Equivalent circle diameter value

Once an image has been segmented, the microstructural characteristics can be measured, for example ice crystal and air bubbles size. Figure 6.1 shows that the ice crystals and air bubbles are not spherical. Therefore, several different measurements of size can be made, for example the maximum diameter, the minimum diameter, or the equivalent circular diameter i.e. the diameter of a circle with the same area). The shape factor (defined by equation 6.3) is a measure of how far a particle is from being circular it takes a value of one for a sphere and becomes smaller as the particle becomes less spherical. 

The dynamics of capillary flow in confined channels, is now well known in the case of composite walls. In the case of a cylindrical channel, the Lucas-Washburn-Rideal (LWR) expression produces the relation between the travel distance or velocity with the time. But using an equivalent hydraulic diameter for describing the motion in an arbitrary cross section channel introduces a bias, which is important if the cross-section differs notably from the circle. An expression generalizing the LWR expression has been derived, which details the dynamics of the capillary flow under the condition that inertia is negligible, which is often the case at the microscale. In such a case, the advancing contact angle has been found to be constant, and close to the static value. 

Fig. 14.3 Experimental ( solid lines) and simulated (open circles) voltammograms obtained when solid Fc particles are adhered to a 25 pm diameter Pt microdisk electrode in contact with [C4mim] [PFg] in the absence a) and presence (b) of 10 mM Fc. The simulated voltammogram open circles) was calculated using parameter values of iP = 0.0025 cm s , Z) = 3.0 x 10 cm s for both Fc and Fc, n= 1, a = 0.5, and an electrode area of 4.91 x 10 cm and normalized to the peak current in b) in order to demonstrate the shape and peak potential equivalence of voltammograms obtained from dissolved and adhered material. (iP, D, n, and a are standard heterogeneous electron-transferrate constants for the electrode reactions, diffusion coefficient, the number of electrons, and electron-transfer rate constant). Adapted with permission from Zhang et al.yAnal. Chem. 2003, 75, 2694-2702 [24]. Copyright 2013, American Chemical Society...

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