Optical interferometric studies of a confined liquid free surface : meniscus-effect compensation and time evolution of the surface

Lea V. Bourimborde Alejandro Tonso Lía M. Zerbino Mario Garavaglia Centro de Investigaciones Opticas (CONICET CIC) Casilla de Correo 124 La Plata 1900, Argentina E-mail: postmaster@ciop.edu.ar Abstract. A fruitful approach to the studies of a liquid free surface is demonstrated. Using optical interferential techniques, the free surface of nonvolatile and volatile confined liquids is analyzed. Various wall con tainer types are investigated. Besides the classical plane wall, experi­ ments are performed by using cylindrical and toroidal walls. In these last cases, the meniscus effect that affects the free surface of the liquid is compensated. Then, it is possible to obtain completely flat free surfaces of liquids up to 80% of their total. Interferometric experiments are also described to measure the inclination of the site with respect to the local horizon, represented by the liquid flat free surface, and to follow the temporal evolution of such free surfaces affected by different conditions.


Introduction
As is well established, the free surface of a confined liquid is not a plane.In the case of a container of large dimensions, however, it is possible to consider that a small portion of the free surface be planar.To some extent, this small portion is located at the central part of the entire liquid surface.
Nevertheless, in some particular and practical situations it is convenient or necessary that all of the free surface be a plane, in spite of the fact that the container had small di mensions.These cases are present in the studies of aged liquid surfaces or evaporation produced at liquid surfaces.In ad dition, planar free surface of liquids are important factors in the design and development of high accuracy levels.
Various optical methods were introduced to experimen tally analyze the different physical phenomena that occur at the interface of two media.Holographic interferometry,1 differential interferometry,2 and ultrasonic holography3 can be Paper ARG 12 received Apr.18. 1995: revised manuscript received May 29, 1995: accepted for publication May 30.1995.© 1996 Society of Photo-Optical Instrumentation Engineers.0091-3286/96/S6.00.
cited as examples.The free surface of a liquid has also been used as a metrological reference surface.4 6 In this paper, we offer 1. a new experimental solution to obtain plane free surfaces of confined liquids in small containers 2. the use of such an approach in the development of an optical device of very small dimensions to check in a real-time mode the flatness of the liquid free surface 3. the possibility to follow up the temporal evolution of the free surface of a confined volatile liquid due to its evaporation 4. the possibility to follow up the changes in the horizontal position of small pieces in a real-time mode.
The experimental results obtained with the liquid-optical device are the magnitude, the direction, and the sign of the angular changes of the liquid surface.The threshold of the sensitivity of the overall device is A ± 7X 10-6 rad.
As a first step, a container with toroidal borders confining nonvolatile liquids was studied.A loading tube serves to load The free surface of the liquid can be considered as a phase object and then the monochromatic light reflected and refracted on it contain information related with its topography.Such information can be revealed by simple interferential techniques.
The dynamic analysis o f such optical information, how ever, presents a high degree of complexity, because it is necessary to control a large number o f experimental parameters to achieve quantitative evaluations of acceptable quality.

Description of the Experimental Method
The topological shape of the free surface of a confined liquid depends on the equilibrium o f the gravitational and capillary forces.Formally, they depend on the capillary constant a value and the contact angle formed between the liquid surface and the container wall.In the case o f a plane vertical wall, the profile of the liquid free surface is expressed as If the level of the liquid is lower or higher than h> the shape of the surface will appear as concave or con vex according to the wetting function of the liquid cylinder interface.
Assuming that the topological shape of the free surface is flat, it is possible to use it as a horizontal reference plane.Then, a container whose bottom is a transparent optical planeparallel window can serve as an interferometrical level.Fig ure 2   As long as the container is loading with the liquid, the free surface adopts different topologies: concave, plane, and convex, as shown in Fig. 3.Such surfaces act as mirrors that change shape according to the liquid level.When h reaches the appropriate value to compensate the meniscus effect mak ing a 0, the free liquid surface will be flat.This position is considered to be the setting point of the device.If the base platform on which the device is mounted adopts the hori zontal position, the interference fringes that are observed while the free liquid surface shape is modified by loading liquid into the container appear as a symmetric pattern.This fact is assumed as to be the best criteria to fill the container until a is equal to 0. In addition, near the setting point, the fringes in the interference pattern become wider and more and more spaced, but they always maintain their symmetry.

Experimental Results
As mentioned before, when the liquid entering the container adopts level positions deeper or higher than h, the free surface looks like concave or convex mirrors.Then, the interference pattern observed on a screen changes according to the amount of liquid loaded into the container, as shown in Fig. 4(a).If the mounting base of the liquid-optical device is arbi trarily inclined, it is easy to measure its lack of horizontality.Every picture shows the fringe patterns and their correspond ing densitométrie traces.Fringes, that are equally spaced by e, are identified by correlative digits representing the inter ferential order with respect to the center of the patterns, as shown in Fig. 12.
These observations enable us to demonstrate that evap oration is preferentially produced at the middle of the free surface.In fact, comparing the consecutive temporal pictures it is easy to observe that fringes corresponding to equal liquid thickness appeared at distances farther and farther from the center o f the pattern.In addition, in these zones of the liquid free surface the distances between fringes are also greater and greater as a function of time.Thus, the evaporation phe nomena begin at the middle of the liquid free surface and slowly propagate to the borders of the container, as stated before.

Conclusions
A method to compensate the effect of the border to obtain a plane free liquid surface appears to be of great interest in studying the properties of fluids.It enables us to easily per form experiments at the laboratory, on which can be assumed conditions of infinitely extended surfaces by using, in fact, very small containers.
The liquid optoelectronic device is easy to build and is versatile and flexible to use.It acts as an interferential liquid level, the performance of which represents progress with respect to other liquid levels.911 The proposed device is also very stable from the mechanical point of view and the method has an extended range to observe and measure different kinds of effects with a threshold sensibility at least 10 times greater than others.
70 / OPTICAL ENGINEERING / January 1996 / Vol.35 No. 1 liquid into the cavity of the container.The loading process was followed by optical interference and the interferometrical information was real-time recorded and each image was digitally processed.
describes the experimental setup.The He Ne laser and the inverted telescope with spatial filter provide a well collimated monochromatic light beam.By using a front surface mirror, the plane wave illuminates the liquid container from the top.A beamsplitter collects the light waves coming from the free liquid surface and from first plane optical surface at the bottom o f the container.A CCD TV camera captures the interference between both waves, sending the signal to the real-time image processor.The liquid container is a 70-X 50-mm plastic rectangular cavity, whose walls are formed by cylindrical glass rods 8 mm in diameter.The container is sealed at its bottom by a plane parallel glass plate 10 mm thick and X /10 flat.The entire container is located on a platform that is horizontally aligned using appropriate fine screws.Inside the described cavity, the toroidal ring is mounted, simply supported by the bottom glass plate.The dimensions o f the toroidal ring are 5.4 mm for section diameter and 16.8 mm for the inner di ameter.OPTICAL ENGINEERING / January 1996 /V ol.35 No. 1 /71 336 where xQ is determined taking into account that (dy)/(d;c) coté at jc 0, and that y vanishes at jc » o (Ref.7).Nevertheless, it is impossible to develop a plane liquid free surface using plane vertical walls because o f the influence of meniscus.Because of that, to obtain a plane liquid free surface it is necessary to introduce a cylindrical wall.Figure1answers this question.If the level of the liquid inside of the container is equal to h, its free surface will form with the geometrical tangent to the cylinder an angle a whose value will be equal to 0 .In that case, the influence o f the meniscus is compensated by the wall, and the liquid free surface will be completely flat.

F
ig . 1 W h en the surrounding w alls h a ve cylind rical sh a p e , it is p o s sible that y 0 (horizontality) w hen a 0. F ig . 2 E xperim ental setup.conveniently isolated to avoid mechanical perturbations.It was designed and constructed as a hydraulic device to load and unload liquid to or from the container, respectively, which enables changes in the liquid free level surface with an accuracy A h ± 100 nm, without perturbing the surface.The different kind of experiments and measurements were performed using silicone oil (Dow Corning Fluid 350).At 25°C it has the following physical characteristics: viscos ity 3 5 0 cS, density 0.97 g/cm 3, refractive index 1.403, and surface tension 21.1 dyn/cm (Ref.8).

Figure 4 (Figures 5 , 6 ,
Figures 5, 6, and 7 are pictures of the interference pattern produced with the device.In these experiments, those surfaces that are less than 0.633 p m from a geometrical plane are accepted as flat" surfaces.Obviously, 0.633 p,m is the wavelength of the red He Ne laser used to illuminate the device.Figure 5 corresponds to the rectangular container 50 mm wide and 70 mm long with vertical plane walls.The interference pattern is deformed because of the lack of flatness along the entire free liquid surface.The zone that can be considered as a plane is less than 28% of the total surface.

F ig . 3 D
epending o n the liquid level, the free surface will be c o n ca ve , plane, or c o n ve x.

Figure 6 F ig . 6
Figure 6 corresponds to the same sized rectangular container but with circular cylinders acting as walls.In spite of the fact that the liquid level did not reach a high enough altitude h to be a 0, the zone that is considered a plane is almost 37% of the total surface.Figure 7 corresponds to the same experimental setup as that of Fig. 6, but the level o f the liquid is almost that for

Fig. 8
Fig. 8 (a) E le ctro n ic picture and (b) densitom étrie trace to m easure inclination c h a n g e s o f the optoliquid de vice .

Figure 8 Figures 9 , 10
Figure 8 is a picture of the interferential pattern observed and its densitométrie profile captured by perpendicularly scanning the fringe family.Measurements resulted in incli nation of <p 3.1 X 10 4 rad in a direction that forms an angle o f 19.5 deg with respect to the x axes.Figures 9, 10, and 11 correspond to a series of consecutive pictures that demonstrate the temporal evolution of the in terferential pattern.Along the time of observation, the effect Figures 9, 10, and 11 correspond to a series of consecutive pictures that demonstrate the temporal evolution of the in terferential pattern.Along the time of observation, the effect of the meniscus was compensated by maintaining a 0.

FF
Fig. 10 (a) Electronic picture and (b ) densitom étrie trace.F rin g e s 5, 6. a nd 7, w hich are equally sp a ce d , are m o ved from the center to the bo rd e r of the container be ca u se of liquid evap ora tion .