Dynamic processes in the liquid crystal-water emulsion under shear flow and electric field

We present the results of experimental investigation of dynamical processes arising in liquid crystal-water emulsion under action of a decay shear flow and ac electric field. The 10 : 1 emulsion, consisting of the well-studied nematic mixture E7 and ionized water was prepared by usage of ultrasonic (29 kHz) mixer. It made possible to get a number of water droplets with the distribution of diameters in the range 2… 20μm. So, the slow decreasing of sizes of these instabilities resulted in corresponding slow motion of the attracted water droplets. The strong electric filled, which stabilized the initial homeotropic orientation of LC suppressed the flow induced instabilities and the slow motion of water droplets mentioned above. It also induced the aggregation of droplets in the vicinity of boundary between regions with strong field and free of field. So, combined action of shear flow and electric field can be effectively used for manipulation of the motion and interaction of water droplets. The obtained results are discussed within the existing theory of liquid crystals.


Introduction
Liquid crystals (LC), which differ from classical solid crystals by partly (smectic liquid crystals) or totally (nematic liquid crystals) destroyed long range positional order are known as modern smart materials widely used in display industry and also perspective for non-display applications [1,2].It is provided, in particular, by high sensitivity of LC to the action of different external factors, like electric or magnetic fields, pressure gradients and impurities dispersed in isotropic liquids, which contacted with liquid crystals [1,2].In the latter case, both plane layers and LC droplets immersed into isotropic environment were considered as platforms for realization of LC biosensors [3].Recently [4], the opposite composite system -isotropic droplets of water immersed in nematic liquid crystals was proposed for a controllable transit of isotropic liquids through microfluidic channels.Such approach was based on formation of line defects in LC along the channel due to the proper surface treatment of the inner surfaces of the channel.These defects played the role of the droplets' attractors which provided railway type of a droplets' motion along the channel, induced by a shear flow of liquid crystal.Previously it was shown, that intensive shear flow induced in a plane channel with the initial homeotropic orientation a number of hydrodynamic instabilities of different types [1].
In this paper we present the results of experimental investigation of dynamical behavior of water droplets in the decay capillary flow of LC, which is similar to the previously investigated decay flows of LC throw plane channels [1] and porous polymer films [5], except for the driving force (capillary force instead of hydrostatic pressure gradient).

Experimental
The capillary flow was realized at filling the wedge like open cell with LC -water emulsion.The construction of the cell, shown in Figure 1 was similar to that, previously used in experiments with a capillary rise of LC [6].The cell consisted of the two glass plates, separated by two cylindrical nylon spacers of different diameters.It made possible to get a capillary of the variable gap (60 . . .100µm) after fixing the plates with a clue.The inner surfaces of the glass plates were coated by the conductive ITO layers, which were partly deleted on the one plate.It made possible to reveal the peculiarities of a capillary flow in the absence and presence of ac electric field with frequency f = 3kHz, supplied by the high frequency generator.The inner surfaces of the capillary were treated preliminary (spin coating of 0.5% solution of chromolane in propanol with further drying) to provide initial homeotropic surface orientation of LC.

Figure 1. The construction of the cell
Before filling, the cell was placed horizontally on the stage of the polarizing microscope POLAM L-213M (LOMO).It simplifies the description of a capillary flow in the comparison with a capillary rise, as only the capillary and viscous forces (F c and F v ) without gravity force define dynamics of a capillary flow [7].The corresponding geometry of the experiment is shown in Figure 2. The 10 : 1 LC-water emulsion, used in experiments was prepared by ultrasonic mixing of deionized water and the well-studied nematic mixture E7 with high (about 13) positive value of the dielectric permittivity anisotropy.It made possible to control the complicated non-linear phenomena, taking place in shear flows of liquid crystals.In particular, previously it was found, that in the case of the initial homeotropic orientation application of the stabilizing electric field may strongly suppress arising of the hydrodynamic instabilities [1].At the initial stage of an experiment the electric voltage of amplitude U was applied to the cell.Afterwards a portion of LC emulsion was put in a contact with the open edge of the cell.It resulted in arising of the capillary flow, which was registered in a polarizing light (crossed polarizers was oriented at 45 • relatively to the flow direction) with the help of the video camera, connected to the personal computer.Additionally, the experiments with the capillary rise of LC were performed to get an information about the combination σcosθ C of the surface tension coefficient σ and contact angle cosθ C .In experiments, the same vertically orientated cylindric capillary (300µm) was used for registration of the maximal heights of ethanol (H e ) and LC (H LC ) rise.To get the homeotropic surface orientation of LC the capillary was treated in the same manner as described above for the plane capillary.
where ρ e = 0.022 N/m and ρ LC = 0.98 N/m are the densities of ethanol and LC, H e max = 30 mm, H LC max = 22 mm corresponding values of a capillary rise.

Results and discussion
The microscopic polarized images of the central part of the cell, taken off at different times after beginning of the capillary flow are shown in Figure 3.One can observe the motion of the contact line L(t) with the decreasing velocity.Such decay type of the flow can be easily explained taking into account the balance between capillary and viscous forces, which defines the motion of a contact line [6]: where is the capillary pressure, and is the pressure drop caused by viscosity losses during the laminar flow of a liquid through the plane capillary; σ is the coefficient of the surface tetion, θ c is the contact angle, η is the effective value of the shear viscosity of a liquid.The increase in the vicous of pressure drop over time as well as the indendence on time of the capillary drop explains the decay character of the capillary flow.By inserting (3) and (4) into expression (2), it is simple to obtain the next differential equation for L(t): with the solution, written as: IC-MSQUARE-2023 Journal of Physics: Conference Series 2701 (2024) 012131 Using equation ( 6) and values of dL dt = 190 µm s at L = 10 mm obtained from Figure 2 it is possible to estimate the effective value of the shear viscosity.The combination σcosθ C which enters in (5) was calculated from the results of the experiments with the rise of LC in the vertical cylindrical capillary in an accordance with equation (1).Using the experimentally measured values H e = 30 mm and H LC = 22 mm the value of the combination σcosθ C was determined as 0.013 P a * s.
The value of the effective shear viscosity coefficient was estimated as η ef f = 0.092P a * s.This value is intermediate between maximal (η 1 = 0.264P a * s) and minimal (η 2 ≈ η 1 −γ 1 ≈ 0.04P a * s, γ 1 = 0.224 P a * s -the rotational viscosity) values of the shear viscosity of E7 [1,8,9].It corresponds to the chaotic distribution of a director shown seen in Figure 3.It is of importance that such nonuniform distribution of LC orientation can be observed for a long time past after the capillary flow stopped (see in Figure 3).Previously, similar long living instabilities were observed after action of the decay shear flow of MBBA [1].
The interesting effect observed due to the action of the capillary flow was the aggregation of droplets in the region of high values of the electric field gradient that occurs in the vicinity of the electrode's boundary.This effect is illustrated by the images shown in Figure 4.This aggregation takes place due to distortions of the orientational structure of the liquid crystal in the vicinity of the drops, which leads to the appearance of an excess Frank energy associated with orientational structure gradients.In particular, it leads to the appearance of an attractive force F a (r) acting between two drops located at distance r.The equation of droplet motion, which determines the dependence of distance r on time t, can be obtained taking into account the balance of attractive and viscous forces acting on each droplet [10]: where a and m are the radius and mass of the droplet.
In the case of a stationary motion equation ( 7) leads to the next expression for F a (r): The estimate of the attractive force F a (r) acting between two droplets shown in Figure 4 gives the value 0.87 pN at η ef f = 0.092 P a * s, a = 4µm.The obtained value has the same order of magnitude as that obtained for attractive forces between two ferrofluidic droplets of the similar sizes immersed into nematic LC mixture with a comparable value (0.023 P a * s) of the effective shear viscosity.

Conclusion
The capillary flow of LC -water emulsion in the presence and absence of electric field is realized for the first time.The strong aggregation of water droplets induced by the shear flow was observed in the vicinity of a boundary between "field on" and "field off" regions of the experimental cell.The value of the effective shear viscosity of the emulsion was estimated and used for calculation of the attractive force acting between two water droplets.The value of this force has the same order of magnitude as that obtained in emulsions ferroelectric droplets immersed into nematic liquid mixture.It indicates on the general nature of droplet's interaction for both cases.

Figure 3 .
Figure 3. Microscopic images of the central part of the cell with the contact line at different times after arising of a capillary flow

Figure 4 .
Figure 4. Formation of droplet's conglomerates at the boundary between regions with and without an electric field