Maximum capillary tension, determination

A block-scheme of the apparatus for the study of foam films under applied pressure is shown in Fig. 2.11. The films are formed in the porous plate of the measuring cell (Fig. 2.4, variant D and E). The hydrodynamic resistance in the porous plate is sufficiently small and the maximum capillary pressure which can be applied to the film is determined by the pore material. The porous plate measuring cell (Fig. 2.4, variants D and E) permits to increase the capillary pressure up to 105 Pa, depending on the pore size and the surface tension of the solution. When the maximum pore size is 0.5 pm, the capillary pressure is 310s Pa (at cr = 70 mN/m). The cell is placed in a thermostating device, mounted on the microscopic table. 

Figure 6.3 Liquid surface tension determination by the maximum bubble pressure method. The maximum pressure, P needed to push a bubble out of a capillary into a liquid is determined just prior to the detachment of the bubble hL is the distance below the surface of the liquid to the tip of the tube. The value of Pmax is usually found by measuring the height of a water column, hc. a. If the tube is completely wetted by the liquid, then the radius, r, is its internal radius, b. If the liquid is non-wetting towards the tube, then the radius, r, is its external radius. The bubble becomes fully hemispherical, as can be seen in the middle shapes of a and b.

The functioning of the instrument, as described in detail also in the book chapter mentioned above [176], is different from most of the other instruments. Due to the large internal gas volume (about 35 cm ) an easy procedure for determining the effective adsorption time in the moment of maximum pressure was derived (see below). The surface tension y can be calculated from the measured maximum capillary pressure P and the known capillary radius r jp using the Laplace equation in the simplified form for spherical drop/bubble shapes... 

Maximum-bubble-pressure method [313,316,329-336] measures pressure in a bubble formed at the end of a capillary when a gas (e.g., air) is blown through the capillary into the liquid. The pressure increases when the bubble grows and attains its maximum value when the bubble has obtained the shape of a hemisphere (Fig. 9.23). The pressure decreases when the bubble grows further and finally bursts. Maximum-bubble-pressure methods have been compared [383] and equipment for automated surface tension determination by maximum-bubble-pressure measurement has been developed [384—387]. 

Interfacial tension may be measured by a number of techniques, including determining how far a solution rises in a capillary, by measuring the weight, volume or shape of a drop of solution formed at a capillary tip, measuring the force required to pull a flat plate or ring from the surface or the maximum pressure required to form a bubble at a nozzle immersed in the solution. Ring or plate techniques are most commonly used to determine y of milk. 

In the Maximum-bubble-pressure method the surface tension is determined from the value of the pressure which is necessary to push a bubble out of a capillary against the Laplace pressure. Therefore a capillary tube, with inner radius rc, is immersed into the liquid (Fig. 2.9). A gas is pressed through the tube, so that a bubble is formed at its end. If the pressure in the bubble increases, the bubble is pushed out of the capillary more and more. In that way, the curvature of the gas-liquid interface increases according to the Young-Laplace equation. The maximum pressure is reached when the bubble forms a half-sphere with a radius r/s V(j. This maximum pressure is related to the surface tension by 7 = rcAP/2. If the volume of the bubble is further increased, the radius of the bubble would also have to become larger. A larger radius corresponds to a smaller pressure. The bubble would thus become unstable and detach from the capillary tube. 

Fundamental knowledge about the behavior of charged surfaces comes from experiments with mercury. How can an electrocapillarity curve of mercury be measured A usual arrangement, the so-called dropping mercury electrode, is shown in Fig. 5.2 [70], A capillary filled with mercury and a counter electrode are placed into an electrolyte solution. A voltage is applied between both. The surface tension of mercury is determined by the maximum bubble pressure method. Mercury is thereby pressed into the electrolyte solution under constant pressure P. The number of drops per unit time is measured as a function of the applied voltage. 

There are static and dynamic methods. The static methods measure the tension of practically stationary surfaces which have been formed for an appreciable time, and depend on one of two principles. The most accurate depend on the pressure difference set up on the two sides of a curved surface possessing surface tension (Chap. I, 10), and are often only devices for the determination of hydrostatic pressure at a prescribed curvature of the liquid these include the capillary height method, with its numerous variants, the maximum bubble pressure method, the drop-weight method, and the method of sessile drops. The second principle, less accurate, but very often convenient because of its rapidity, is the formation of a film of the liquid and its extension by means of a support caused to adhere to the liquid temporarily methods in this class include the detachment of a ring or plate from the surface of any liquid, and the measurement of the tension of soap solutions by extending a film. 

Equipment. A Brookfield synchro-lectric viscometer, serial no. 758, is used to measure viscosity in the range of 0-100,000 cP. Sugden s double capillary modification of the maximum bubble pressure method is used to determine surface tensions. The apparatus is calibrated with benzene and is checked by determining the surface tension of chloroform at 25°C, which is found to be 23.5 dyn cm"1 (26.5 dyn cm 1) (35). 

Fig. 2.4 presents a measuring cell with a porous plate made of sintered glass (similar to variant C, Fig. 2.2). Porous plates of various pore radii can be used (usually the smallest radius is about 0.5 p.m) [23]. In this case the meniscus penetrates into the pores and their radius determines the radius of curvature, i.e. the small pore size allows to increase the capillary pressure until the gas phase can enter in them. The radius of the hole in which the film is formed is usually 0.025 - 0.2 cm. To provide a horizontal position of the film the whole plate is made very thin. In the porous plate measuring cell (Fig. 2.4) the capillary pressure can be varied to more than 10s Pa, depending on the pores size and the surface tension of the solution. When the maximum pore radius is 0.5 (tm, the capillary pressure is 3- 10s Pa at a - 70 mN/m.

In surface tension measurements using the maximum bubble pressure method several sources of error may occur. As mentioned above, the exact machining of the capillary orifice is very important. A deviation from a circular orifice may cause an error of 0.3%. The determination of the immersion depth with an accuracy of 0.01 mm introduces an error of 0.3%. The accuracy of 1 Pa in the pressure measurement causes an additional error of 0.4%. The sum of all these errors gives an estimated total error of approximately 1%. Using the above-described apparatus, the standard deviations of the experimental data based on the least-squares statistical analysis were in the range 0.5% < sd > 1%. 

On the basis of the GAI, it is clear that the interfacial tension y is the most important experimental quantity. Three methods are commonly used to determine y at liquid liquid interfaces, namely, the capillary electrometer method, the maximum bubble pressure method, and the drop weight or drop time method. 

In this method, the surface tension of a liquid is determined from the value of the maximum pressure needed to push a bubble out of a capillary into a liquid, against the... 

If the radius of the capillary is large, so that (r/a) > 0.05, then the Basforth-Adams equation (Equation (481)) or the Lane equations (Equations (482) and (483)) can also be used in the surface tension calculation from the maximum bubble pressure method. This method can also be used to determine the surface tension of molten metals. It has been a popular method in the past, but now it is not very common in surface laboratories because of its poor precision. 

The Marangoni elasticity can be determined experimentally from dynamic surface tension measurements that involve known surface area changes. One such technique is the maximum bubble-pressure method (MBPM), which has been used to determine elasticities in this manner (24, 26). In the MBPM, the rates of bubble formation at submerged capillaries are varied. This amounts to changing A/A because approximately equal bubble areas are produced at the maximum bubble pressure condition at all rates. Although such measurements include some contribution from surface dilational viscosity (23, 27), the result will be referred to simply as surface elasticity in this work. 

In work with a dropping mercury electrode, the height of the mercury column above the capillary tip governs the pressure driving mercury through the DME, thus it is a key determinant of m (13, 14). In turn, m controls the drop time because the maximum mass that the surface tension can support is a constant defined by... 

It is possible to determine the surface tension from the maximum pressure required to blow a bubble at the end of a capillary tube immersed in a liquid. In Fig. 18.8, three stages of a bubble are shown. In the first stage the radius of curvature is very large, so that the difference in pressure across the interface is small. As the bubble grows, R decreases and the pressure in the bubble increases until the bubble is hemispherical with R = r, the radius of the capillary. Beyond this point, as the bubble enlarges, R becomes greater than r the pressure drops and air rushes in. The bubble is unstable. Thus the situation in Fig. 18.8(b) represents a minimum radius and therefore a maximum bubble pressure, by Eq. (18.9). From a measurement of the maximum bubble pressure the value of y can be obtained. If is the maximum pressure required to blow the bubble and is the pressure at the depth of the tip, h, then... 

The maximum take-up velocity is very reproducible and depends essentially on every process variable, e.g., polymer composition and molecular weight, spinning dope composition, bath composition, bath temperature, spinneret capillary diameter, and flow rate. A parameter that seems to determine the upper limit in take-up velocity is the free velocity, Vf [244,323]. Recall that the free velocity is the velocity at which the filament leaves the spinneret under zero tension. The free velocity will increase in an approximately linear manner with the volumetric flow rate through the capillary, and at a fixed flow rate it will increase as the capillary diameter is decreased. When the take-up velocity, Fi, is increased while Ff is held constant, the magnitude of the rheological force, F(rheo), will increase until the filament breaks at the spinneret face. 

CT = (7q - CV y where gq is the maximum value for the uncharged surface. Hence the c, V curve is a parabola. This was confirmed by Konig. Lippmann found that a current flows in the circuit if the size of the mercury surface in the capillary electrometer is altered by mechanical means this should cease when the mercury is uncharged and Pellat found that this happens when an electromotive force of 0 97 volt acts against the natural potential difference, agreeing with Lippmann s value of about i volt for the maximum of surface tension. Ostwald found that in different acids the surface tensions could differ by a ratio of more than i to 3. He emphasised that it is the charge on the mercury, and not (as Lippmann thought) the potential difference, which determines the surface tension. 

The two most common methods available to determine the interfacial tension at the mercury-electrolyte interface are the capillary rise method and the maximum... 

As the development of the glass drop is extremely slow, one can also consider the drop as quasi-static and perform a force balance on the constant property drop after Middleman . The volume of the drop having sufficient mass necessaiy to just balance the surface tension will have the maximum diameter. Consider the drop hanging from the inner diameter of a capillary tube as shown in figure 1. The angle 0, formed by the line tangent to the free surface at the capillary tube exit is used to determine the vertical component of the surface tension force. 

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