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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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Dolganov PV, Spiridenko NA, Zverev AS. Dynamics of viscous droplet coalescence in the confined geometry of optical cells. Phys Rev E 2024; 109:014702. [PMID: 38366422 DOI: 10.1103/physreve.109.014702] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/13/2023] [Accepted: 12/28/2023] [Indexed: 02/18/2024]
Abstract
The dynamics of quasi-two-dimensional coalescence of isotropic droplets in nematic liquid crystal environment was studied. Investigations were made in confined geometry of a Hele-Shaw optical cell with different transverse droplet sizes. The existence of three distinct dynamic regimes was found for coalescence, namely, short-, middle-, and long-time regimes. The fast dynamics of bridge transformation was visualized. At short time the dynamics of droplet transformation is similar to the transformation of free (three-dimensional) droplets. At later stages, two regimes of the coalescence at different timescales are determined by Poiseuille flow. Experimental data are discussed on the basis of existing theories.
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Affiliation(s)
- P V Dolganov
- Osipyan Institute of Solid State Physics RAS, 142432 Chernogolovka, Moscow Region, Russia
| | - N A Spiridenko
- Osipyan Institute of Solid State Physics RAS, 142432 Chernogolovka, Moscow Region, Russia
| | - A S Zverev
- Osipyan Institute of Solid State Physics RAS, 142432 Chernogolovka, Moscow Region, Russia
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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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Vitral E, Leo PH, Viñals J. Phase-field model for a weakly compressible soft layered material: morphological transitions on smectic-isotropic interfaces. SOFT MATTER 2021; 17:6140-6159. [PMID: 34080608 DOI: 10.1039/d1sm00488c] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/12/2023]
Abstract
A coupled phase-field and hydrodynamic model is introduced to describe a two-phase, weakly compressible smectic (layered phase) in contact with an isotropic fluid of different density. A non-conserved smectic order parameter is coupled to a conserved mass density in order to accommodate non-solenoidal flows near the smectic-isotropic boundary arising from density contrast between the two phases. The model aims to describe morphological transitions in smectic thin films under heat treatment, in which arrays of focal conic defects evolve into conical pyramids and concentric rings through curvature dependent evaporation of smectic layers. The model leads to an extended thermodynamic relation at a curved surface that includes its Gaussian curvature, non-classical stresses at the boundary and flows arising from density gradients. The temporal evolution given by the model conserves the overall mass of the liquid crystal while still allowing for the modulated smectic structure to grow or shrink. A numerical solution of the governing equations reveals that pyramidal domains are sculpted at the center of focal conics upon a temperature increase, which display tangential flows at their surface. Other cases investigated include the possible coalescence of two cylindrical stacks of smectic layers, formation of droplets, and the interactions between focal conic domains through flow.
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Affiliation(s)
- Eduardo Vitral
- Department of Mechanical Engineering, University of Nevada, 1664 N. Virginia St., Reno, NV 89557, USA.
| | - Perry H Leo
- Department of Aerospace Engineering and Mechanics, University of Minnesota, 110 Union St. SE, Minneapolis, MN 55455, USA
| | - Jorge Viñals
- School of Physics and Astronomy, University of Minnesota, 116 Church St. SE, Minneapolis, MN 55455, USA
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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, Eremin A. On Droplet Coalescence in Quasi-Two-Dimensional Fluids. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2020; 36:10615-10621. [PMID: 32787035 DOI: 10.1021/acs.langmuir.0c02139] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Coalescence of droplets plays a crucial role in nature and modern technology. Various experimental and theoretical studies explored droplet dynamics in three-dimensional (3D) and on 2D solid or liquid substrates. In this paper, we demonstrate the complete coalescence of isotropic droplets in thin quasi-2D liquids-overheated smectic films. We observe the merging of micrometer-sized flat droplets using high-speed imaging and analyze the shape transformations of the droplets on the timescale of milliseconds. Our studies reveal the scaling laws of the coalescence time, which exhibits a different dependence on the droplet geometry from that in the case of droplets on a solid substrate. A theoretical model is proposed to explain the difference in behavior.
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Affiliation(s)
- Christoph Klopp
- Institute of Physics, Department of Nonlinear Phenomena, Otto von Guericke University, Magdeburg 39106, Germany
| | - Alexey Eremin
- Institute of Physics, Department of Nonlinear Phenomena, Otto von Guericke University, Magdeburg 39106, Germany
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