Note: This was one of the first technical photography papers that I published. Additional papers can be found in the the SPSE Journal dating from the very early 70's.

Abstract: Movements of the surface of a liquid and convection currents within the liquid during heating and cooling are shown simultaneously using a dual reflection-refraction photographic schlieren system. Means are furnished for identifying and measuring hills and valleys and correlating these with rising and descending streams within the liquid. Two models are selected, melted paraffin wax and isopropyl alcohol, the latter evaporating quietly into its pure vapor, with air excluded.

Photographs of the movements of the free liquid surface that have been made during the past 70 years have mostly followed the lead of Henri Benard (1-3) who photographed convection patterns in and on shallow layers of melted paraffin wax heated purposefully from below and cooled from above by natural convection. Methods employed then and later have comprised chiefly interference and schlieren photography, the latter occasionally done at oblique angles. Interest has centered more often (4) on movements within the liquid than on the surface, and the factor common to nearly all cases is that the liquid has been in contact with air.

This laboratory is concerned chiefly with movements in and on volatile liquids heated out of contact with air and thus evaporating quietly into their own unsaturated vapors.* Excluding air permits observation of evaporation patterns uncomplicated by foreign gas and the later allows one to watch the effect of gases added to the supernatant vapor. Thermal convection in an unstirred liquid is maintained by two natural mechanisms, differences in density within the liquid and differences in tension of the surface. Heated, buoyant streamers rise, and as they break the surface are pulled to areas of higher tension that have already cooled, becoming cooler themselves until they are ready to sink back into the main bulk. The cumulative effect is to cause departures from the mean level of the surface amounting to about 10 u for layers 1 cm deep. The deviations were measured by Benard using interference photography, a method of great precision and mechanical delicacy, though often the relief patterns are too large for the working range of the interferometer.

The system of schlieren photography now put forward is less quantitative but is simple to construct and operate and records convective movements of the surface or of the liquid beneath or of the two subjects simultaneously, the camera making a direct vertical approach and thus securing rectilinear pictures. The method allows the observer to distinguish hills from valleys on the disturbed surface and thus make direct identification of rising and descending streams in the companion pictures.

The optical procedure, sketched in Fig. 1, was developed as an exercise using the primitive observation cell shown in Fig. 2 and repeating Benard's classic experiment with melted wax. When the technique had been mastered it was applied (see Figs. 9 and 10) to the photography of liquids evaporating out of contact with air.

Fig. 1. Three diagrams of an optical system for schlieren photography of liquid surfaces. In each diagram the light source D projects a beam through the field lens H to the large mirror I which is positioned at 45 degrees above the liquid surface and slanted slightly sideways. Rays reflected from the liquid are directed to the small mirror E and thence to the camera lens which houses the knife edge or diaphragm assembly and come to a focus on the ground glass G. The lowest perspective view shows an idealized liquid surface with area A supposedly flat and B and C sloping towards (+) and away from (-) the camera. One half of the ray-bundle reflected from A is intercepted by the knife edge at F and the other half produces a grey image of A on the ground glass. Rays reflected from B miss the knife edge and form a bright image of B in the camera. Since most or all of the rays from C are intercepted, a dark image of C appears by default on the ground glass.

Referring now to Figs. 1 and 2, the upper part of a beaker, 10 cm diameter, was cemented onto a slab of heat resistant plate glass and filled to a depth of 5-30 mm with paraffin wax melting at 400C. An annular heater was mounted beneath the slab and monitored by a wattmeter and variable transformer. Glass wool batting (cross hatched) and screens (not shown) protected the assembly from draughts. A thermocouple recorded the average wax temperature while opposed couples held in vertical alignment indicated the direction and degree of thermal gradients.

The optical model diagrammed in Fig. 1 consists of a light source, a field lens of 40 in. focal length and 4 in. diameter, a 5 x 7 in. first surface mirror, a second smaller mirror, a beam splitter, a knife edge, and a 35 mm camera equipped with a long focus lens.

Rays from a 1000 watt light source are condensed by a small lens and directed at the field lens from a distance of about 80 in. or two focal lengths. The large mirror reflects the light beam from the field lens vertically down onto the surface under examination. A small amount of the light incident on the surface is returned to the mirror, carrying information about surface irregularities in the form of rays which have deviated from the path they would have taken had the surface been plane. From the mirror the reflected beam passes in the reverse direction through the field lens to become focused somewhere near the original light source. In order to utilize the focused beam without interfering with the source, the small mirror is placed near the focus to deflect the beam 90~ to one side to the knife edge and camera.

The camera is moved back and forth until the beam from the field lens is focused sharply on the lens diaphragm or a knife edge substituted for it. The camera is then focused accurately on the surface of the liquid and the beam relocated if necessary onto the diaphragm. The camera is now ready to be moved up or down so that the knife edge will split the beam in two at the focal point. This allows half the light to pass above the knife edge and half to be interrupted.

Fig. 2. Half beaker observation cell. Two sets of thermocouples, center, are positioned against the side of the beaker above the gap in the annular heating coil. Opposed thermocouples measure the direction and degree of thermal gradients. The single thermocouple is balanced against a reference couple maintained at known temperature in the cell to the right and measures the average wax temperature.

When the liquid presents an absolutely flat surface, becoming a plane mirror, represented as area A of a formalized surface in Fig. 1, a uniformly grey image of area A will appear on the focusing screen of the camera. However, if a bundle of rays is reflected from an uneven surface so that it strikes below the edge of the knife in the camera lens, it's absence will appear as a dark spot on the ground glass. Conversely, if it is bent so that the whole bundle passes the edge, it will appear as a brighter region than the average grey of the flat area which received only half a ray -bundle. As with any schlieren system, this one is sensitive to surface slopes (or refractive index differences) in one direction only. This is determined by the position of the knife edge. Any displacement of the light source image in a direction perpendicular to the edge will be recorded as a gradual lightening or darkening of the ground glass. The system is not sensitive to horizontal displacements. In the arrangement described in Fig. 1, the edge is parallel to the optical axis from the light source to the field lens and it is placed so that it cuts off the bottom half of the image of the light source. Thus any inclined surface which has a negative slope, such as area B, which slants away from the light source, will produce a dark image on the ground glass and an inclined surface with a positive slope, area C, a bright image.

Fig. 3. Geometry for ascertaining surface deviation. The significant parameters are A, the distance from the surface to the knife edge, and B, the dimension of the light source normal to the knife edge. It is arranged that half the beam reflected from the vertical surface 1 passes beyond the knife edge. All of the beam reflected from surface 2, tipped at angle 0, is just intercepted. The angle 0 is thus determined by the attainment of complete interruption.

The approximate heights of elevations of the surface are calculated from two parameters, the distance of the field lens from the knife edge (A in Fig. 3) and the dimension normal to the knife edge of the image of the light source (B in Fig. 3) as focused onto the knife edge. Then, if the surface is optically flat, as in position 1, and the knife edge is positioned to cut off half of the image of the light source, the brightness of the image of this flat area on the camera screen is diminished by 50%, that is, acquires a virtual reflectance of r = 0.316.

Where the liquid surface is inclined, e.g., 0 = ± 2 degrees, the image of the source is shifted with respect to the knife edge and the image of the surface at the camera is brightened (+) or darkened (-). At those points on the liquid surface where maximum brightness or complete darkness (produced by position 2 in Fig. 3) have just been reached, the surface has attained a maximum slope, which can be calculated. These points are always less elevated or depressed than the maximum height or depression of surface deformations.

For instance, let B = 0.4 cm and A = 200 cm, then because A » B

0 in radians 12B 0.2
A 200 0.001

or in degrees = 0 degrees 4'

Fig. 4. Trigonometry for calculating surface deviation. The liquid elevation GB extends d cm from the limits of grey to the limits of black. E~, the maximum angle of slope, is tangent to the surface at B. Elevation h above the mean surface is determined from e, Fig. 3, and (x + y) = d.

To utilize this angle to determine elevations or depressions the approximation is made that due to surface tension the rate of change of the surface angle is constant over the distance between flatness and maximum slope. The surface in Fig. 4 is thus represented by a segment of a circle, more properly a catenary, but the approximation to a circle is well within the limits of sensitivities of the method, of radius a. At point G the image just begins to darken from uniform greyness, ie, from r=0.316. characteristic of optical flatness, and at point B just reaches minimum illumination, the image in between becoming progressively darker from G to B. By trigonometry the height h of point B over point G is determined from the distance, d, between them, since

d = x+y

x = h / sin O

y = h / tan O

h = d sin O tan O / tan O + sin O

A 1: 1 scale photograph of the surface was measured and d found to be 1.0 ± 0.1 cm. Since 0 was calculated as 4', then

h = 1 x 0.001 x0.001 / 0.001 x 0.001 = 1 / 2000 = 0.0005 cm

Fig. 5. Image juxtaposition by semisilvered rhomboidal prism. Raybundles from the interior of the liquid and from the surface enter appropriate face of the prism and are reflected along a common axis to the camera lens.

Thus the system is capable of resolving an elevation of 5 microns over 1 cm of surface if the slope at one end reaches or exceeds 4'. Once the slope of a hill is over 4' the sensitivity of the particular setup has been exceeded and measurements can be made only by increasing the size of the light source or shortening the distance between the field lens and the knife edge. On the other hand, slopes and elevations of smaller magnitude can be detected. In our photographs most changes from grey to black take place in distances of less than 1 cm. If an area does not reach blackness in 1 cm we can assume it has a lower slope and lower height than an area which in 1 cm does reach blackness. Finally, the system's sensitivity can be increased proportionally by increasing the focal length of the field lens or decreasing the size of the light source. Usually the limiting factor is not the optics but background noise, namely the residual vibration which in spite of elaborate precautions continues to shake the liquid surface.

The above description applies to the light that is reflected from the liquid surface. About 95% of the incident beam proceeds through the density gradients in the liquid and on to the glass-air interface at the bottom of the vessel where again a minor fraction is reflected. The reflected portion retraverses the disturbances in the liquid and is finally focused at a point near the focus of the beam reflected from the liquid surface.

If the supporting plate is exactly parallel to the free surface, and the large mirror is positioned at an angle of exactly 45 degrees to the surface, an observer intercepting the reflected rays will perceive all surfaces and phenomena superimposed. If the base plate is tilted slightly, the observer, by shifting eye or camera, may view the top surface or the bulk liquid layer at will without mutual interference. To place the two views side by side for simultaneous photography of the surface and liquid interior, a rhomboidal prism with a beam splitter at one end is used to deviate the rays reflected from the glass slab to a focus on the knife edge in a fashion similar to the procedure described for the rays reflected from the free surface. There is no specific requirement as to the direction in which the base plate needs to be tilted to separate the two views; however, we have tilted it so that the image of the liquid surface is just to one side of the image of the interior, see Fig. 5. This has been done for Fig. 6 which shows top and internal views of the melted wax. (A motion picture which illustrates the experiment is available for loan).

Fig. 6. (left) Simultaneous photograph through melted wax, left, and of surface, right. Areas on right which are bright to their north are raised above median level. The lower pair were photographed a half minute after the upper.

Fig. 7. (right) Cooling sequence of melted paraffin wax. Series begins upper left and ends lower right. Crystallization occurs along markings which are dark to north, bright to south, identifying them as troughs of cooler material.

Without further reference to the optical geometry, it may be stated that the right-hand picture presents a view as though illuminated from the top of the picture. Where a displacement shows bright on the upper side, then the displacement may be identified as a hill, or a ridge. Where the lighter side is below, one recognizes a hollow or a plunge line. Now, the details in the left band picture are due to changes in refraction caused by changes in temperature and density of local streamers. Since reflection features in the right hand picture are directly above refraction features in the left one, it follows that features identified as hills in the right hand picture have up-streamers beneath them in the left, while depressions have down-streamers or plunge lines.

It can also be inferred that during thermal, buoyancy-driven convection, hills and sometimes ridges are hotter than the average surface temperature while hollows, whirlpools, and plunge lines are cooler. A verification of this diagnosis is furnished rather strikingly by allowing the wax to solidify and remelt during motion picture photography - crystalline solidification occurs in the regions previously identified as cooler; the transitions are shown in Fig. 7.

Photography of volatile liquids out of contact with air requires a more complicated container.

The apparatus seen in Fig. 8 relies heavily on the technique used for boule-making.(5,6) A new feature, 7 the annular bulge in the center of the 4 in. cylindrical Pyrex container, is to damp standing waves on the liquid surface. A modified 2-liter flask serves as an evaporator which provides enough vapor to blanket the test liquid without ebullition. To prevent the heated air which streams above the observation window in the thermostat box from superimposing a schlieren pattern on the surface pattern being photographed, a fan was placed some distance from the box. This entailed placing another fan inside the box to keep the window warm enough to prevent condensation on the top of the test vessel. At present the flat bottom is not in place since the liquid layer required for this section of our studies is too deep for photography throughout the mass.

Fig. 8. Apparatus for photography of liquids in absence of air. Observation cell A is fed with vapor from boiler B. Casing is kept hot by heater and fan C. Note, expansion in upper walls of A for damping externally acquired vibrations.

The apparatus was put through its test paces using isopropyl alcohol. Surface pictures obtained during heating with stepwise increasing degrees of superheat are shown in Fig. 9 and pictures taken during cooling, labeled for equivalent temperatures, occupy Fig. 10. It will be noticed that during the heating period the surface pattern is determined preset) by the striae of hot liquid which ascend around the walls of the container. After streaming across the surface, cooling the while, they form whirlpools generally in pairs which carry the exhausted liquid down into the general bulk. During the cooling cycle, the surface abandons this pattern, showing a strong preference for plunge lines but retaining an occasional whirlpool at the end of a line. The plunge line thus does not descend vertically but flows diagonally toward the vortex end, as though each molecule "thought" it could get down faster there. We may conclude, provisionally, with Spangenberg and Rowland, 8 that a deep liquid finds it easier to bury its heavier portions in long independent lines rather than in shorter lines linked into the squares or hexagons that it forms when convecting in shallow layers. In deep liquids the vortex is adopted only under externally applied force though this force may itself be exerted by a plunge line.

Fig. 9. (left) Surface movements of isopropyl alcohol evaporating in aparatus of Fig. 8. Wattage input increases throughout the series.
Fig. 10. (right) Surface of isopropyl alcohol cooling from highest degree of superheat of Fig. 9. Heater-induced patterns change to the natural plunge lines of a spontaneously cooling liquid, with the passage of time.

Acknowledgment

The operational techniques other than photographic have been made available to me from the laboratory. I thank Dr. K. Hickman for direction and assistance in preparing this paper.

* This work was performed under grant from the Office of Saline Water, U.S. Department of the Interior. Received November 4, 1968; Revised March 4, 1969.

REFERENCES:

1. H. Benard, Ann. cAirn. PAys., (7) 23, 62(1901).
2. H. Benard, compt. Rend., 134, 260(1912).
3. H. Benard, Rull. Soc. Franc. I’hys., 266, 1125(1928).
4. John C. Berg, Acrivos, Andreas, and Boudart, Michel, "Evaporative Convection," Ads, in Chem. Pag., 6, 61(1966).
5. K. Hickman, md. Eng. them., 56, 18—31(1964).
6. K. Hickman, J. R. Maa, A. Davidhazy, and 0. Mady, Ind. Eng. Chem., 59, 19-41 (1967).
7. See K. Hickman in OSW Research and Development Progress Report. 1969, now in preparation.
8. W. G. Spangenberg and w. R. Rowland, ‘Convective Circulation in water Induced by Evaporative Cooling," Phys. of Fluids, 4, 743-750 (June, 1961).

Copyright, 1969, by the Society of Photographic Scientists and Engineers, Inc.

You can write to the author at: andpph@rit.edu

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