Role of Electrolyte in Liesegang Pattern Formation

Matsue, Masayo; Itatani, Masaki; Fang, Qing; Shimizu, Yushiro; Unoura, Kei; Nabika, Hideki

doi:10.1021/acs.langmuir.8b02335

Cited by 18 publications

(22 citation statements)

References 42 publications

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“…In this section we derive equations for the chemical reactions. We follow the 'nucleation and growth' model of precipitation (Matsue et al 2018) and separate the reaction into two sequential parts: in the first, two reactants come together to form an aqueous product, and the second describes the aggregation of the aqueous product into a solid precipitate. While many aqueous chemical reactions do not alter the solution volume significantly, the formation of a membrane excludes fluid volume and therefore can alter the local concentration of the dissolved species.…”

Section: Model For Chemical Reactionsmentioning

confidence: 99%

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Multiphase modelling of precipitation-induced membrane formation

et al. 2020

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We formulate a model for the dynamic growth of a membrane developing in a flow as the result of a precipitation reaction, a situation inspired by recent microfluidic experiments. The precipitating solid introduces additional forces on the fluid and eventually forms a membrane that is fixed in the flow due to adhesion with a substrate. A key challenge is that the location of the immobile membrane is unknown a priori. To model this situation, we use a multiphase framework with fluid and membrane phases; the aqueous chemicals exist as scalar fields that react within the fluid to induce phase change. To verify that the model exhibits desired fluid-structure behaviors, we make a few simplifying assumptions to obtain a reduced form of the equations that is amenable to exact solution. This analysis demonstrates no-slip behavior on the developing membrane without a priori assumptions on its location. The model has applications towards precipitate reactions where the precipitate greatly affects the surrounding flow, a situation appearing in many laboratory and geophysical contexts including the hydrothermal vent theory for the origin of life. More generally, this model can be used to address fluid-structure interaction problems that feature the dynamic generation of structures.dynamically according to equations governing the chemistry. We choose to model the fluid-structure combination as a single multiphase material: one component fluid or solvent and one component structure or precipitate membrane. Such multiphase models have proven useful in a variety of complex-fluid applications, such as bacterial biofilms [13,14], tumor-growth [9,21,37,44], and biological membranes [27]; their formulation is based on averaging momentum and stresses in separated, multi-component fluids [17,18].The multiphase framework developed here builds on previous ones [13,25,52], but with some keys differences that are guided by a combination of physical principles, model simplicity, and the micro-fluidic experiments mentioned above. First, our formulation conserves the total mass of the components solvent, dissolved species, and precipitate membrane throughout evolution. In particular, the model accounts for changes in solute concentrations that result from the formation of new membrane and the associated exclusion of solvent volume. This effect is neglected in previous models that treat reaction chemicals as scalar fields distinct from the multiphase material, but is essential for overall mass conservation. The treatment of reaction chemicals as additional components of a multiphase material has been successfully modeled by many [35, 51, see] but greatly complicates the analysis, interpretation, and simulation of the governing equations. Second, by making certain choices in the averaging procedure for the multicomponent stress, our formulation becomes equivalent to an incompressible Brinkman system with variable permeability. This equivalence is important for a few reasons. First, it guarantees that the model reduces to the Stokes equations in...

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Section: Model For Chemical Reactionsmentioning

confidence: 99%

“…We now specify our choice for the form for the precipitation term R m . Although complicated models of precipitation exist [31,36], we employ a simple model in which the rate of membrane mass growth is proportional to the amount of product, provided that the product concentration exceeds some precipitation threshold, i.e.…”

Section: B Mass Balance Equationsmentioning

confidence: 99%

Multiphase modelling of precipitation-induced membrane formation

et al. 2020

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“…They are the spacing law, the time law, the width law, and the Matalon–Packter law . Pre- and post-nucleation models were developed over the years as experimental observations to explain the above generic laws of LB. , In addition, simulations using various models were performed to explain the pattern diversity. − …”

Section: Introductionmentioning

confidence: 99%

Precise Evaluation of Spatial Characteristics of Periodically Precipitating Systems via Measurement of RGB (Red, Green, and Blue) Values of Pattern Images

Walimbe¹,

Takale²,

Kulkarni

et al. 2021

Langmuir

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In the present study, a method is described for precise determination of spatial characteristics of Liesegang bands formed by employing a classical 1D setup using a web-based free resource (). The method involves the compartmentalization of the information on each pixel into R (red), G (green), or B (blue) values from the pattern images obtained using a simple digital camera. The values can further be converted to absorbance values by using the system blank. Each trough (or peak) in the graph of RGB values (or absorbance values) corresponds to a band in the pattern. The method is employed to determine the spacing and width of the periodically precipitating AgCl, AgBr, and Co(OH)2 in an agar gel. It is observed that AgCl shows revert banding, and AgBr shows revert banding at the top of the tube and then diverges to regular banding at the bottom of the tube, whereas the Co(OH)2 patterns explicitly show regular banding under given experimental conditions. It is also observed that minute instabilities, such as the formation of secondary bands, can also be visualized by the present method.

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“…By changing the shape of the gel, it is possible to yield gel materials with periodic Co(OH) 2 precipitates with one [2], two [3] and three dimensions [4]. In addition to Co(OH) 2 , gels with various materials include hydroxide salts [5,6], chromate and dichromate salts [7][8][9][10], phosphate salts [11,12], metal nanoparticles [13][14][15] and polymers [16,17].…”

Section: Introductionmentioning

confidence: 99%

Regular-Type Liesegang Pattern of AgCl in a One-Dimensional System

et al. 2021

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The Liesegang phenomenon can be used for micro- and nanofabrication processes to yield materials with periodic precipitation of diverse types of materials. Although there have been several attempts to control the periodicity of the Liesegang patterns, it remains unclear whether the periodic precipitation of AgCl in gel medium causes regular- or revert-type patterns. To confirm the periodicity of the AgCl pattern, we conduct one-dimensional experiments under various ion concentration conditions. From microscopic observations, three different precipitation modes were observed, i.e., continuous precipitation with a sharp front, periodic precipitation and continuous precipitation with a gradual front. For these three modes, numerical analyses of the pattern geometry are performed for the periodic precipitation. It was confirmed that the regular-type pattern appeared for all concentration conditions conducted in the present experiments. Furthermore, the pattern was found to obey the spacing law and the Matalon–Packter law. From our experiments, we concluded that AgCl forms regular-type Liesegang patterns, regardless of the dimension of diffusion.

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Role of Electrolyte in Liesegang Pattern Formation

Cited by 18 publications

References 42 publications

Multiphase modelling of precipitation-induced membrane formation

Multiphase modelling of precipitation-induced membrane formation

Precise Evaluation of Spatial Characteristics of Periodically Precipitating Systems via Measurement of RGB (Red, Green, and Blue) Values of Pattern Images

Regular-Type Liesegang Pattern of AgCl in a One-Dimensional System

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