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Klopp C, Trittel T, Harth K, Stannarius R. Coalescence of biphasic droplets embedded in free standing smectic A films. SOFT MATTER 2024; 20:1036-1046. [PMID: 38205564 DOI: 10.1039/d3sm01549a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/12/2024]
Abstract
We investigate micrometer-sized flat droplets consisting of an isotropic core surrounded by a nematic rim in freely suspended smectic A liquid-crystal films. In contrast to purely isotropic droplets which are characterized by a sharp edge and no long-range interactions, the nematic fringe introduces a continuous film thickness change resulting in long-range mutual attraction of droplets. The coalescence scenario is divided in two phases. The first one consists in the fusion of the nematic regions. The second phase involves the dissolution of a thin nematic film between the two isotropic cores. The latter has many similarities with the rupture of thin liquid films between droplets coalescing in an immiscible viscous liquid.
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Affiliation(s)
- Christoph Klopp
- Institute of Physics, Otto von Guericke University Magdeburg, Universitätsplatz 2, D-39106 Magdeburg, Germany.
- MARS, Otto von Guericke University Magdeburg, Universitätsplatz 2, D-39106 Magdeburg, Germany
| | - Torsten Trittel
- MARS, Otto von Guericke University Magdeburg, Universitätsplatz 2, D-39106 Magdeburg, Germany
- Department of Engineering, Brandenburg University of Applied Sciences, Magdeburger Straße 50, D-14770 Brandenburg an der Havel, Germany
| | - Kirsten Harth
- MARS, Otto von Guericke University Magdeburg, Universitätsplatz 2, D-39106 Magdeburg, Germany
- Department of Engineering, Brandenburg University of Applied Sciences, Magdeburger Straße 50, D-14770 Brandenburg an der Havel, Germany
| | - Ralf Stannarius
- Institute of Physics, Otto von Guericke University Magdeburg, Universitätsplatz 2, D-39106 Magdeburg, Germany.
- MARS, Otto von Guericke University Magdeburg, Universitätsplatz 2, D-39106 Magdeburg, Germany
- Department of Engineering, Brandenburg University of Applied Sciences, Magdeburger Straße 50, D-14770 Brandenburg an der Havel, Germany
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Pikina ES, Shishkin MA, Kolegov KS, Ostrovskii BI, Pikin SA. Circulating Marangoni flows within droplets in smectic films. Phys Rev E 2022; 106:055105. [PMID: 36559366 DOI: 10.1103/physreve.106.055105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/04/2022] [Accepted: 10/13/2022] [Indexed: 11/16/2022]
Abstract
We present a theoretical study and numerical simulation of Marangoni convection within ellipsoidal isotropic droplets embedded in free-standing smectic films (FSSFs). The thermocapillary flows are analyzed for both isotropic droplets spontaneously formed in FSSF overheated above the bulk smectic-isotropic transition and oil lenses deposited on the surface of the smectic film. The realistic model for which the upper drop interface is free from the smectic layers, while at the lower drop surface the smectic layering persists is considered in detail. For isotropic droplets and oil lenses this leads effectively to a sticking of fluid motion at the border with a smectic shell. The above mentioned asymmetric configuration is realized experimentally when the temperature of the upper side of the film is higher than at the lower one. The full set of stationary solutions for Stokes stream functions describing the Marangoni convection flows within the ellipsoidal drops are derived analytically. The temperature distribution in the ellipsoidal drop and the surrounding air is determined in the frame of the perturbation theory. As a result, the analytical solutions for the stationary thermocapillary convection are obtained for different droplet ellipticity ratios and the heat conductivity of the liquid crystal and air. In parallel, the numerical hydrodynamic calculations of the thermocapillary motion in drops are made. Both analytical and numerical simulations predict the axially symmetric circulatory convection motion determined by the Marangoni effect at the droplet-free surface. Due to a curvature of the drop interface a temperature gradient along its free surface always exists. Thus, the thermocapillary convection within the ellipsoidal droplets in overheated FSSF is possible for the arbitrarily small Marangoni numbers. Possible experimental observations enabling the checking of our predictions are proposed.
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Affiliation(s)
- E S Pikina
- Landau Institute for Theoretical Physics of the RAS, 142432, Chernogolovka, Moscow region, Russia.,Institute of Solid State Physics of the RAS, 142432 Chernogolovka, Moscow region, Russia.,Oil and Gas Research Institute of the RAS, 119333 Moscow, Russia
| | - M A Shishkin
- Institute of Solid State Physics of the RAS, 142432 Chernogolovka, Moscow region, Russia.,HSE University, 101000, Moscow, Russia
| | - K S Kolegov
- Institute of Solid State Physics of the RAS, 142432 Chernogolovka, Moscow region, Russia.,Astrakhan State University, 414056 Astrakhan, Russia
| | - B I Ostrovskii
- Institute of Solid State Physics of the RAS, 142432 Chernogolovka, Moscow region, Russia.,FSRC "Crystallography and Photonics" of the RAS, 119333 Moscow, Russia
| | - S A Pikin
- FSRC "Crystallography and Photonics" of the RAS, 119333 Moscow, Russia
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Polychronopoulos ND, Benos LT, Stergiou CI, Sarris IE, Vlachopoulos J. Viscous coalescence of unequally sized spherical and cylindrical doublets. SOFT MATTER 2022; 18:4017-4029. [PMID: 35575129 DOI: 10.1039/d2sm00129b] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
A coalescence model is developed for pairs of unequally sized particles, assuming surface tension driven flow opposed by viscosity. The flow field is extensional, biaxial for spheres and planar for cylinders. The balance of surface energy and viscous dissipation results in a system of two ordinary differential equations for each of the two doublet shapes studied. The solution of the differential equations provides growth of neck radius (or width) as well as surface and cross-sectional area evolution. For an infinitely large size ratio, the model describes the coalescence of a sphere or a cylinder with a semi-infinite wall of the same material. The model is compared to some numerical simulations and experimental measurements available in the literature. The comparison to experiments includes PDMS spheres, macromolecule-rich droplets, spherical bitumen particles, and a smectic circular island with a meniscus.
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Affiliation(s)
| | - Lefteris Th Benos
- Institute for Bio-Economy and Agri-Technology (IBO), Centre of Research and Technology-Hellas (CERTH), 6th km Charilaou Thermi Rd, Thessaloniki, GR 57001, Greece
| | | | - Ioannis E Sarris
- Department of Mechanical Engineering, University of West Attica, Athens, 12210, Greece
| | - John Vlachopoulos
- Department of Chemical Engineering, McMaster University, Hamilton, Ontario, L8S 4L7, Canada
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Dolganov PV, Zverev AS, Baklanova KD, Dolganov VK. Quasi-two-dimensional coalescence of nematic and isotropic droplets and Rayleigh-Plateau instability in flat optical cells. SOFT MATTER 2021; 18:126-136. [PMID: 34817480 DOI: 10.1039/d1sm01334c] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We investigated the coalescence of nematic droplets in an isotropic environment and that of isotropic droplets in a nematic environment in quasi-two-dimensional geometry of a flat optical cell. Two different regimes of coalescence were found. In the circular meniscus between the nematic and isotropic regions both nematic and isotropic phases exist. As a result, two bridges form at coalescence: a nematic and an isotropic bridge. In this work, we focus on the situation when nematic wets the cell surface. The coalescence of nematic droplets starts near the cell surfaces where the droplet bridge from the nematic phase is formed. An outer bridge connecting the isotropic environment is localized in the middle of the cell. When the outer bridge gets thinner it becomes unstable and breaks up. A series of pinch-offs leads to the formation of satellite droplets. On the contrary, when isotropic droplets coalesce, the coalescence starts in the middle of the cell and breaking of the bridges occurs without instability and without the formation of satellite droplets. Breakup of the outer bridge is a new example of Rayleigh-Plateau instability in addition to actively studied transformation and breaking of filaments and stretched droplets.
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Affiliation(s)
- P V Dolganov
- Institute of Solid State Physics RAS, 142432, Chernogolovka, Moscow Region, Russia.
- National Research University Higher School of Economics, Moscow, 101000, Russia
| | - A S Zverev
- Institute of Solid State Physics RAS, 142432, Chernogolovka, Moscow Region, Russia.
| | - K D Baklanova
- Institute of Solid State Physics RAS, 142432, Chernogolovka, Moscow Region, Russia.
- National Research University Higher School of Economics, Moscow, 101000, Russia
| | - V K Dolganov
- Institute of Solid State Physics RAS, 142432, Chernogolovka, Moscow Region, Russia.
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Dolganov PV, Zverev AS, Baklanova KD, Dolganov VK. Dynamics of capillary coalescence and breakup: Quasi-two-dimensional nematic and isotropic droplets. Phys Rev E 2021; 104:014702. [PMID: 34412240 DOI: 10.1103/physreve.104.014702] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/04/2021] [Accepted: 06/04/2021] [Indexed: 11/07/2022]
Abstract
We observed the formation of small satellite droplets from the bridge at droplet coalescence. Investigations were made using a Hele-Shaw cell in the two-phase region at the nematic-isotropic phase transition. In previous works on coalescence it was considered that before the start of coalescence there exists a bridge between the outer fluid connecting regions on the two sides of the droplets (outer bridge). After the start of coalescence, a bridge connecting the two droplets appears (droplet bridge) and the outer bridge is broken. We have shown that there are coalescence processes where after the start of coalescence both the droplet bridge and the outer bridge can exist. This cardinally changes the coalescence process. During the first coalescence stage the size of the outer bridge decreases and the size of the droplet bridge increases. During the second stage the outer bridge becomes unstable which leads to pinch-off, formation of pointed end domains, secondary instability, splitting of pointed end domains, and formation of satellite droplets. We found the linear dependence of the minimum bridge radius on time near bridge breakup. This behavior confirms the capillary viscous regime of bridge breakup. Our work connects two areas of fluid dynamics: coalescence and breakup with formation of satellite droplets.
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Affiliation(s)
- P V Dolganov
- Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Moscow district, Russia
| | - A S Zverev
- Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Moscow district, Russia
| | - K D Baklanova
- Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Moscow district, Russia.,National Research University Higher School of Economics, Moscow 101000, Russia
| | - V K Dolganov
- Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Moscow district, Russia
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Pikina ES, Ostrovskii BI, Pikin SA. Benard-Marangoni convection within isotropic droplets in overheated free standing smectic films. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2021; 44:81. [PMID: 34146180 DOI: 10.1140/epje/s10189-021-00082-1] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/03/2021] [Accepted: 05/23/2021] [Indexed: 06/12/2023]
Abstract
We study theoretically internal flows in isotropic droplets formed in horizontal free-standing smectic films (FSSF) overheated above the bulk smectic-isotropic transition. The convection is due to vertical temperature gradient in the film and is driven by the surface tension variations at the drop interfaces. Using a conventional linear instability theory, we have found analytically the conditions under which the mechanical equilibrium within isotropic droplets in FSSFs becomes unstable relative to the thermocapillary convection. An explicit expression for the Marangoni number characterizing the onset of the convection as a function of the wave vector of in-plane instability and parameters of heat transfer is obtained. The cellular instability in FSSF with isotropic droplets behaving as a normal fluid (surface tension is a decreasing function of temperature) is possible for both directions of thermal gradient across the film: from bottom to top and conversely. We propose possible experimental observations enabling to check our predictions.
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Affiliation(s)
- Elena S Pikina
- Landau Institute for Theoretical Physics of the RAS, 142432, Chernogolovka, Russia.
- Institute of Solid State Physics of the RAS, Chernogolovka, Russia.
- Oil and Gas Research Institute, Russian Academy of Sciences, Gubkin str. 3, Moscow, Russia, 119333.
| | - Boris I Ostrovskii
- Institute of Solid State Physics of the RAS, Chernogolovka, Russia
- FSRC Crystallography and Photonics of the RAS, Leninsky pr. 59, Moscow, Russia, 119333
| | - Sergey A Pikin
- FSRC Crystallography and Photonics of the RAS, Leninsky pr. 59, Moscow, Russia, 119333
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Dolganov PV, Shuravin NS, Dolganov VK, Kats EI. Dynamics of island-meniscus coalescence in free-standing smectic films. SOFT MATTER 2020; 16:8506-8511. [PMID: 32840550 DOI: 10.1039/d0sm00791a] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
In free-standing smectic films islands (regions of larger thickness than the film) can be considered as two-dimensional analogues of liquid droplets in a three-dimensional medium. The dynamics of droplet coalescence is an important but up to now incompletely solved problem in non-equilibrium mechanics. Here, we report on our investigations of island coalescence with the film meniscus. This phenomenon is analogous to the coalescence of a 3D droplet with a flat liquid surface. We found that the time evolution of island dimension is described by universal power-law dependencies for different stages of coalescence. Limited agreement with existing theory was found. In particular, in the final stage of coalescence the domain dynamics differs from theoretical predictions.
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Affiliation(s)
- P V Dolganov
- Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, Moscow Region 142432, Russia.
| | - N S Shuravin
- Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, Moscow Region 142432, Russia.
| | - V K Dolganov
- Institute of Solid State Physics, Russian Academy of Sciences, Chernogolovka, Moscow Region 142432, Russia.
| | - E I Kats
- Landau Institute for Theoretical Physics, Russian Academy of Sciences, Moscow Region, 142432, Chernogolovka, Russia
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Klopp C, Trittel T, Stannarius R. Self similarity of liquid droplet coalescence in a quasi-2D free-standing liquid-crystal film. SOFT MATTER 2020; 16:4607-4614. [PMID: 32352134 DOI: 10.1039/d0sm00457j] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Coalescence of droplets is an ubiquitous phenomenon in chemical, physical and biological systems. The process of merging of liquid objects has been studied during the past years experimentally and theoretically in different geometries. We introduce a unique system that allows a quasi two-dimensional description of the coalescence process: Micrometer-sized flat droplets in freely suspended smectic liquid-crystal films. We find that the bridge connecting the droplets grows linearly in time during the initial stage of coalescence, both with respect to its height and lateral width. We also verify self-similar dynamics of the bridge during the first stage of coalescence. We compare our results with a model based on the thin sheet equations. Our experiments confirm that the most important geometrical parameter influencing the coalescence rate is the contact angle of the droplets.
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Affiliation(s)
- Christoph Klopp
- Institute of Physics, Otto von Guericke University, Department of Nonlinear Phenomena, Universitätsplatz 2, D-39106 Magdeburg, Germany.
| | - Torsten Trittel
- Institute of Physics, Otto von Guericke University, Department of Nonlinear Phenomena, Universitätsplatz 2, D-39106 Magdeburg, Germany.
| | - Ralf Stannarius
- Institute of Physics, Otto von Guericke University, Department of Nonlinear Phenomena, Universitätsplatz 2, D-39106 Magdeburg, Germany.
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