Capillary rise time

Capillary rise time is the time required to reach equilibrium capillary rise height, T/q. The performance of many microsystems is dependent on the transient behavior of the capillary flow. Therefore, we intend to calculate the rate at which the capillary will rise to the equilibrium height. Let us assume the velocity profile at any instant of time to be fully developed Poiseuille profile. This assumption is justified from the fact that the developing length is expected to be very small compared to the length of the capillary due to the small diameter of the capillary tube. The instantaneous average velocity of the interface can be expressed from Poiseuille flow relation and the movement of interface as 

Let us consider the force balance equation between a point immediately below the interface and a point at the same level as the reservoir surface. The pressure at point below the interface, (Pq - AP), is expressed by Young-Laplace equation, and the water surface of the reservoir is at atmospheric pressure, Pq. The corresponding unbalance pressure difference driving the flow is 

the left-hand side of the above equation is the capillary number (—). and the second 

This equation can be integrated for calculating the capillary advancement time of the meniscus. Assuming low Bond number, the above differential equation can easily be integrated by separation of HdH and dt resulting in 

The above equation indicates that the capillary rise rate increases with decrease in capillary diameter and increase is small) in surface tension. 

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Once formed, the LNAPL is referred to as a pool that is really a continuous accumulation of LNAPL. Subpools are individual accumulations of relatively uniform free-product types based on geochemistry (API gravity, specific constituents, isotope ratios, etc.) that have coalesced, reflecting multiple-source accumulations with time. The LNAPL pool, once formed, also maintains a capillary fringe. The anticipated capillary rise of LNAPL can be calculated as follows ... 

However, the model applied in this study is hardly realistic, since it is assumed that the foam consists of capillaries (borders) whose length is equal to the foam column height but the liquid capillary rise in them varies with time. 

Textile can take up a lot of moisture, but the paper tissue on the window sill can take up even more it still feels dry with four times its own weight of water. An estimate of the density of the roll tells you that over 90% of the volume consists of air. It is not easy to make a structure like that. The tissue takes up water rapidly, but the capillary rise is limited to about twelve centimetres as a simple experiment shows. You need to understand capillary flow if you want to improve such products. You do not see much under the microscope, but where two sheets have been torn apart you can see the separate cellulose fibres. They are about 10 am thick. 

A difficulty encountered in the measurement of the surface tension of solutions is that it is often different when measured by so-called dynamic methods (vibrating jets, etc.), in which the value for a freshly-formed surface is measured rapidly, and when measured by so-called static methods (capillary rise, etc.), which determine the value for a surface which has been in existence for some time. The difference is due to the fact that the composition of the surface is different from that in the bulk of the solution, and in a fresh surface a change of concentration occurs, which, as it involyes diffusion, usually occurs slowly, so that rapid measurements give results different from those which deal with a surface which has come into equilibrium. In capillary active solutions, the surface is enriched in solute, whilst in capillary inactive it is usually richer in solvent. In the case of electrolyte solutions, the surface layer is considered to consist of a unimolecular layer of solvent molecules. The thermodynamic theory was established by Gibbs, and indicates that when the solute... 

Fig. 2 Separation of synthetic, protected tetrapeptide intermediates (9) A-methyl C- and N-protected tetrapeptide (10) non-A-methyl C- and N-protected tetrapeptide. The structures of these compounds is proprietary information and consequently cannot be disclosed. Detection wavelength of 210 nm with a 10-nm bandwidth and a 1-s rise time. Electrochromatography was performed on a 250 mm X 50 iJim i.d. spherisorb ODS-1 packed capillary using an acetonitrile-Tris (50 mmol/L, pH 7.8) buffer 80 20 v/v mobile phase, capillary temperature of 15°C, and an electrokinetic injection of 5 kV/15 s. (a) Synthetic mixture of protected tetrapeptides 9 and 10. Efficiency values of 124,000 and 131,000 plates/m were obtained for analytes 9 and 10, respectively, (b) Chromatogram of synthetically prepared 9, the presence of residual nonmethylated tetrapeptide (10) can be seen, (c) Chromatogram of synthetically prepared 9, spiked with 10% of the nonmethylated tetrapeptide (10). Efficiency values of 83,000 and 101,000 plates/m were obtained for analytes 9 and 10, respectively, (d) Chromatogram of synthetically prepared 9, the presence of residual nonmethylated tetrapeptide (10) can be clearly seen at the 3% level. Additional conditions are indicated in Ref. 38. (From Ref. 38 reproduced with permission of the authors and John Wiley and Sons, Inc.)...

Beginning with penetration time, Eq. (21-98h) defines key formulation properties controlling capillary rise in powder beds. From considering a distribution of macro- and micropores in the moving powder bed as shown in Fig. 21-102, Hapgood (loc. cit.) determined a total drop penetration time tp of... 

When compared with the other methods, the capillary rise method is the ultimate standard method in terms of the degree of theoretical exactitude, and, although it is the oldest method, it still gives the most precise liquid surface tension results if carefully applied, and when the time of measurement is allowed to be sufficiently long. However, with the improvement in computer-controlled electronic equipment, other methods now also have a very high precision. Some of the surface tension results are summarized in Table 6.1, and the interfacial tension between pure liquids in Table 6.2. 

Equation (478) is the exact analytical geometry expression of capillary rise in a cylindrical tube having a circular cross section, which considers the deviation of the meniscus from sphericity, so that the curvature corresponds to (AP = A pgy) at each point on the meniscus, where y is the elevation of that point above the flat liquid level (y = z+h). Unfortunately, this relation cannot be solved analytically. Numerous approximate solutions have been offered, such as application of the Bashforth and Adams tables in 1883 (see Equation (476)) derivation of Equation (332) by Lord Rayleigh in 1915 a polynomial fit by Lane in 1973 (see Equation (482)) and other numerical methods using computers in modern times. 

The capillary rise method is a static method, which measures the tension of practically stationary surfaces that have been formed and equilibrated for an appreciable amount of time. The use of a cathetometer and suitable illumination of the menisci is required during the measurement. The capillary tubes must be very clean, be placed as accurately vertical, and be circular in cross section with an accurately known and uniform radius. The... 

In TLC separations, Eq. (2-1) assumes that all solvent on the bed (at any time during separation) originates from the capillary rise of solvent through the bed solvent loss to the surrounding air by evaporation and/or solvent gain by adsorption from the vapor phase render this assumption invalid. 

It was necessary to use a new cell each time, as removal of the metals with acid, or with alkaline detergent, even though followed by surface treatment, did not return the cell to the same condition as a new one, as evidenced by different capillary rises. 

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