Influence of Surface on the Development and Dynamics of Droplet Coalescence in Optical Cells at the Isotropic Liquid–Liquid Crystal Phase Transition

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Abstract

The work presents results of studies of coalescence of nematic liquid crystal droplets surrounded by isotropic liquid. With the aid of high-resolution optical microscopy and high-speed video recording coalescence of droplets in thin optical cells has been studied. Cells with planar and homeotropic boundary conditions for the liquid crystal director were used. It is shown that depending on boundary conditions at the cell surface the coalescence process at the initial stage develops in a different manner. In a cell with planar boundary conditions at the initial stage we observe linear dependence of the width of the neck between droplets on time. At subsequent stages the influence of surface leads to slower dynamics. The final stage of coalescence is characterized by exponential relaxation of the droplet to the equilibrium shape. At coalescence of droplets whose diameter exceeds the cell thickness, we observed an intermediate stage with power-law dependence of the neck width on time. The duration of this stage increases with increasing the droplet size. Capillary velocity and characteristic times at different stages of coalescence were determined. Characteristic times for the initial stage increase linearly with increasing the droplet size. For the middle stage the characteristic times increase proportionally to the third power of the droplet radius.

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About the authors

P. V. Dolganov

Osipyan Institute of Solid State Physics RAS

Author for correspondence.
Email: pauldol@issp.ac.ru
Russian Federation, Chernogolovka, 142432

N. A. Spiridenko

Osipyan Institute of Solid State Physics RA

Email: pauldol@issp.ac.ru
Russian Federation, Chernogolovka, 142432

V. K. Dolganov

Osipyan Institute of Solid State Physics RA

Email: pauldol@issp.ac.ru
Russian Federation, Chernogolovka, 142432

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2. Fig. 1. Schematic representation of the stages of fusion of a pair of round droplets: drops before fusion (a); a dumbbell-shaped drop at the initial stage of fusion (b); an elliptical drop (c); the final state after relaxation, a round drop (d). The dotted line shows the area of the isthmus between the drops. W is the width of the isthmus (b), which transforms into a short axis of an elliptical drop (c).

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3. Fig. 2. Sections of two nematic droplets (N) in the area of their contact and fusion surrounded by an isotropic liquid (Iso) under planar boundary conditions (cell 1): droplets 0.01 s before the start of fusion (a); formation of an isthmus between the droplets, after 0.01 (b), 0.02 (c) and 0.03 s (d) after the start of their fusion. The horizontal size of the images is 20 microns.

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4. Fig. 3. Sections of two drops of nematic (N) surrounded by an isotropic liquid (Iso) under homeotropic boundary conditions (cell 2): drops before fusion, the visible boundaries of the drops are at a considerable distance from each other (a); drops after the beginning of fusion, the distance between the visible boundaries of drops Δ1 remains finite (b); formation of a layer of the isotropic phase between the droplet boundaries, the thickness of the isotropic phase section Δ2 decreases on both sides of the center (c); rupture of the isotropic phase section with the formation of a central droplet and satellites (d). Images (c) and (d) were obtained 0.3 and 0.6 seconds after (b), respectively. The horizontal size of the images is 32 microns.

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5. Fig. 4. Time dependence of the interval between the visible boundaries of drops Δ1 in cell 2 (solid symbols). The moment t = t0 corresponds to the rupture of the isotropic phase interlayer. The empty symbols are the width of the gap in the thinnest sections on both sides of the center Δ2 (Fig. 3b). The rate of width reduction before tearing is ~15 microns/s. An increase in Δ1 at t — t0 > -0.25 s is associated with the formation of a central droplet.

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6. 5. Time dependence of the isthmus width between merging droplets under planar (solid symbols) and homeotropic (empty symbols) boundary conditions. The drop radii are 9.3 microns (1), 15.5 microns (2), 27.1 microns (3), 32.8 microns (4). The dotted line is an approximation by linear dependence, the solid line is a power dependence with an exponent of 1/5.

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7. 6. Characteristic times of droplet fusion at the initial (dots) and average (squares) stages of coalescence under planar boundary conditions. The solid line is an approximation by the linear dependence t ~R, the dotted line is by the dependence tS ~ R3.

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