Interaction Between Two Dissimilar Soft Cylinders

Consider the electrostatic interaction between two parallel dissimilar cylindrical soft particles 1 and 2. We denote by di and d2 the thicknesses of the surface charge layers of cylinders 1 and 2, respectively. Let the radius of the core of soft cylinder 1 be fli and that for soft cylinder 2 be U2- We imagine that each surface layer is uniformly charged. Let Z and N, respectively, be the valence and the density of fixed-charge layer of cylinder 1, and Z2 and N2 for cylinder 2. 

Consider first the case of two parallel soft cylinders (Fig. 15.7). With the help of Derjaguin s approximation for two parallel cylinders [8,9] (Eq. (12.38)), namely, 

FIGURE 15.7 Interaction between two parallel soft cylinders 1 and 2 at separation H. Cylinders 1 and 2 are covered with surface charge layers of thicknesses di and d2, respectively. The core radii of cylinders 1 and 2 are ai and 2 respectively. 

The interaction force Pcy//(H) acting between two soft cylinders per unit length is given by P yz/iH) = —dVcy// H)ldH, which gives [9] 

Consider next the case of two crossed soft cylinders (Fig. 15.8). Deijaguin s approximation for two crossed cylinders under condition (15.43) is given by Eq. (12.48), namely. 

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