The Capillary Length

There exists a particular length, denoted beyond which gravity becomes important. It is referred to as the capillary length. It can be estimated by comparing the Laplace pressure 7/to the hydrostatic pressure at a depth in a liquid of density p submitted to earth s gravity g = 9.8 m/s. Equating these two pressures defines the capillary length  

The distance is generally of the order of few mm (even for mercury, for which both 7 and p are large). If one wants to increase in a liquid by a factor 10 to 1,000, it is necessary to work in a microgravity environment or, more simply, to replace air by a non-miscible liquid whose density is similar to that of the original liquid. 

Gravity is negligible for sizes r When this condition is met, it is as though the liquid is in a zero-gravity environment and capillary effects 

FIGURE 2.1. Liquid bath rising to form a capillary bridge (From Nucleation Radius and Growth of a Liquid Meniscus, by G. De-bregeas and F. Brochard-Wyart. In Journal of Colloid and Interface Science, 190, p. 134 (1997), 2001 by Academic Press. Reproduced by permission.) 

FIGURE 2.2. A small floating object (a) or a wall (b) perturbs the surface of the liquid over s distance called the capillary length.  

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In order to simplify the analysis, we will consider the capillary flow of a hquid L in a horizontal small tube (diameter much smaller than the capillary length), in order to avoid complications due to gravity effects (Fig. 14). 

OS 33] ]R 16h] [P 25] For the nitration of a single-ring aromatic in a capillary-flow micro reactor, experiments were performed at two temperature levels, 60 and 120 °C [94]. Owing to the assumed increase in conversion rate with higher temperature, attempts were made to compensate for this by decreasing the capillary length at otherwise constant dimensions. For the 60 °C experiment, a very low... 

Groendes and Mesler (1982) studied the saturated film boiling impacts of a 4.7 mm water droplet on a quartz surface of 460 °C. The fluctuation of the surface temperature was detected using a fast-response thermometer. The maximal temperature drop of the solid surface during a droplet impact was reported to be about 20 °C. Considering the lower thermal diffusivity of quartz, this temperature drop implies a low heat-transfer rate on the surface. Biance et al. (2003) studied the steady-state evaporation of the water droplet on a superheated surface and found that for the nonwetting contact condition, the droplet size cannot exceed the capillary length. 

Capillary length is one of the parameters commonly used to improve resolution, but in our experience, more dramatic effects can be accomplished by changing the mobility of the sample components through manipulation of pH or the use of buffer additives. In fact, we usually develop a method in the shortest capillary possible, and only when the separation is adequate do we increase the capillary length for final optimization. This practice saves time in methods development because more data can be collected if the analysis time is short. 

The length of capillaries used for single-step CIEF is very important, especially when EOF is the driving force. The capillary length must be optimized according to the size of the injection and the velocity of EOF or flow due to hydraulic forces so that the sample will not reach the detection point before it has finished focusing. 

We should not forget that the capillary plays a key role in the separation. Even if a fused silica capillary is usually used, the choice of diameter and capillary length has a major impact. Decreasing the capillary diameter or increasing the capillary length will lower the current and... 

Separation conditions can be optimized with respect to the capillary length (L), capillary ID, separation voltage (V), and separation temperature (T). 

The migration of a charged species, e.g., its motion under the force of an electric field, is given by Eq. (2), where the strength of the electric field E is simply a function of the applied voltage U divided by the capillary length L ... 

From this equation it is evident that the maximum voltage depends on the square root of the maximum heat that can be dissipated, the conductivity of the buffer, and the two geometry parameters of the capillary, length L and diameter d. Equation (19) can be rewritten to yield an expression for /i iax ... 

From the physics point of view, cellulose fibers can indeed be considered as tiny roughly cylindrical capillary tubes of radius r and length h. Consequently, a wetting liquid placed into contact with this highly hydrophilic material penetrates it by capillary action. Actually, in capillaries with radii much smaller than the capillary length, gravity may be... 

About 50 % of the temperature rise occurs near the capillary entrance, z < 0.2L. Thus, shortening the capillary length does not decrease the temperature rise due to viscous heating, proportionally. 

Joule heating is the increase in temperature that results when analyte and buffer molecules collide as a result of the conduction of electric currents. It does not adversely affect efficiency if the capillary length is less than 90 cm and the internal diameter is less than 80 pirn. 

Three pressure stages are relevant to design the capillary lengths and diameters as shown in Fig. 15 The pressure regimes for stable operation were evaluated by measurements using pressure sensors and mass flow controllers. They are summarized in Table 1 ... 

The influence of interphase mass transfer between liquid-liquid slugs was investigated for nitration of aromatic compounds in a capillary-flow reactor (see Figure 5.2) [22]. This was achieved by changing flow velocity via volume flow setting, while residence time was kept constant by increasing the capillary length. 

This apparent mobility can be easily calculated with the capillary length to the detector (Ld), the migration time of the analyte (tm), and the electric field strength (E). 

Even if the separation is still incomplete, increasing the buffer concentration from 20 mM to 50 or 75 mM and even higher may provide for a complete separation. If the currents get too high (>100 pA), consider the use of a 25-pm-i.d. capillary. Once a good separation is obtained, try shortening the capillary length. 

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