ELECTROHYDRODYNAMIC FLOW IN NEMATIC THIN FILMS WITH TWO FREE SURFACES

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ELECTROHYDRODYNAMIC FLOW IN NEMATIC THIN FILMS WITH TWO FREE SURFACES

S. Faetti, L. Fronzoni, P. Rolla

To cite this version:

S. Faetti, L. Fronzoni, P. Rolla. ELECTROHYDRODYNAMIC FLOW IN NEMATIC THIN FILMS WITH TWO FREE SURFACES. Journal de Physique Colloques, 1979, 40 (C3), pp.C3-497-C3-501.

�10.1051/jphyscol:1979399�. �jpa-00218796�

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JOURNAL DE PHYSIQUE Colloque C3, supplkment au no 4, Tome 40, Avril 1979, page C3-497

ELECTROHYDRODYNAMIC FLOW IN NEMATIC THIN FILMS WITH TWO FREE SURFACES

S. FAETTI, L. FRONZONI and P. A. ROLLA Istituto di Fisica dell'Universit8 di Pisa, Pisa, Italy

and

Gruppo Nazionale di Struttura della Materia del CNR, Pisa, Italy

RCsum6. - Lorsqu'on applique un champ klectrique sur une lame mince de cristal liquide nkma- tique avec deux surfaces libres, on observe une structure hydrodynamique caracterisee par quelques tourbillons. Dans cet article nous reportons des nouvelles observations qui dkmontrent que ce regime ne peut pas &tre interpret6 par le modble de Felici de l'injection de charges. Les lignes d'un nouveau modkle, qui explique les principales proprietks de ce regime, sont proposkes dans cet article.

Abstract. - Thin layers of nematic LC with two free surfaces show a peculiar vortex-pattern when subjected to an electric field. In this paper we report some new observations on the vortex motion and we show that the Felici's model of the charge injection from the electrodes cannot account for some experimental results. The lines of a new electrohydrodynamic model are proposed and compared with the experimental data.

1. Introduction. - The electrohydrodynamic pro- perties of the nematic LC are usually investigated in thin films sandwiched between two parallel glass plates. With these experimental conditions one obser- ves the well known electrohydrodynamic instabilities (WDM [l], DSM [2].

.

.).

We obtain very different hydrodynamic and orien- tational boundary conditions by building a nematic liquid thin layer with two free surfaces. A peculiar vortex-pattern is observed when an electric field, parallel to the free surfaces, is applied in a thin free layer. This vortex motion has been observed both in a square free film [3] and in a rectangular free film [4].

Similar vortices have been observed in the early thirties by Advsec et al. [5] in some isotropic liquid samples having a single free surface. In a previous paper it has been shown that the Helfrich's model [6] cannot explain the main features of this vortex mode (VM).

In this paper we report some new experimental data which cannot be explained on the basis of the Felici's model

[q

of the charge injection from the electrodes. However the experimental data indicate that the VM can be interpreted considerating the electric charges which lie on the two free surfaces.

These charges are driven and accumulated on the free surfaces by the electric field until a stationary arrangement is reached. The electric field interacts with the surface charges and generates a shear stress which moves the liquid.

2. Experiment. - 2.1 APPARATUS. - The free films aie obtained by suspending a nematic drop on a rectangular frame made of four wires of diameter 30 pm : two oppqsite wires are conducting, whilst the other ones are insulating (Fig. 1). The interwires distances (d and h in Fig. 1) can be gradually changed so to obtain different geometries of the film. The voltage is applied in a symmetric way in order to obtain the greatest symmetry of the electric field and of the surface charges (Fig. 1). The temperature of the nematic layer is regulated within f 0.1 OC by means of a thermostatic box. The liquid crystal used in all measurements is MBBA produced by FASTMAN KODAK Co. with a nematic-isotropic transition temperature of 41.5 OC.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1979399

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C3-498 S. FAETTI, L. FRONZONI AND P. A. ROLLA

The nematic layer has been observed either with white light, by means of a polarizing microscope, or with monochromatic light (He-Ne laser) by means of a strioscopic device [8]. The latter method has been utilized by other authors [S] for investigations of electrohydrodynamic motions in polar liquids.

As a main advantage of this arrangement we remark that we are able to detect very small thickness varia- tions induced by the hydrodynamic flow also in the isotropic phase.

The shape of the layers is measured by observating the interference patterns produced by the beams reflected from the two free surfaces.

a) The appearance of the VM is, often, preceded by a strong oscillation of the whole free layer;

b) Some times the VM appears even if V < V,.

In this case, however, the vortices are not stationary and decay in a short time. When V

5

V,, the layer becomes very unstable and, often, we may observe an intermitted start and decay of the vortices. These instabilities are clearly visible in the current-voltage characteristic in figure 2 for V

5

V,. Finally the VM becomes stationary if V > VC ; therefore this value must be considerated as the VM stability threshold voltage ;

2.2 RESULTS. - The molecular orientation of the nematic layer is strongly dependent on many parameters [9] as the temperature, the thickness and the bending of the free surfaces. A suitable adjustment of these parameters allows us to obtain a homeotropic orientation of the director all over the layer. This condition is very important in order to obtain repro- ducible measurements on the VM. In fact an electric field, applied to a layer having a dishomogeneous molecular orientation, induces a bulk space charge which may trouble strongly the VM.

Furthermore we remark that our measurements are performed with very elongated layers (h > 10 d).

In this conditions, the electric field does not substan- tially change along the x axis, parallel to the conducting wires, so that the VM phenomenology is more repro- ducible.

Must of the experiments have been performed using d.c. electric fields and the experimental dispo- sition of figure 1 ; however some experimental observations have been carried out using a.c. electric fields and insulated electrodes in order to avoid the charge injection from the electrodes.

2.3 THRESHOLD OF THE VORTEX MODE. - AS reported in a previous paper we never observe a threshold of the hydrodynamic motion in thin nematic layers.

In fact a very slow and uncorrelated motion starts as soon as a low voltage is applied between the two conducting wires.

However, with the help of the strioscopic method, we observe a sudden change of the hydrodynamic motion when the voltage exceeds a threshold value V,.

If V > V,, a stationary vortex pattern appears all over the layer. If the voltage is further increased, the hydrodynamic motion induces a relevant tilt of the director all over the layer. This orientation is evidenced by a sharp increase of the light diffused from the nematic layer at a voltage very close to the

V , value.

The phenomenology of the VM is very different from the one characterizing the well known electrohydrodynamic regimes as the Williams Domain Mode [l] and the Dynamic Scattering Mode [2].

As a matter of the fact we point out that :

FIG. 2. - Current-voltage characteristic of a thin free layer at the temperature of 30 OC.

c) A sudden change of the hydrodynamic velocity is observed when the threshold voltage is reached.

The hydrodynamic velocity in a vortex is about 100 times the velocity measured when V < V,.

This sudden change is, also, evidenced by measuring the electric current which flows across the nematic layer. To perform this measurement the layer is immersed in a dry atmosphere in order to reduce the current flow across the air. The current-voltage characteristic is shown in figure 2. We point out that the electric current shows a sudden change when V = V, and it shows several fluctuations below V,.

The same effect is observed in the isotropic phase, so that it cannot be attributed to a change of the molecular orientation. The sharp variation of the electric current indicates that the charges velocity increases according with the dragging effect of the hydrodynamic motion. The curve in figure 2 contri- bute to evidence the peculiarity of the VM. In fact, the electric current, as measured in the usual glass cells 110, 111, only shows a change of slope when the electrohydrodynamic threshold voltage is reached.

By studying the dependence of VC on the average thickness of the layer we have observed that the VM is not a peculiar characteristic of very thin layers.

In fact the VM can be also observed if the average

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ELECTROHYDRODYNAMIC FLOW IN NEMATIC THIN FILMS C3-499 thickness of the layer exceeds 10 pm. In this case a

domain-like texture [4] appears when the voltage exceeds a V, value, whilst the VM occurs when the voltage exceeds a second threshold value V,. We find that V, and

V,

are increasing or decreasing functions of the average thickness of the layer. If the average thickness s is

-

^{5 pm,} ^V. ^V,^and

domains and vortices may coexist on the same layer ; i f s 4 5 pm, the domain-like texture is not observed.

2.4 OBSERVATIONS WITH INSULATH) ELECTRODES. -

In a previous experiment we found that the vortex motion was also present when an a.c. electric voltage was applied between two conducting wires coated with an insulating paint. From this experiment we can infer that the charge injection from the electrodes is not determinant to explain the a.c. phenomenology.

However this observation does not exclude that the injection of charges contribute to generate the VM.

To test the relative influence of the charge injection on the a.c. and d.c. regimes we have built a special cell which allows us to compare directly on the same layer the VM with and without charge injection.

This cell is schematically drawn in figure 3. The conducting wires are insulated on the right of the

FIG. 3. - Nematic free layer \ \ ~ t h insulated and not insulated electrodes.

A points, whilst they are not insulated on the left.

In the B region between the electrodes (Fig. 3), the electric field strongly depend on the frequency v of the applied field. If v > 0.1 Hz the electric field is

-

equal in the B and C regions of the layer, whilst its value in the B region decreases if v is reduced below 0.1 Hz. The threshold of the VM is the same in both regions if v > 0.1 Hz, whilst it is higher in the B region if v < 0.1 Hz. The threshold value in the C region does not change appreciably when the frequency is changed in the range from zero up to 0.1 Hz. These experimental results demonstrate that the injection of charges from the electrodes does not influence appreciably the VM both in a.c. and d.c. electric fields.

2.5 OBSERVATIONS WITH EXTERNAL ELECTRODES. -

To explain the VM we suggest that it is produced by the interaction between the electric field and the surface charges which lie on the two free surfaces of the layer.

In order to support this interpretation, we have performed the following experiment which tests the influence of the surface charges on the VM. A d.c.

electric voltage is applied between two electrodes external to the nematic layer (Fig. 4). An external d.c.

electric field does not penetrate into the nematic layer but only modifies the charge arrangement on the two free surfaces. The surface charge density decreases when the external voltage has the same sign of the internal voltage (Fig. 4) whilst it increases in the opposite case. If these surface charges influence the VM, one expects that the external voltage changes appreciably the threshold voltage of the VM. We find that the threshold voltage increases or decreases if the external and internal voltages have the same or the opposite sign. These results show that the surface charges play an important role in the VM phenomenology.

I

FIG. 4. - Experimental geometry with electrodes external to the free layer.

3. Concluding remarks. - It is shown from the experimental results that the VM phenomenology cannot be easily accounted by Felici's model. This conclusion can be deduced from the observations performed with insulated and not insulated electrodes.

Also the increase of the V, threshold with the thickness of the layer hardly agrees with the Felici's model.

However the experimental observations seem to agree with a surface charge model. In fact, as soon as a d.c. voltage is applied between the two electrodes, the bulk ionic charges move along the lines of the electric field. Some charges are accumulated on two free surfaces because of the discontinuity of the electric conductivity between the nematic liquid crystal and the surrounding air [12]. The final charge arrangement is reached after a few relaxation times

where ^Eand k are respectively the dielectric constant and the electric conductivity constant of the MBBA.

The field lines and the surface charge arrangement in the stationary state afe schematically drawn in figure 5a and 5b. A surface force F = oE results from the interaction between the surface charge density o and the electric field E, as schematically shown in figure 5b. This force cannot be balanced by a static pressure gradient but only by a shear stress so that, as experimentally observed, the liquid cannot be at rest. If the surface charge arrangement is uni-

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S. FAETTI, L. FRONZONI AND P. A. ROLLA

FIG. 6 . - Top view of the surface charge distribution produced by the hydrodynamic flow.

a flow line does not vanish and therefore the vort,ex motion can be emphasized. If the driving force exceeds the resisting viscous force, the hydrodynamic velocity increases until the stationary vortex mode is reached. As a main characteristic of this stationary vortex pattern induced by surface charges, the hydro- dynamic velocity v lies along planes parallel to the xy plane but it is not constant along the z vertical axis since av/dz = 0.

The threshold voltage of the VM can be deduced by equating the integral of the surface electric force along a flow line with the integral of the surface viscous force along the same flow line. A semi- quantitative evaluation of these forces gives : FIG. 5a. - Top view of the nematic layer with the surface charge

arrangement. The vectors represent the surface force cE.

where r] and k are respectively viscosity and electric conductivity coefficients and a is a coefficient which depends on the dielectric constant and on the geome- trical parameters of the layer. The coefficient cc a has the dimension of a length and is an increasing function of the layer thickness, as experimentally observed.

Equation (1) can be also derived by using a simple dimensional analysis.

Let us remark, however, that for an accurate determination of a one needs to solve the Navier Stokes equation and the Laplace equation of the electric field with the proper hydrodynamic boundary conditions. This is a very difficult problem since the boundary conditions of the hydrodynamic motion and of the electric field strongly depend on the free surface shape which, in turn, is a function of the hydrodynamic motion.

Finally we notice that, at present, our results do not exclude that a bulk (not injected) space charge contributes to establish the VM according to a mechanism of the type reported by Barnik et al. [13]. The experimental and theoretical analysis of the electrohydrodynamic instability is now in progress in our laboratory in order to distinguish between these two possible mechanisms.

FIG. 5b. - Side view of the nematic layer. The picture shows the electric field lines (broken lines) and the charge distribution on the two free surfaces. The outside vectors represent the surface force

direction.

form along the ^X axis, it should result in a hydrodynamic motion along planes parallel to yz. Indeed the integral of the surface force along any closed line in the xy plane vanishes and therefore no sta- tionary motion can occur along this line if V V,.

Let us remark however that, in our experimental conditions, some disuniformity of the surface charge distribution may occur especially near the wires, so that slow and irregular motions may occur in the xy plane also below V,. In order to explain the VM instability we propose a very simplified mechanism shown in figure 6. If a vortex fluctuation occurs in the xy plane, the initial charge is modified due to the hydrodynamic flow. When the surface charges are dragged by the hydrodynamic flow, the electric field inside the nematic layer changes and new ionic charges move from the bulk towards the two surfaces.

This rearrangement is completed in a few dielectric relaxation times. The new surface charge is schematically shown in figure 6. We notice that, in this case, the integral of the surface electric force along

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ELECTROHYDRODYNAMIC FLOW I N NEMATIC THIN FILMS

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[l21 See for example LANDAU, L., Electrodynamique des Milieux Continus (Editions Mir) 1969.

[l31 BARNIK, M. I., BLINOV, L. M., GREBENKIN, M. F. and TRU- FANOV, A. N., M o ~ . C l y ~ t . Liq. C r y ~ t . 37 (1976) 47.