the planar growth of a precipitate membrane formed at the interface between two parallel fluid streams in a 2D microfluidic reactor. The growth rate of the precipitate is found to be proportional to the square root of time, which is characteristic of diffusive transport. However, the dependence of the growth rate on the concentrations of hydroxide and metal ions is approximately linear and quadratic, respectively. We show that such a difference in ionic transport dynamics arises from the enhanced transport of metal ions across a thin gel layer present at the surface of the precipitate. The fluctuations in transverse velocity in this wavy porous gel layer allow an enhanced transport of the cation, so that the effective diffusivity is about one order of magnitude higher than that expected from molecular diffusion alone. Our theoretical predictions are in excellent agreement with our laboratory measurements of the growth of a manganese hydroxide membrane in a microfluidic channel, and this enhanced transport is thought to have been needed to account for the bioenergetics of the first single-celled organisms.

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.

Fingering dynamics driven by a precipitation reaction: Nonlinear simulations

A fingering instability can develop at the interface between two fluids when the more mobile fluid is injected into the less-mobile one. For example, viscous fingering appears when a less viscous (i.e., more mobile) fluid displaces a more viscous (and hence less mobile) one in a porous medium. Fingering can also be due to a local change in mobility arising when a precipitation reaction locally decreases the permeability. We numerically analyze the properties of the related precipitation fingering patterns occurring when an A+B→C chemical reaction takes place, where A and B are reactants in solution and C is a solid product. We show that, similarly to reactive viscous fingering patterns, the precipitation fingering structures differ depending on whether A invades B or vice versa. This asymmetry can be related to underlying asymmetric concentration profiles developing when diffusion coefficients or initial concentrations of the reactants differ. In contrast to reactive viscous fingering, however, precipitation fingering patterns appear at shorter time scales than viscous fingers because the solid product C has a diffusivity tending to zero which destabilizes the displacement. Moreover, contrary to reactive viscous fingering, the system is more unstable with regard to precipitation fingering when the high-concentrated solution is injected into the low-concentrated one or when the faster diffusing reactant displaces the slower diffusing one.

Growing a Chemical Garden at the Air-Fluid Interface

Here we grow chemical gardens using a novel, quasi two-dimensional, experimental configuration. Buoyant calcium chloride solution is pumped onto the surface of sodium silicate solution. The solutions react to form a precipitation structure on the surface. Initially, an open channel forms that grows in a spiral. This transitions to radially spreading and branching fingers, which typically oscillate in transparency as they grow. The depth of the radial spreading, and the fractal dimension of the finger growth, are surprisingly robust, being insensitive to the pumping rate. The curvature of the channel membrane and the depth of the radially spreading solution can be explained in terms of the solution densities and the interfacial tension across the semipermeable membrane. These unusually beautiful structures provide new insights into the dynamics of precipitation structures and may lead to new technologies where structures are grown instead of assembled.

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.

Periodic Precipitation Patterns during Coalescence of Reacting Sessile Droplets

The coalescence behavior of two sessile drops that contain different chemical reactants (cerium nitrate and oxalic acid) and its impact on the formation of the solid precipitate (cerium oxalate) are investigated. With different liquids, the surface tension difference in the moment of drop-drop contact can induce a Marangoni flow. This flow can strongly influence the drop-drop coalescence behavior and thus, with reacting liquids, also the reaction and its products (through the liquid mixing). In our study we find three distinctly different coalescence behaviors ("barrier", "intermediate", "noncoalescence"), in contrast to only two behaviors that were observed in the case of nonreacting liquids. The amount of liquid mixing and thus the precipitation rate are very different for the three cases. The "intermediate" case, which exhibits the strongest mixing, has been studied in more detail. For high oxalic acid concentrations, mainly needle-like aggregates, and for low concentrations, mainly flower-like precipitate morphologies are obtained. In a transition range of the oxalic acid concentration, both morphologies can be produced. With the applied coalescence conditions, the different aggregate particles are arranged and fixed in a precipitate raft in a regular, periodic line pattern. This confirms the drop-drop coalescence configuration as a convection-reaction-diffusion system, which can have stationary as well as oscillatory behavior depending on the system parameters.

Chemical gardens without silica: the formation of pure metal hydroxide tubes

Contrary to common belief, hollow precipitation tubes form in the absence of silicate if sodium hydroxide solution is injected into solutions of various metal ions. In many cases, the growth speed has a power law dependence on the flow rate. For vanadyl, we observe damped oscillations in the tube height.