An Automatic Diver Balance

The diver balance constructed by Zeuthen (1948) was based on the Cartesian principle, i.e. that the specific gravity of a floating body containing an air bubble may be changed by variation of the pressure above the surface of the floatation medium. This instrument was a further development of the Cartesian diver, the microrespiro-meter developed by Linderstram-Lang (1943) and Holter (1943).

The diver balance is used for weighing objects submerged in the floatation medium, and it can therefore determine only the submerged or—to use an expression coined by Linderstrom-Lang & Holter (1940)—the reduced weight (RIP).

RW determinations have been of good service in the solution of various biological problems, e.g. for reference to the size of biological objects (cf. Avery & Linderstram-Lang, 1941 ; Holter & Løvtrup, 1949), and in studies of the utilization of endogenous energy sources in starving organisms (cf. Holter & Zeuthen, 1948; Lavtrup, 1959). The use of the diver balance for studies of water permeability, using D₂O as a tracer, was introduced by Pigon & Zeuthen (1951) and Løvtrup & Pigon (1951).

The diver balance has also been used in studies on eggs of marine animals. Thus Zeuthen (1951) studied the changes in RW during the early stages of sea-urchin development. Rhythmical changes, consonant with the mitotic rhythm, were observed, but these changes were superimposed upon a very extensive change in RW, apparently not associated with changes in the living material. Some years ago experiments were initiated to determine the rate of water exchange in sea-urchin embryos. During this work Zeuthen’s observation was confirmed; it could actually be established that if the equilibrium of an unloaded balance was upset by a large change of presssure in the floatation vessel, then the diver balance would float at a pressure widely different from the original one. A gradual change occurred, however, and after about half an hour the original level was reached and no further changes were observed.

Subsequent control experiments have shown that this phenomenon occurs even in fresh water, but the absolute change is slight, and the original value is reached in a few minutes. Consequently the measurement of water exchange in fresh water is not seriously interfered with.

It is evident that, whatever the reason of the observed RIP-change—various suggestions have been made, but no definite explanation seems agreed as yet—the Cartesian diver balance can never be used for water-exchange studies in salt water. A diver balance, working on some completely different principle, is required for this purpose. Since the difficulties encountered. with the manometric diver balance probably are concerned with the exchange between the enclosed air bubble and the surrounding medium, the electromagnetic balance devised by Brzin, Kovič and Oman (1964) may meet this demand.

In permeability studies the time course of the RW changes must be recorded in order to establish the rate constant for the water-exchange reaction. Simultaneous adjustment and observation of the floating position of the diver, reading of equilibrium pressure and time are such complicated operations that the participation of two technicians is required, at least during the early phase of the process when the rate of change is very fast.

It was from the outset obvious to us that if any substantial improvement of the diver balance technique were to be achieved, it would be necessary to do away with this tedious work.

This requires not only that the readings be automatically recorded—this can be done with the electromagnetic balance mentioned above—but also that the control of the floating level be automatic. The electromagnetic diver balance presented here fulfils both demands.

The electromagnetic diver balance is based on the principle that a balance pan— the diver—with specific gravity less than the surrounding medium is prevented from rising to the surface by an electromagnetic force acting on a small magnet contained in the diver. The adjustment of the equilibrium position is achieved by means of a servo-loop, comprising an optical, an electronic and a magnetic component (Fig. 1).

The light source, a lens bulb (Osram 3644), sends an almost parallel beam of light through a cuvette filled with an appropriate floatation medium, and through a narrow slit in the photocell housing to the photocell (Siemens photodiode APY 11 I). The latter controls by means of an amplifier the current passing through an electromagnet placed under the cuvette. When the diver is pulled down by the current, its lower end will cut off the light to the photocell. Since the current in the coil is proportional to the light reaching the photocell the force will diminish as the diver moves down.

When the electromagnetic force exactly balances the upward force of the diver the latter has reached its equilibrium position, and no further changes occur.

Upon loading, the equilibrium force will decrease and the diver will accordingly sink until a new equilibrium is reached.

The weighing system is very sensitive to temperature changes, and the cuvette, lamp housing, photocell housing and coil are therefore immersed in a thermostat-regulated water bath with efficient circulation. In very sensitive work we have found that an inner bath, of Plexiglass, may be necessary. The water in this bath is not heated, but it is stirred by a circulation pump.

The mechanical construction of the various units is shown in Fig. 2.

The lamp housing and the photocell housing are made of nickel-plated brass. The small windows are made of Plexiglass, provided with grooves for o-rings ; great care must be devoted to the finish of the surfaces in order to keep down the losses of light. The slit (0·5-1 × 2-3 mm.) in the window of the photocell housing reduces the width of the light beam, and thus permits the use of thinner divers.

The electromagnetic coil consists of 0·55 mm. copper wire, 2000 turns wound on a Plexiglass spool with a central opening of 10 mm. A wide Plexiglass tube covers the spool ; the tightening is achieved with o-rings. If required an iron core may be placed in the central hole.

All the submerged components are attached to a 12 mm. Plexiglass plate, including the cuvette holder. Allowance is made for adjustment to varying cuvette sizes.

The servo amplifier (Fig. 3) is designed as a transistorized a.c.-amplifier with an output of 10 W. The photodiode is fed by pulses from a pulse generator (1000 cyc./sec.). The amplitude of this signal is modulated by the light reaching the photocell, and transferred to the a.c.-amplifier which, through a transformer and a rectifier, is coupled to the coil. The latter is thus being fed with a d.c.-potential. The input signal may be regulated by a potentiometer, by which the floating level may be adjusted. The signal from the photodiode is also fed to a circuit containing a meter on which may be read the relative height of the diver in the light beam, i.e. the floating level.

The measuring circuit contains two 10-turn helical potentiometers, by which the sensitivity and the zero-position on the recorder may be adjusted. A 10 mV potentio-meter recorder—multichannel if desired—is used for recording the changes in the equilibrium current.

In cases where no continuous changes are to be recorded, a simple zero instrument may replace the recorder. Reading of the equilibrium current is then made on the zero-position potentiometer.

The divers are made of polypropylene, which may be obtained as wires and sticks of varying width. Most of the divers prepared so far have been made of 3-4 mm. wire. Suitable pieces are cut off and placed in a lathe. In order to get the lower end as plane as possible, 1-2 mm. is cut off from the free end with a sharp knife, while the lathe is rotating. Subsequently a hole is drilled in the piece, 0·1-0·2 mm. wider and 1 mm. longer than the magnetic material to be inserted.

The magnets are made out of 0·5 mm. Koerzit T^*; except for special purposes pieces of 1-3 mm. were employed. The pieces are hardened in an oven at 530-570° C. ; after cooling they are put into the hole in the plastic and the opening is fused with a hot wire. Subsequently the material is magnetized by placing the diver in a magnetic field, the strength of which is adjusted according to the desired sensitivity of the diver. The lower end of the diver is then cleaned with a knife, and ground with various grades of oil-resistant carborundum paper, to make the surface as smooth as possible.

The loading capacity of the diver (= — RW_d, where RW_d is the reduced weight of the diver, cf. below) will be determined by the amount of polypropylene. This cha-racteristic may be adjusted by cutting off slices from the upper end. An approximate estimate of the capacity can be made by putting the diver in a beaker with water and loading it with known weights.

As we shall discuss later, the sensitivity of the balance varies inversely with the ‘magnetic quantity ‘in the diver ; in order to make a sensitive diver the magnet must therefore be very small. Under these circumstances the amount of plastic required to give a reasonable RW_dmay be quite low. In order to bring the diver to a convenient size a small piece of platinum wire may be introduced below the magnet before the hole is closed.

It has been observed that the divers change their RW_d in water, especially during the initial period. This change is rather slow, and may easily be corrected for.

A loaded floating diver is shown in Fig. 4.

In the Cartesian diver balance the RW of the diver proper is a measure of the sensitivity of the balance (cf. Løvtrup, 1951). The loading capacity depends on details of the construction of the apparatus, viz. the space available for expansion of the air bubble, and the range of the manometer.

In the electromagnetic diver balance the opposite relation holds ; here the numerical value of the reduced weight of the diver, RW_d, represents the maximum load, the loading capacity L_max. The sensitivity may, on the contrary, be changed by adjustment of the amplifying system.

In some cases it may be expedient to work with a diver having so large capacity that it cannot be equilibrated when empty. This situation arises if in a heavy object relatively small changes are to be measured. The recording can then be made only after the object has been placed on the diver. As we shall see, the calibration is linear as long as the displacement of the diver is small compared with I, so that this procedure will consequently entail no changes as concerns the conversion of the readings to absolute units.

It will be realized from the definition of R W that the capacity is a function of both volume and specific gravity of the diver. There is thus no direct proportionality between the size of the diver and the capacity.

It is not easy to determine these parameters with sufficient accuracy for calculating the RW_d. Approximate determination of the capacity may be achieved by loading with gradually increasing loads until the diver sinks. A somewhat more accurate method will be described below. However, since this parameter is of no importance for the calibration of the balance, an exact determination of the capacity is in general of no particular interest.

Thus, in cases where very high sensitivity is required, it is necessary to use a diver with a weak magnet, but adjustment of the other factors mentioned above may also help to reach the required sensitivity. All these factors that tend to improve the sensitivity will at the same time reduce the maximum value of RW_d, but it is important to note that the loading capacity of the diver, — RW_d, has no influence on the sensitivity.

The electromagnetic force acting on the empty floating diver is equal to — RW_d. As the diver is loaded the force required to keep the system floating diminishes. The diver sinks in the container until the current through the magnet coil suffices to balance the RWof balance + load. When the load is equal to — RW_d this force, and thus the current, is zero. This situation obtains when the diver just cuts off the whole light beam. This relation is shown in Fig. 5. Since amplification is linear, the ratio between diver displacement and current change is also linear. The slope of the line may be changed by the floating-level adjustment knob, controlling the amplification. The floating position of the empty diver will change correspondingly, as shown in the figure. It will be realized that the absolute value of Δh, the change in position resulting from loading the diver, will be changed proportionally by this expedient.

The distance l between the magnet and the coil will be changed by the amount Δh when the floating position is changed. This fact will cause a deviation from linearity in the calibration curve. The ratio AA/Z is very small, however, and may be further reduced by increasing the amplification. In our work with the diver balance we have adjusted the magnification so that no significant deviation from linearity obtains (cf. Fig. 6).

If the amplification is increased too much the effect of disturbing influences of various kinds, e.g. convection currents, particles in the light path, etc., will also be magnified, since a small displacement of the diver will entail a large change in current.

At high magnifications the risk also increases that the diver may begin to oscillate. This may be prevented by raising the viscosity of the medium and enlarging the diameter of the diver, or electronically by a negative feed-back system. In the work carried out with the diver balance so far, we have had no trouble with self-oscillations, and none of the mentioned expedients have therefore been introduced, but it may be necessary to consider these possibilities under different experimental conditions.

Under any circumstances it will be realized that in practical work with the diver balance the degree of magnification must strike a practical compromise between the demands for linearity and stability.

Application

The electromagnetic diver balance may be used for the same purposes as the Cartesian diver, for weighings in general, including metabolic studies on starving organisms, and for water-exchange studies (cf. fig. 7). As far as the last application is concerned both diffusion and permeability coefficients may be determined (cf. Løvtrup, 1963). Obviously these determinations are not necessarily limited to work with biological objects, or to water exchange. It may just as well be possible to follow the diffusion of organic solvents in various plastic objects, etc.

The electromagnetic diver balance may also be used for manometric studies, thus substituting for the Cartesian diver. If an object is placed in a drop in a capillary, surrounded by air bubbles, then any consumption or production of gas will change the volume of the bubbles, and consequently the R W of the capillary. If the latter is placed on the diver, it will thus be possible to follow the gasometric reaction. By appropriate modification and enlargement of the present model it should be possible to construct an apparatus that might to all intents and purposes function as an automatically recording Warburg apparatus.

The electromagnetic diver balance may also be used to determine various kinds of forces and tensions. In the method of Cole (1932) the mechanical properties of the cortex in the sea-urchin egg are determined from the deformation of the egg arising after application of a known compressive force (cf. also Hiramoto (1963) and Yoneda (1964)). In a study of the tension in amphibian eggs the diver balance has successfully replaced the torsion-beam balance employed by Hiramoto (Bemtsson, unpublished results).