Two Parallel Torus-Shaped Particles

FIGURE 19.13 Two parallel rings of radii and r-i, respectively, separated by a distance h. 

It is interesting to note that Eq. (19.56) agrees with the energy between two parallel rods of length 2nr carrying molecules of line densityTV [9]. 

A torus-shaped particle can serve as a model for biocolloids such as biconcave human red blood cells. The interaction between two parallel biconcave-shaped red 

FIGURE 19.14 Two parallel toms-shaped particles at separation R between their centers. a is the radius of the tube and b is the distance from the center of the tube to the center of the toms. From Ref. [9]. 

Consider two parallel similar toms-shaped particles at separation R between their centers (Fig. 19.14) [9]. A toms can be constmcted by joining the ends of a cylindrical tube. We denote the radius of the tube by a and the distance from the center of the tube to the center of the toms by b. The length of the cylindrical tube is thus 2iib and the closest distance H between the surfaces of these tori is H=R 2 a. Let N be the number of molecules contained within the particles. The interaction energy V R) between two parallel tori can be calculated with the help of Eqs. (19.1) and (19.54) (Fig. 19.15), namely. 

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