Phase Separation Process Research Articles

Pectin Nanoporous Structures Prepared via Salt-Induced Phase Separation and Ambient Azeotropic Evaporation Processes.

Polysaccharide nanoporous structures are suitable for various applications, ranging from biomedical scaffolds to adsorption materials, owing to their biocompatibility and large surface areas. Pectin, in particular, can create 3D nanoporous structures in aqueous solutions by binding with calcium cations and creating nanopores by phase separation; this process involves forming hydrogen bonds between alcohols and pectin chains in water and alcohol mixtures and the resulting penetration of alcohols into calcium-bound pectin gels. However, owing to the dehydration and condensation of polysaccharide chains during drying, it has proven to be challenging to maintain the 3D nanoporous structure without using a freeze-drying process or supercritical fluid. Herein, we report a facile method for creating polysaccharide-based xerogels, involving the co-evaporation of water with a nonsolvent (e.g., a low-molecular-weight hydrophobic alcohol such as isopropyl or n-propyl alcohol) at ambient conditions. Experiments and coarse-grained molecular dynamics simulations confirmed that salt-induced phase separation and hydrogen bonding between hydrophobic alcohols and pectin chains were the dominant processes in mixtures of pectin, water, and hydrophobic alcohols. Furthermore, the azeotropic evaporation of water and alcohol mixed in approximately 1:1 molar ratios was maintained during the natural drying process under ambient conditions, preventing the hydration and aggregation of the hydrophilic pectin chains. These results introduce a simple and convenient process to produce 3D polysaccharide xerogels under ambient conditions.

Visualization of isothermal crystallization and phase separation in poly[(R)-3-hydroxybutyrate]/poly(L-lactic acid) by low-frequency Raman imaging

The visualization of the variation of the inter/intra molecular interaction (C = O⋯CH3) between poly[(R)-3-hydroxybutyrate] (PHB) and poly-L-lactic acid (PLLA) in the PHB/PLLA miscible blend during phase separation and crystallization process was successfully investigated using Raman imaging. Images of the blend were developed using high- and low-frequency Raman spectra acquired during the isothermal crystallization of the blend, and both of them were compared. The low-frequency region allowed to observe the changes in the hydrogen bonds between the molecular chains in the blend during phase separation and crystallization via a band at 75 cm−1 derived from PHB. The imaging results obtained using the band at 75 cm−1 due to hydrogen bonding (C = O⋯CH3) between molecular chains were in good agreement with the results obtained using the C = O stretching band at 1720 cm−1. Herein, we demonstrated that the low-frequency region of the Raman spectrum is more sensitive to detecting the start of the phase separation and crystallization of PHB than the corresponding high-frequency region.

Atom probe tomography-assisted kinetic assessment of spinodal decomposition in an Al-12.5 at.%Zn alloy

The rates of atomic clustering and precipitation hardening are closely related to the diffusivity of solutes and the concentration of vacancies during the natural aging of aluminum alloys. The measurement of the diffusivity of solutes at room temperature, especially in systems with an equilibrium vacancy concentration, is beneficial to the design of the aging process. However, this measurement has long been challenging because of the extremely low diffusion rates of solutes in aluminum at room temperature and the presence of supersaturated vacancies. In this work, we propose a method to quantify the diffusivity of solutes based on the kinetic evaluation of the spinodal decomposition process. This evaluation involves conducting atom probe tomography experiments, analyzing the radial distribution function, and modeling the phase separation process using the Cahn–Hilliard theory. The aging experiments were conducted on nanoscale samples, where excess vacancies can be eliminated at free surfaces due to a high surface-to-volume ratio. The results yielded a diffusivity of Zn in the Al-12.5 at.% Zn alloy of (1.32±0.46)×10−25 m2/s at 295 K. This work introduces a novel approach to assess the solute diffusivity under conditions of equilibrium vacancy concentration at room temperature and expands the temperature range for measuring the diffusivity in systems with spinodal decomposition, particularly in cases where kinetic data at low temperatures are scarce.

Design Rationale for CO2 Separation Membranes with Micropatterned Surface Structures.

Here, we report the design rationale of CO2 separation membranes with micropatterned surface structures. Thin film composite (TFC) membranes with micropatterned surface structures were fabricated by spray coating amine-containing hydrogel particles on the top of micropatterned porous support membranes, which were synthesized by a polymerization-induced phase separation process in a micromold (PIPsμM). The pore size of the support membranes was optimized by tuning the proportion of good and poor solvents for the polymerization process so that the microgels would be assembled as a defect-free separation layer. The relationship between the size of the micropatterned structures on the surface of the support membrane and the thickness of the separation layer was optimized to maximize the surface area of the separation layer. The rationally designed micropatterned TFC membrane showed a CO2 permeability (835.8 GPU) proportional to the increase in surface area relative to the flat membrane with a high CO2/N2 selectivity of 58.7. The rational design for micropatterned TFC membranes will enable the development of inexpensive and high-performance functional membranes not only for CO2 separation but also for other applications such as water treatment and membrane reactors.

Nanocomposite Material Based on Polyvinyl Alcohol Modified with Carbon Nanotubes: Mechanism of Formation and Electronic Energy Structure

The physical chemistry of surface phenomena in polymers is an important issue when studying the interaction of polymers with solid surfaces. This is due to the fact that most of the modern polymer materials are heterogeneous systems with highly developed phase separation surfaces. An example of such materials can be reinforced plastic, filled thermoplastics, reinforced rubber, paint coatings, etc. Polymer adsorption at the boundary of the phase separation process in solids plays an important role in the reinforcing effect of fillers, adhesion, gluing and obtaining composite materials with high strength properties. Compositions based on polyvinyl alcohol (PVA) modified with carbon nanotubes (CNTs) can be used as an interesting and informative system for studying the structure and properties of polymer nanocomposites, especially in a highly oriented state. PVA has one of the simplest chemical structure among the polymers, containing a functional (hydroxyl) group capable of participating in interphase interactions. In turn, carbon nanotubes with unique strength properties are currently products of industrial production, which makes it possible to control and modify their properties. To prove the possibility of creating new composite materials with improved strength characteristics, the mechanisms of interaction between PVA and CNTs are studied by modeling the adsorption processes of a polymer fragment on the outer surface of single-layer carbon nanotubes of different chirality, performed within the framework of the modern DFT calculation method. The main adsorption characteristics of the process and the features of the electron energy structure of the resulting composite systems are determined.

APC mutations disrupt β-catenin destruction complex condensates organized by Axin phase separation

The Wnt/β-catenin pathway is critical to maintaining cell fate decisions. Recent study showed that liquid–liquid-phase separation (LLPS) of Axin organized the β-catenin destruction complex condensates in a normal cellular state. Mutations inactivating the APC gene are found in approximately 80% of all human colorectal cancer (CRC). However, the molecular mechanism of the formation of β-catenin destruction complex condensates organized by Axin phase separation and how APC mutations impact the condensates are still unclear. Here, we report that the β-catenin destruction complex, which is constructed by Axin, was assembled condensates via a phase separation process in CRC cells. The key role of wild-type APC is to stabilize destruction complex condensates. Surprisingly, truncated APC did not affect the formation of condensates, and GSK 3β and CK1α were unsuccessfully recruited, preventing β-catenin phosphorylation and resulting in accumulation in the cytoplasm of CRCs. Besides, we propose that the phase separation ability of Axin participates in the nucleus translocation of β-catenin and be incorporated and concentrated into transcriptional condensates, affecting the transcriptional activity of Wnt signaling pathway.

Smart pillar[5]arene-based PDMAEMA/PES beads for selective dye pollutants removal: design, synthesis, chemical-physical characterization, and adsorption kinetic studies.

This article reports on the synthesis of an innovative smart polymer, P5-QPDMAEMA, opportunely developed with the aim of combining the responsiveness of PDMAEMA polymer and the host-guest properties of covalently linked pillar[5]arenes. Thanks to a traditional Non-Induced Phase Separation (NIPS) process performed at various coagulation pH, the blending of P5-QPDMAEMA with polyethersulfone gave rise to the formation of functional beads for the removal of organic dyes in water. Adsorption tests are carried out on all the produced blend-based beads by employing two representative dyes, the cationic methylene blue (MB), and the anionic methyl orange (MO). In particular, the P5-QPDMAEMA based beads, prepared at acidic pH, featured the best MO removal rate (i. e., 91.3 % after 150 minutes starting from a 20 mg ⋅ L-1 solution) and a high selectivity towards the removal of the selected anionic dye. Based on the adsorption kinetics and isotherm calculations, the pseudo-first order and Freundlich models were shown to be the most suitable to describe the MO adsorption behavior, achieving a maximum adsorption capacity of 21.54 mg ⋅ g-1. Furthermore, zwitterionic beads are obtained by a post-functionalization of the PDMAEMA and the P5-QPDMAEMA based beads, to test their removal capability towards both anionic and cationic dyes, as shown.

Sodium alginate/epoxy resin was separated by emulsion phase to fabricate a strong superhydrophobic coating

It has been recognized that good mechanical robustness and chemical stability are the keys to superhydrophobic coatings. Here, we used epoxy resin/sodium alginate emulsion phase separation method to prepare the coating body, and polydimethylsiloxane/vapor phase silicon dioxide as the superhydrophobic material to prepare a superhydrophobic silicon dioxide coating. Sodium alginate is enriched on the coating surface by phase separation process, which greatly improves the interaction force between the superhydrophobic material and the coating body. The water contact angle of the EP/SA/SiO2 superhydrophobic coating is 157.6° and the sliding angle is 2.3° The EP/SA/SiO2 superhydrophobic coating has good mechanical robustness, chemical stability and self-cleaning performance. Thanks to the micro-nano structure of the surface Cassie-Baxter model, air can be trapped on the solid-liquid contact surface of the coating. The impedance value of the EP/SA/SiO2 coating is two orders of magnitude higher than that of the epoxy coating, which has excellent anti-corrosion properties. It is believed that this study can provide a new idea for preparing strong superhydrophobic coatings.

Multi-functional microparticles constructed by steerable phase separation process for synchronous uranium selective extraction and heat storage

Nuclear wastewater contains large amounts of uranium and waste heat, and hence synchronous uranium selective extraction and heat storage from nuclear wastewater are of prime importance. Herein, a series of distinctive dual-functional absorbents, such as P(St-VA)-1, P(St-VA)-2, P(St-VA)-3, were developed through photoinitiated interfacial polymerization via emulsion templates, using styrene and ethylene phosphate as co-monomers. The P(St-VA) has dual-functions, i.e., waste heat storage and uranium extraction. The uranium extraction feature is derived from the phosphoric acid group, while paraffin was encapsulated inside the P(St-VA). The concentration of sodium dodecyl sulfate (SDS) determines the rate and extent of phase separation between styrene and paraffin via tuning the size and stability of the emulsion, and hence the morphology and functionality of the P(St-VA). The P(St-VA) demonstrates excellent uranium adsorption performance with prominent selectivity. Furthermore, the P(St-VA) underwent multiple phase transitions between 25℃ and 70℃, displaying endothermic and exothermic behaviours and great heat storage potential. This study has provided an innovative path for the synchronous recycling of uranyl ions and waste heat from nuclear wastewater for practical applications.

Casein micelle formation as a calcium phosphate phase separation process: Preparation of artificial casein micelles through vacuum evaporation and membrane processes

Industrial-scale production of artificial casein micelles (ACM) is required to produce dairy alternatives from recombinant casein. However, the currently common micelle preparation method of dropwise mixing casein and salt solutions is inefficient and may prove difficult to scale up. Here, we view casein micelle formation as a process driven by calcium phosphate phase separation in the presence of casein. On this basis, we developed novel routes to prepare ACM through vacuum evaporation, forward osmosis, or reverse osmosis. ACM prepared through these methods have similar properties and improved coagulation behaviour compared to those prepared through the currently common method and natural bovine casein micelles. The properties and functionality of the micelles depend on the preparation time and surface area available for micelle formation, with longer times and larger surfaces (i.e. lower fluxes) yielding smaller ACM that form firmer curds. These novel processes enable fast, efficient, and continuous production of ACM for application in future dairy alternatives. Industrial relevanceArtificial casein micelles can be used as a building block in the production of animal-free milk and cheese based on precision fermentation. The herein described novel processes to prepare artificial casein micelles are based on vacuum evaporation, forward osmosis, and reverse osmosis, which are mild, resource-efficient, and easily scalable processes. The processes require a dilute feed stream (e.g. caseins after precision fermentation), provide an elegant way to minimise local differences in the concentration of caseins and ions during micelle production, and offer the opportunity to design continuous micelle formation processes. These are all advantages over the existing methods to prepare artificial casein micelles with regard to industrial application.

Phase separation as a possible mechanism for dosage sensitivity

BackgroundDeletion of haploinsufficient genes or duplication of triplosensitive ones results in phenotypic effects in a concentration-dependent manner, and the mechanisms underlying these dosage-sensitive effects remain elusive. Phase separation drives functional compartmentalization of biomolecules in a concentration-dependent manner as well, which suggests a potential link between these two processes, and warrants further systematic investigation.ResultsHere we provide bioinformatic and experimental evidence to show a close link between phase separation and dosage sensitivity. We first demonstrate that haploinsufficient or triplosensitive gene products exhibit a higher tendency to undergo phase separation. Assessing the well-established dosage-sensitive genes HNRNPK, PAX6, and PQBP1 with experiments, we show that these proteins undergo phase separation. Critically, pathogenic variations in dosage-sensitive genes disturb the phase separation process either through reduced protein levels, or loss of phase-separation-prone regions. Analysis of multi-omics data further demonstrates that loss-of-function genetic perturbations on phase-separating genes cause similar dysfunction phenotypes as dosage-sensitive gene perturbations. In addition, dosage-sensitive scores derived from population genetics data predict phase-separating proteins with much better performance than available sequence-based predictors, further illustrating close ties between these two parameters.ConclusionsTogether, our study shows that phase separation is functionally linked to dosage sensitivity and provides novel insights for phase-separating protein prediction from the perspective of population genetics data.

Liquid DNA Coacervates form Porous Capsular Hydrogels via Viscoelastic Phase Separation on Microdroplet Interface

AbstractLiquid–liquid phase separation (LLPS) droplets of biopolymers are known as functional microdroplets in living cells and have recently been used to construct protocells and artificial cells. The formation of DNA coacervates (also referred to as DNA droplets) from branched DNA nanostructures and the control of their physical properties via DNA nanostructure design are demonstrated previously. For the construction of artificial cells or protocells, however, even though physical effects such as surface tension, wetting, and viscoelasticity are more important in a tiny (micrometer‐sized), confined environment than in a bulk solution environment, they have not been explored yet. This study shows that a tiny, confined environment using a water‐in‐oil (W/O) microdroplet interface modulates the phase separation dynamics of DNA coacervates, leading to micrometer‐sized porous capsular structures. The porous structures are produced via two types of viscoelastic phase separation (VPS) processes in DNA coacervates: i) simple VPS and ii) cluster‐cluster aggregation after VPS. Finally, it is shown that environmental chemical stimulation can manipulate porous capsular DNA hydrogels extracted from W/O microdroplets. These results provide an approach for designing and fabricating artificial cells or protocells with complex structures and physicochemical properties.

On the complex version of the Cahn–Hilliard–Oono type equation for long interactions phase separation

Abstract This paper focuses on the complex version of the Cahn-Hilliard-Oono equation with Neumann boundary conditions, which is used to capture long-range nonlocal interactions in the phase separation process. The first part of the paper establishes the well-posedness of the corresponding stationary problem associated with the equation. Subsequently, a numerical model is constructed using a finite element discretization in space and a backward Euler scheme in time. We demonstrate the existence of a unique solution to the stationary problem and obtain error estimates for the numerical solution. This, in turn, serves as proof of the convergence of the semi-discrete scheme to the continuous problem. Finally, we establish the convergence of the fully discrete problem to the semi-discrete formulation.

Temperature dependent extensions of the Cahn–Hilliard equation

The Cahn–Hilliard equation is a fundamental model that describes phase separation processes of binary mixtures. In this paper we focus on the dynamics of these binary media, when the underlying temperature is not constant.The aim of this paper is twofold. We first derive two distinct models that extend the classical Cahn-Hilliard equation with an evolutionary equation for the absolute temperature. Secondly, we analyse the local well-posedness of classical solution for one of these systems.Our modelling introduces the systems of PDEs by means of a general and unified formalism. This formalism couples standard principles of mechanics together with the main laws of thermodynamics. Our work highlights how certain assumptions on the transport of the temperature effect the overall physics of the systems.The variety of these thermodynamically consistent models opens the question of which one should be more appropriate. Our analysis shows that one of the derived models might be more desirable to the well-posedness theory of classical solutions, a property that might be natural as a selection criteria.We conclude our paper with an overview and comparison of our modelling formalism with some equations, which were previously derived in literature.

Dynamic fluorescence imaging and controllable capture/release of guests based on thermo-responsive perylene-cyclodextrin conjugates

In view of the fact that multivalent intermolecular noncovalent interactions are the main elements for the formation of phase separation, supramolecular entities are a type of multivalent system. However, the phase separation system based on single supramolecular molecules was limited. In this paper, two permethyl-β-cyclodextrin modified perylene monoamide derivatives (PMI-B-CD and PMI-N-CD) with modification of benzene and naphthalene groups at the bay position of perylene backbone were synthesized. Of interest, PMI-B-CD and PMI-N-CD showed a LCST effect due to a self-inclusion interaction between PMCD and the benzene or naphthalene groups in the bay position of perylene monoamide backbone. Dynamic confocal fluorescence imaging of PMI-B-CD and PMI-N-CD showed thermo-responsive phase separation process. It is surprised that PMI-B-CD and PMI-N-CD achieved thermo-responsive capture and release of aromatic guests. Dynamic phase separation and controllable capture and release of guests with thermo-responsive phase transition process are found, which opens a novel supramolecular principle of liquid-liquid transition.

TWO-PHASE FLOW METERING OF MALDISTRIBUTION INSIDE A HEADER BY MEANS OF VENTURI FLOWMETER SOLELY

In evaporators, the distribution of the liquid and vapor phases among the channels is a convoluted problem, depending on a wide range of parameters. However, maldistribution causes important losses of performance. Due to their complexity, the accurate modeling of such two-phase flows is difficult to handle. Hence, experimental studies are still of great importance to help the understanding of maldistribution behaviors inside evaporators. Most of the experimental investigations of two-phase flow distribution are measuring the liquid and vapor quantities in the channels through a phase separation process, increasing the test duration and complexity. As a consequence, the number of parameters investigated is usually limited. Therefore, a new inline instrumentation method would allow for a more complete study by simplifying the measurement process. In the present work, an isothermal air/water mixture was used as fluid. The distribution of the two phases in eight channels of 10-mm I.D. connected to a simplified header was investigated. The inlet mass flow rates considered ranged from 0 to 0.025 kg/s for the water, and from 0 to 0.022 kg/s for the air. Consequently, qualities x up to 0.7 and void fractions α up to 0.9 were reached. All the tests were carried at a pressure condition of 7 bar to reach a liquid to vapor density ratio similar to what is encountered for traditional refrigerant. Finally, to allow a continuous measurement process, the mass flow rates in each of the 10-mm I.D. channel were measured using a flowmeter calibrated on a separate line. Since no void fraction meter was coupled, a new iterative methodology, based on the Venturi pressure drops measurement solely, was developed and is proposed here. It proved to successfully predict the vapor and liquid phase flow rates in each channel.

Evaporation and phase separation of acoustically levitated aqueous two-phase-system drops

As a ground-based experimental method for simulating the containerless state in space, acoustic levitation provides excellent containerless and contact-free conditions for studying droplet dynamics, including droplet evaporation and phase separation. Meanwhile, the nonlinear effects of the acoustic field, such as acoustic radiation pressure and acoustic streaming, bring novel characteristics to the droplet evaporation process and phase separation process. In this work, the evaporation and phase separation of aqueous two-phase-system (ATPS) droplet composed of polyethylene glycol (PEG) and ammonium sulfate (AMS) are investigated by a single-axis acoustic levitator through the combination of image acquisition and processing technique. During the evaporation of the ATPS droplet, the square of its equatorial diameter, <inline-formula><tex-math id="M5">\begin{document}$ {d}^{2} $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20230963_M5.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20230963_M5.png"/></alternatives></inline-formula>, decreases linearly with time, and its aspect ratio, <inline-formula><tex-math id="M6">\begin{document}$ \gamma $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20230963_M6.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="3-20230963_M6.png"/></alternatives></inline-formula>, increases linearly with time. The PEG-AMS droplet initially in the single-phase regime can enter into the two-phase regime as the water evaporates, resulting in phase separation. The phase separation of the acoustically levitated PEG-AMS ATPS droplet includes three stages: first, a large number of PEG-rich globules form inside the ATPS droplet, and then these PEG-rich globules collide, coagulate and migrate outward, and finally a horizontal layered structure of the whole droplet comes into being. The evaporation constant, the evolution of the PEG-rich globules and the AMS-rich phase area, are analyzed for ATPS droplets with different initial aspect ratios and different initial compositions. It is concluded that the greater the initial aspect ratio and the smaller the volume fraction of the PEG-rich phase, the faster the evaporation rate of the droplet is; the greater the initial aspect ratio and the lager the volume fraction of the PEG-rich phase, the faster the phase separation is. Numerical simulations show that the acoustically levitated droplets with a large aspect ratio are subjected to greater acoustic radiation pressure on the surface, and that the corresponding sound field is more intense and the acoustic streaming is stronger, which accelerates the evaporation and phase separation of the levitated droplets. These findings contribute to deepening our understanding of the motion characteristics, evaporation dynamics and phase separation of acoustically levitated droplets, and provide a foundation for studying the containerless preparation and processing the materials under acoustic levitation.

A Ti3C2 MXene-integrated near-infrared-responsive multifunctional porous scaffold for infected bone defect repair.

Infected bone defect repair has long been a major challenge in orthopedic surgery. Apart from bacterial contamination, excessive generation of reactive oxygen species (ROS), and lack of osteogenesis ability also threaten the defect repair process. However, few strategies have been proposed to address these issues simultaneously. Herein, we designed and fabricated a near-infrared (NIR)-responsive, hierarchically porous scaffold to address these limitations in a synergetic manner. In this design, polymethyl methacrylate (PMMA) and polyethyleneimine (PEI) were used to fabricate the porous PMMA/PEI scaffolds via the anti-solvent vapor-induced phase separation (VIPS) process. Then, Ti3C2 MXenes were anchored on the scaffolds through the dopamine-assisted co-deposition process to obtain the PMMA/PEI/polydopamine (PDA)/MXene scaffolds. Under NIR laser irradiation, the scaffolds were able to kill bacteria through the direct contact-killing and synergetic photothermal effect of Ti3C2 MXenes and PDA. Moreover, MXenes and PDA also endowed the scaffolds with excellent ROS-scavenging capacity and satisfying osteogenesis ability. Our experimental results also confirmed that the PMMA/PEI/PDA/MXene scaffolds significantly promoted new bone formation in an infected mandibular defect model. We believe that our study provides new insights into the treatment of infected bone defects.

RNP granules in ALS and neurodegeneration: From multifunctional membraneless organelles to therapeutic opportunities.

Amyotrophic lateral sclerosis (ALS) and related neurodegenerative diseases are characterised by dysfunction of a host of RNA-binding proteins (RBPs) and a severely disrupted RNA metabolism. Recently, RBP-harbouring phase-separated complexes, ribonucleoprotein (RNP) granules, have come into the limelight as "crucibles" of neuronal pathology in ALS. RNP granules are indispensable for the multitude of regulatory processes underlying cellular RNA metabolism and serve as critical organisers of cellular biochemistry. Neurons, highly specialised cells, heavily rely on RNP granules for efficient trafficking, signalling and stress responses. Multiple RNP granule components, primarily RBPs such as TDP-43 and FUS, are affected by ALS mutations. However, even in the absence of mutations, RBP proteinopathies represent pathophysiological hallmarks of ALS. Given the high local concentrations of RBPs and RNAs, their weakened or enhanced interactions within RNP granules disrupt their homeostasis. Thus, the physiological process of phase separation and RNP granule formation, vital for maintaining the high-functioning state of neuronal cells, becomes their Achilles heel. Here, we will review the recent literature on the causes and consequences of abnormal RNP granule functioning in ALS and related disorders. In particular, we will summarise the evidence for the network-level dysfunction of RNP granules in these conditions and discuss considerations for therapeutic interventions to target RBPs, RNP granules and their network as a whole.

Numerical Solution of Cahn-Allen Equations by Wavelet Based Lifting Schemes

The Cahn-Allen equation is a reaction-diffusion equation of mathematical physics that describes the process of phase separation in multi-component alloy systems and order-disorder transitions. This paper presented a numerical solution of Cahn-Allen equations by Lifting scheme using different wavelet filter coefficients. The numerical results obtained using this scheme are compared with the exact solution to demonstrate the accuracy and fast convergence in less computational time than the existing scheme. Some problems are taken to show the validity and applicability of the scheme.