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Huisman M, Digard P, Poon WCK, Titmuss S. Evaporation of Concentrated Polymer Solutions Is Insensitive to Relative Humidity. PHYSICAL REVIEW LETTERS 2023; 131:248102. [PMID: 38181132 DOI: 10.1103/physrevlett.131.248102] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/30/2022] [Revised: 06/12/2023] [Accepted: 10/24/2023] [Indexed: 01/07/2024]
Abstract
A recent theory suggests that the evaporation kinetics of macromolecular solutions is insensitive to the ambient relative humidity (RH) due to the formation of a "polarization layer" of solutes at the air-solution interface. We confirm this insensitivity up to RH≈80% in the evaporation of polyvinyl alcohol solutions from open-ended capillaries. To explain the observed drop in evaporation rate at higher RH, we need to invoke compressive stresses due to interfacial polymer gelation. Moreover, RH-insensitive evaporation sets in earlier than theory predicts, suggesting a further role for a gelled "skin." We discuss the relevance of these observations for respiratory virus transmission via aerosols.
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Affiliation(s)
- Max Huisman
- SUPA and School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Paul Digard
- Department of Infection and Immunity, The Roslin Institute, The University of Edinburgh, Easter Bush Campus, Edinburgh EH25 9RG, United Kingdom
| | - Wilson C K Poon
- SUPA and School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Simon Titmuss
- SUPA and School of Physics and Astronomy, The University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
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2
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Talini L, Lequeux F. Formation of glassy skins in drying polymer solutions: approximate analytical solutions. SOFT MATTER 2023. [PMID: 37470281 DOI: 10.1039/d3sm00522d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 07/21/2023]
Abstract
We study the formation of a glassy skin at the air interface of drying polymer solutions. We introduce a simple approximation, which is valid for most diffusion problems, and which allows us to derive analytical relationships for the polymer concentration as a function of time. We show that the approximate results differ by less than 15% from those obtained by numerically solving the diffusion equation. We use the approximation to study skin formation in evaporating solutions. We focus on the influence of variations of the mutual diffusion coefficient with concentration, when the latter decreases sharply at high concentrations, as observed in the vicinity of the glass transition. We show that the skin thickness depends very strongly on the exponent characterising the decrease of the diffusion coefficient, in contrast to the polymer volume fraction at the interface, which varies only slightly with the exponent.
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Affiliation(s)
- Laurence Talini
- CNRS, Surface du Verre et Interfaces, Saint-Gobain, Aubervilliers, France.
| | - François Lequeux
- CNRS Sciences et Ingénierie de la Matière Molle, ESPCI Paris, PSL Research University, Sorbonne Université, Paris, France
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3
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Lin J, Li P, Liu Y, Wang Z, Wang Y, Ming X, Gao C, Xu Z. The Origin of the Sheet Size Predicament in Graphene Macroscopic Papers. ACS NANO 2021; 15:4824-4832. [PMID: 33682415 DOI: 10.1021/acsnano.0c09503] [Citation(s) in RCA: 13] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
The larger size of graphene sheets should intuitively generate higher overall properties of their macroscopic materials. However, this intuitive notion still remains ambiguous. Here, we uncover that the wrinkle formation causes the counterintuitive size predicament of graphene sheets in their macroscopic materials. In the model of graphene oxide assembled papers, we reveal that the giant size of graphene oxide sheets aggravates the formation of larger wrinkles and more microvoids, causing the negative size effect in mechanical strength. A major microscopic origin of the size predicament is the skin wrinkling in the drying process, and the wrinkling behavior follows a general rule of deformation of an elastic thin plate. We use a wrinkle-engineering strategy to depress the spontaneously formed large wrinkles and succeed in the resolution of the size predicament. After wrinkle modulation, an authentically positive size effect reversely appears in which giant graphene sheets generate ultrahigh mechanical strength and superior functionalities of graphene papers. The origin of the size predicament reminds us of the hidden importance of modulating wrinkles for graphene macroscopic materials and provides a guidance of wrinkle engineering for graphene materials with advanced performances.
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Affiliation(s)
- Jiahao Lin
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province, Zhejiang University, 38 Zheda Road, Hangzhou, 310027, P. R. China
| | - Peng Li
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province, Zhejiang University, 38 Zheda Road, Hangzhou, 310027, P. R. China
| | - Yingjun Liu
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province, Zhejiang University, 38 Zheda Road, Hangzhou, 310027, P. R. China
| | - Ziqiu Wang
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province, Zhejiang University, 38 Zheda Road, Hangzhou, 310027, P. R. China
| | - Ya Wang
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province, Zhejiang University, 38 Zheda Road, Hangzhou, 310027, P. R. China
| | - Xin Ming
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province, Zhejiang University, 38 Zheda Road, Hangzhou, 310027, P. R. China
| | - Chao Gao
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province, Zhejiang University, 38 Zheda Road, Hangzhou, 310027, P. R. China
- Graphene Industry and Engineering Research Institute, Xiamen University, No. 422 Siming Road, Xiamen, 361005, P. R. China
| | - Zhen Xu
- MOE Key Laboratory of Macromolecular Synthesis and Functionalization, Department of Polymer Science and Engineering, Key Laboratory of Adsorption and Separation Materials & Technologies of Zhejiang Province, Zhejiang University, 38 Zheda Road, Hangzhou, 310027, P. R. China
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Tang Q, Müller M. Evaporation-Induced Liquid Expansion and Bubble Formation in Binary Mixtures. PHYSICAL REVIEW LETTERS 2021; 126:028003. [PMID: 33512230 DOI: 10.1103/physrevlett.126.028003] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2020] [Accepted: 12/18/2020] [Indexed: 06/12/2023]
Abstract
We observe an anomalous liquid expansion after quenching a binary mixture at coexistence to low pressures in the vapor phase by numerical calculations. This evaporation-induced expansion can be attributed to the pressure imbalance near the liquid-vapor interface, which originates from the interplay between the complex thermodynamics of binary mixtures both in the vapor and liquid phases, as well as their dynamical asymmetries. In addition, careful modulation of the pressure quench in the vapor phase can result in spinodal bubble formation inside liquid phase. The results indicate that the thermodynamics-kinetics interplay could foster our fundamental understanding of the evaporation process and promote its practical applications.
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Affiliation(s)
- Qiyun Tang
- Institut für Theoretische Physik, Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Marcus Müller
- Institut für Theoretische Physik, Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
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Tang Q, Müller M, Li CY, Hu W. Anomalous Ostwald Ripening Enables 2D Polymer Crystals via Fast Evaporation. PHYSICAL REVIEW LETTERS 2019; 123:207801. [PMID: 31809069 DOI: 10.1103/physrevlett.123.207801] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/06/2019] [Indexed: 06/10/2023]
Abstract
We demonstrate by molecular simulations that the Ostwald ripening of crystalline polymer nuclei within the fast-evaporation-induced 2D skin layer is retarded at suitable temperatures and evaporation rates. Such an anomalous ripening can be attributed to the interplay between the thermodynamically driven diffusion of noncrystalline fragments toward the growing nuclei and the diffusive current away from the free surface caused by the densification in the nonequilibrium skin layer. The growth orientation of the nuclei inside the skin plane can be adjusted during this anomalous ripening process, which is beneficial for fabricating 2D polymer crystals.
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Affiliation(s)
- Qiyun Tang
- Department of Polymer Science and Engineering, State Key Lab of Coordination Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, 210023 Nanjing, China
- Institut für Theoretische Physik, Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Marcus Müller
- Institut für Theoretische Physik, Universität Göttingen, Friedrich-Hund-Platz 1, 37077 Göttingen, Germany
| | - Christopher Y Li
- Department of Materials Science and Engineering, Drexel University, Philadelphia, Pennsylvania 19104, USA
| | - Wenbing Hu
- Department of Polymer Science and Engineering, State Key Lab of Coordination Chemistry, School of Chemistry and Chemical Engineering, Nanjing University, 210023 Nanjing, China
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Zhang C, Fu N, Quek SY, Zhang J, Chen XD. Exploring the drying behaviors of microencapsulated noni juice using reaction engineering approach (REA) mathematical modelling. J FOOD ENG 2019. [DOI: 10.1016/j.jfoodeng.2018.12.016] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
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Zhou J, Man X, Jiang Y, Doi M. Structure Formation in Soft-Matter Solutions Induced by Solvent Evaporation. ADVANCED MATERIALS (DEERFIELD BEACH, FLA.) 2017; 29:1703769. [PMID: 29058825 DOI: 10.1002/adma.201703769] [Citation(s) in RCA: 45] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2017] [Revised: 08/10/2017] [Indexed: 06/07/2023]
Abstract
Solvent evaporation in soft-matter solutions (solutions of colloidal particles, polymers, and their mixtures) is an important process in material making and in the printing and coating industries. The solvent-evaporation process determines the structure of materials and strongly affects their performance. Solvent evaporation involves many physicochemical processes: flow, diffusion, crystallization, gelation, glass transition, etc. and is quite complex. Here, recent progress in this important process is reported, with a special focus on theoretical and simulation studies.
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Affiliation(s)
- Jiajia Zhou
- Key Laboratory of Bio-inspired Smart Interfacial Science and Technology of Ministry of Education, School of Chemistry, Beihang University, Beijing, 100191, P. R. China
- Center of Soft Matter Physics and Its Applications, Beihang University, Beijing, 100191, P. R. China
| | - Xingkun Man
- Center of Soft Matter Physics and Its Applications, Beihang University, Beijing, 100191, P. R. China
- School of Physics and Nuclear Energy Engineering, Beihang University, Beijing, 100191, P. R. China
| | - Ying Jiang
- Key Laboratory of Bio-inspired Smart Interfacial Science and Technology of Ministry of Education, School of Chemistry, Beihang University, Beijing, 100191, P. R. China
- Center of Soft Matter Physics and Its Applications, Beihang University, Beijing, 100191, P. R. China
| | - Masao Doi
- Center of Soft Matter Physics and Its Applications, Beihang University, Beijing, 100191, P. R. China
- Beijing Advanced Innovation Center for Biomedical Engineering, Beihang University, Beijing, 100191, P. R. China
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Statt A, Howard MP, Panagiotopoulos AZ. Solvent quality influences surface structure of glassy polymer thin films after evaporation. J Chem Phys 2017; 147:184901. [PMID: 29141418 DOI: 10.1063/1.4996119] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Molecular dynamic simulations are used to investigate the structural effects of treating a glassy polymer thin film with solvents of varying quality and subsequently evaporating the solvent. Both a monodisperse film and a polydisperse film are studied for poor to good solvent conditions, including the limit in which the polymer film is fully dissolved. In agreement with previous studies, the dissolved polymer-solvent mixtures form a polymer-rich skin on top of the forming film during evaporation. In the case of the polydisperse films, a segregation of the lower molecular weight polymer to the film interface is observed. We provide a detailed, systematic analysis of the interface structure and properties during and after evaporation. We find that for non-dissolved films, the surface width of the film after solvent evaporation is enhanced compared to the case without solvent. Our results show that due to the kinetic arrest of the surface structure, the increased surface width is preserved after solvent evaporation for both mono- and polydisperse films. We conclude that it is important to take poor solvent effects into account for the surface morphology of already formed thin glassy films, an effect which is often neglected.
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Affiliation(s)
- Antonia Statt
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
| | - Michael P Howard
- Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA
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9
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Bisotti F, Licordari F, Rossi F, Masi M. In Silico Study of Polymer Sheet Drying Process. INT POLYM PROC 2017. [DOI: 10.3139/217.3388] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
Abstract
Abstract
In the last decades polymer sheets have been developed and used for various purposes, for example with electronic devices or solar cells. After polymer processing, they present a high residue of polymer solvent that should be reduced. Indeed, a high presence of solvent could affect their electrical properties or cause high levels of pollution. In addition, uncontrolled drying process can cause bubble formation with consequent film breakage. The aim of this work is to simplify the phenomena involved in the drying process in order to develop a mathematical model able to predict the time evolution of the composition and the mass of the polymer sheet. The model proposed here, therefore, is aimed at stimulating the industrial process and the results were verified against experimental data collected with cellulose acetate-based polymeric sheets. In addition, thanks to its simplicity and to the very low system requirements and central processing unit (CPU) time, our model gives immediate views of the system behavior.
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Affiliation(s)
- F. Bisotti
- Department of Chemistry , Materials and Chemical Engineering “Giulio Natta”, Politecnico di Milano, Milan , Italy
| | - F. Licordari
- Department of Chemistry , Materials and Chemical Engineering “Giulio Natta”, Politecnico di Milano, Milan , Italy
| | - F. Rossi
- Department of Chemistry , Materials and Chemical Engineering “Giulio Natta”, Politecnico di Milano, Milan , Italy
| | - M. Masi
- Department of Chemistry , Materials and Chemical Engineering “Giulio Natta”, Politecnico di Milano, Milan , Italy
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Wang J, Huang S, Fu N, Jeantet R, Chen XD. Thermal Aggregation of Calcium-Fortified Skim Milk Enhances Probiotic Protection during Convective Droplet Drying. JOURNAL OF AGRICULTURAL AND FOOD CHEMISTRY 2016; 64:6003-6010. [PMID: 27420726 DOI: 10.1021/acs.jafc.6b02205] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
Probiotic bacteria have been reported to confer benefits on hosts when delivered in an adequate dose. Spray-drying is expected to produce dried and microencapsulated probiotic products due to its low production cost and high energy efficiency. The bottleneck in probiotic application addresses the thermal and dehydration-related inactivation of bacteria during process. A protective drying matrix was designed by modifying skim milk with the principle of calcium-induced protein thermal aggregation. The well-defined single-droplet drying technique was used to monitor the droplet-particle conversion and the protective effect of this modified Ca-aggregated milk on Lactobacillus rhamnosus GG. The Ca-aggregated milk exhibited a higher drying efficiency and superior protection on L. rhamnosus GG during thermal convective drying. The mechanism was explained by the aggregation in milk, causing the lower binding of water in the serum phase and, conversely, local concentrated milk aggregates involved in bacteria entrapment in the course of drying. This work may open new avenues for the development of probiotic products with high bacterial viability and calcium enrichment.
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Affiliation(s)
- Juan Wang
- Suzhou Key Laboratory of Green Chemical Engineering, School of Chemical and Environmental Engineering, College of Chemistry, Chemical Engineering and Material Science, Soochow University , Suzhou 215123, Jiangsu Province, China
| | - Song Huang
- Suzhou Key Laboratory of Green Chemical Engineering, School of Chemical and Environmental Engineering, College of Chemistry, Chemical Engineering and Material Science, Soochow University , Suzhou 215123, Jiangsu Province, China
- STLO, Agrocampus Ouest, INRA , 35000 Rennes, France
| | - Nan Fu
- Suzhou Key Laboratory of Green Chemical Engineering, School of Chemical and Environmental Engineering, College of Chemistry, Chemical Engineering and Material Science, Soochow University , Suzhou 215123, Jiangsu Province, China
| | | | - Xiao Dong Chen
- Suzhou Key Laboratory of Green Chemical Engineering, School of Chemical and Environmental Engineering, College of Chemistry, Chemical Engineering and Material Science, Soochow University , Suzhou 215123, Jiangsu Province, China
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Meng F, Luo L, Doi M, Ouyang Z. Solute based Lagrangian scheme in modeling the drying process of soft matter solutions. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2016; 39:22. [PMID: 26920525 DOI: 10.1140/epje/i2016-16022-9] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2015] [Accepted: 08/26/2015] [Indexed: 06/05/2023]
Abstract
We develop a new dynamical model to study the drying process of a droplet of soft matter solutions. The model includes the processes of solute diffusion, gel-layer formation and cavity creation. A new scheme is proposed to handle the diffusion dynamics taking place in such processes. In this scheme, the dynamics is described by the motion of material points taken on solute. It is convenient to apply this scheme to solve problems that involve moving boundaries and phase changes. As an example, we show results of a numerical calculation for a drying spherical droplet, and discuss how initial concentration and evaporation rate affect the structural evolution of the droplet.
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Affiliation(s)
- Fanlong Meng
- State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, 100190, Beijing, China.
- Kavli Institute for Theoretical Physics China, 100190, Beijing, China.
- Center of Soft Matter Physics and its Applications, Beihang University, Beijing, China.
| | - Ling Luo
- Center of Soft Matter Physics and its Applications, Beihang University, Beijing, China
| | - Masao Doi
- Center of Soft Matter Physics and its Applications, Beihang University, Beijing, China.
| | - Zhongcan Ouyang
- State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, 100190, Beijing, China
- Kavli Institute for Theoretical Physics China, 100190, Beijing, China
- Center for Advanced Study, Tsinghua University, 100084, Beijing, China
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Sadek C, Schuck P, Fallourd Y, Pradeau N, Jeantet R, Le Floch-Fouéré C. Buckling and collapse during drying of a single aqueous dispersion of casein micelle droplet. Food Hydrocoll 2016. [DOI: 10.1016/j.foodhyd.2015.06.016] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023]
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13
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Mechanical properties of milk protein skin layers after drying: Understanding the mechanisms of particle formation from whey protein isolate and native phosphocaseinate. Food Hydrocoll 2015. [DOI: 10.1016/j.foodhyd.2015.01.014] [Citation(s) in RCA: 42] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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14
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Meng F, Doi M, Ouyang Z. Cavitation in drying droplets of soft matter solutions. PHYSICAL REVIEW LETTERS 2014; 113:098301. [PMID: 25216010 DOI: 10.1103/physrevlett.113.098301] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/06/2014] [Indexed: 06/03/2023]
Abstract
When a droplet of a soft matter solution is dried, cavities are often formed in the droplet, giving a hollow sphere in the end. A theoretical model is given for this phenomenon. It is shown that the formation of a gel-like layer (skin layer), which has a finite shear modulus, is essential for the phenomenon to take place. The condition for cavity formation (how it depends on the shear modulus and thickness of the skin layer), and the variation of the droplet volume and cavity volume after the cavity formation are examined.
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Affiliation(s)
- Fanlong Meng
- State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China and Kavli Institute for Theoretical Physics China, Beijing 100190, China and Center of Soft Matter Physics and Its Applications, Beihang University, Beijing, China
| | - Masao Doi
- Center of Soft Matter Physics and Its Applications, Beihang University, Beijing, China
| | - Zhongcan Ouyang
- State Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China and Kavli Institute for Theoretical Physics China, Beijing 100190, China and Center for Advanced Study, Tsinghua University, Beijing 100084, China
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Arai S, Doi M. Anomalous drying dynamics of a polymer solution on a substrate. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2013; 36:63. [PMID: 23797358 DOI: 10.1140/epje/i2013-13063-6] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/02/2012] [Revised: 06/02/2013] [Accepted: 06/02/2013] [Indexed: 06/02/2023]
Abstract
When a polymer solution with volatile solvent is exposed to open air, an elastic layer (called a skin) is often formed at the surface of the solution due to evaporation of the solvent. After such a skin is formed, further extraction of the solvent from the solution caused by evaporation has generally been considered to reduce the pressure in the solution. We have found that, in PMMA/acetone droplet placed on a substrate, the liquid below the skin layer is pushed out as the solvent evaporates further. These phenomena indicate that the pressure in the solution increases by solvent evaporation. It is considered to be caused by the shrinkage and other structural changes taking place in the skin layer.
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Affiliation(s)
- Shunto Arai
- Graduate School of Engineering, The University of Tokyo, 113-8656, Tokyo, Japan.
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