Generalized capillary length

K is positive, the derivatives in the integrand being of opposite signs. A generalized capillary length f may be defined by ... 

In CE, only small quantities of sample can be introduced onto the capillary if the high efficiencies characteristic of the technique are to be maintained, as discussed in connection with electromigration dispersion in Section 4.3.4. In general, the sample length should be less than 2% of the total capillary length. Although this can be an advantage for applications with limited volumes of sample, it can be a problem from the point of view of detection. 

Consider now a liquid in a crucible that is unwetted by the liquid and surrounded by a vapour phase (Figure 1.36). The triple line between the liquid surface, the crucible wall and the vapour, is at a depth z ax below the general level of the liquid. For a crucible radius much larger than the capillary length lc, z ax is given by (see equation (1.23)) ... 

Electroklnetlc Injection In electrokinetic injection, the sample is introduced in the capillary by applying a voltage (in general, lower than that used for the separation), while the injection end is dipped in the sample (Fig. 3.6). Under these conditions, the analytes contained in the sample are injected by electromigration as well as by electroosmotic flow. The amount of sample loaded increases with the electrophoretic mobility of analyte, the electroosmotic flow mobility, the inner radius, the voltage, the sample concentration, and the injection time. The amount loaded will decrease with the capillary length. 

General aspects of extra-column volumes in the HPLC instrument have been discussed in Section 2.6. Various formulas have been proposed which allow to calculate the maximum allowed capillary length with regard to band broadening an adaption after M. Martin et al. is as follows ... 

The sample, typically a few nanoliters, can be introduced into the capillary by hydrostatic injection (gravity, pressure, or vacuum) or by electromigration. The sample volume should generally be less than 2% of the total capillary length. For gravity introduction, the capillary sample end is dipped into the sample (which may be as small as 5 fiL) and raised for a short predetermined time to allow sample to flow into the capillary. Or, it is inserted into a pressurized vial to force sample into the capillary. Or it is drawn in by suction from the other end of the capillary. After injection, the sample vial is replaced with a buffer reservoir. Alternatively, the sample end is immersed in the sample solution and a relatively low voltage is ap-phed for a few seconds, for example, 2000 V for 10 s. This injects the small volume of sample by electroosmosis. 

For the case of the nucleation of a crystal Ifom a supercooled liquid, Ef = Ap/v, where v is the volume per particle of the solid and Ap is the chemical potential difference between the bulk solid and the bulk liquid. These results, given here for three-dimensional systems, can be easily generalized to an arbitrary d-dimensional case [37]. Often, it is usefiil to use the capillary length = 2uv)l kT) as the unit of length the critical radius is R = I where the supersaturation z t) = E J kT), and the nucleation barrier is (EJkT) = zjz t)), where the dimensionless quantity = / [(47ia)/(3A 7)]. ... 

By defining a Bond number Bo = coJlcY, where the beam waist (Wq is used as the characteristic length scale and Ic = y / fi —p2)g is the capillary length, Eq. 7 leads to a general expression for the height on beam axis h r = 0) in the weak deformation regime ... 

As a general rule, the characteristic size of a meniscus is either the capillary length or the size I of the vessel itself, whichever is smaller. 

Note that Equation 4.167 is approximate and holds for interparticle distances, which are much smaller than the characteristic capillary length, that is, qr-. The general form of the multipolar expansion. Equation 4.167, for arbitrary interparticle distances reads [321-324] ... 

Io(x) and l2(x) are modified Bessel functions of zero and second order, Bb and pe are the bulk elasticity modulus and the density of phase B, / is the capillary length (/ ac). Substituting Eqs. (12) and (14) into (8) one can obtain the general expressions for the bubble (drop) volume variation 6V ,(ico), the pressure variations inside the bubble (drop) 5P, (ici)), and inside the cell 6P (ico) at the given bP, and 6Vp . The effect of both the flow mobility and the compressibility of the medium in the capillary on the oscillating bubble or drop measurements is analysed in details in [26]. Here only the simpler case of quasi-stationary flow of incompressible media in the capillary is described. 

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