Stalagmometry

STALAGMOMETRY (from the Greek stalagma—drop and metron—measure), or the drop method, is a method of measuring the surface tension (see) of liquids by counting the number of drops into which a specific volume of liquid breaks down while flowing out of a vertical capillary tube called a stalagmometer. The method is based on Tate's law, which states that a drop forming on a horizontal circular surface detaches when its weight becomes equal to the product of the surface tension and the base of the drop. When using the same area of detachment, the weight of the drop is proportional to the surface tension; consequently, when the surface tension of a liquid decreases, the number of drops flowing out of a specific volume of the tube increases, and vice versa. Although Tate's law is not absolutely correct, for practical purposes one can consider the proportionality to be almost absolute (Lohnstein, Livingstone-Morgan, and others). The Traube stalagmometer consists of a straight or right-angled tube (see Dropper) (Figs. 1 and 2), a precisely calibrated tube with an expansion between two marks placed on it, indicating the volume of the given instrument. The lower end of the tube, from which the drops must detach, is smoothly polished. The instrument indicates its capacity and the number of drops of water flowing out of it at a temperature of 15°. The measurement is performed as follows: the test liquid (serum) is drawn into the instrument with a rubber bulb up to the upper mark, and it is secured with a clamp in a vertical position. The liquid is allowed to flow out in drops until the lower mark, while simultaneously counting them. The counting of drops can also be performed automatically by means of an automatic counter proposed by the Gerhardt firm. Each drop falling from the stalagmometer onto a special Figure 1 Stalagmometer

Fig. 2. Traube stalagmometer. celluloid plate closes a circuit, which, with the help of an electromagnet, sets in motion a clockwork mechanism that counts the number of drops that have flowed out. Thanks to the graduation marked on the instrument, the accuracy of the count is possible to 0.05 of a drop. Before use, the apparatus must be thoroughly washed so that it does not contain any traces of grease. The same applies to the polished surface. It is necessary to ensure that the entire polished surface is completely wetted by the test liquid. The column of liquid in the instrument must not be interrupted by the slightest air bubbles. Failure to comply with these conditions can lead to an erroneous determination of surface tension. The determination should also be conducted at a specific temperature, since with an increase in temperature by 5°, the number of flowing drops increases (approximately one drop for every 100 drops of water). The number of drops flowing out per unit of time—per 1 minute—should not exceed 20. If a liquid is being investigated that flows out with a larger number of drops per 1 minute, it is necessary to slightly close the upper opening of the apparatus with a finger. Conversely, with a strongly slowed outflow of drops, one should slightly press on the column of liquid with the rubber bulb to accelerate the outflow of the liquid. It is recommended to use different apparatuses for liquids of different viscosities. For blood, it is more convenient to use a straight instrument. To regulate the speed of the outflow of drops, Schemensky proposed connecting the upper opening of the stalagmometer with a wide test tube filled with liquid paraffin (Fig. 3). Through the stopper tightly closing this test tube, two glass

Figure 3. Schemensky's apparatus.

capillaries are passed. One of them is immersed at one end into the paraffin, while the other serves to connect the test tube with the stalagmometer by means of a rubber tube. Depending on whether we have a slowed or accelerated outflow of drops, the capillary is lowered or raised from the paraffin accordingly. The Czapek stalagmometer consists of a bent glass tube having a diameter of 12 mm and ending in a Fleischel-Miescher capillary. Water is poured into the tube up to the mark, and the test liquid is poured into a small cup. The capillary is immersed in it by 1–2 mm. Distilled water is added drop by drop into the open arm until the air in the closed arm, under the pressure of the column of liquid, overcomes the force of the surface tension of the test liquid located in the cup and appears inside it. The amount of added water is a measure of the surface tension of the test liquid. The unit of surface tension of distilled water at a temperature of 16° equals 4.6–4.7 drops. Calculation. If we take the surface tension for water as 100, then for the test liquid it will equal a = (Z / Z_w) * 100 (1), where Z is the number of drops of the test liquid, and Z_w is the number of drops of water in equal volumes. Since a liquid is being investigated whose specific gravity differs from the specific gravity of water, it is necessary to take this into account and introduce this factor into formula (1), and then we will obtain: a = (Z / Z_w) * 100 * specific gravity (2)—an expression of surface tension in percent in relation to water. It is also possible to express a in absolute units of surface tension of water in relation to the contacting Figure 4. Rona and Michaelis pipette.

Fig. 5. Rona and Michaelis pipette. Figure 6. The same in a water bath. medium, namely to air. Since the surface tension of pure water in this case will equal 7.30 mg/mm, the expression of a in mg/mm should be performed according to the formula a = (Z / Z_w) * specific gravity * 7.30 mg/mm, or, if we take the surface tension of water as 75 dyn/cm (Iscovesco), then a = (Z / Z_w) * specific gravity * 75 dyn/cm. According to Traube, the a of serum is lower than the a of water and, expressed in drops, equals 109–112 drops at a temperature of 15°. For clinical purposes, it is quite sufficient when determining the surface tension of serum or other liquids to use formula 1 or 2. Rona and Michaelis, instead of the slowly dripping Traube stalagmometer,

Steffanutti

proposed a fast-dripping pipette with a capacity of about 3 cm³; it ends at the bottom in a slightly tapering point and possesses not very thin walls (Figs. 4 and 5). If it is desirable to work not at room temperature, but at a higher one, one can use the Rona and Michaelis pipette immersed in a water bath (Fig. 6), or the Steffanutti apparatus (Fig. 7). Stalagmometry finds application in the clinic of liver diseases, for the determination of bile and fatty acids in urine and blood serum, which lower surface tension. An increased content of inorganic salts increases the surface tension of a liquid. Stalagmometry also finds application in bacteriology and serology for immunity reactions in the form of the meiostagmin reaction (see Ascoli meiostagmin reaction).