Sedimentation Equilibrium of Mixtures of Charged Colloids

Chapter 4Sedimentation of a polydispersemixtureAt last! I thought you’d never begin. . .Let’s proceed. It is getting interesting now! We’ve had theouverture’, we’ve been introduced to the main characters, their backgroundand the scene. We saw ions, charged and Brownian, only interested in theirentropy and in neutrality. We saw lazy colloids, impenetrable and hard, tornbetween the same feelings as the salt, obsessed by chaos and the ’other side’,and still a preference of direction because of their heavy nature. And hidden,though omnipresent, the medium, firing the Brownians with its temperature,and tempering the Coulombic desires with its dielectric cloak, the backgroundthat lightens our colloids. They came all together. . . and found balance. Thecommunity of colloids was homogeneous and of one kind. Things are stirring,new intentions, new groups, and all for the good of course! But will theyfind it? What will happen if two families meet. . .or 20 families!!4.1 The systemInspired by earlier examples, we are now going to observe suspensions thatcontain multiple colloidal spheres of different kinds. They can be distinguishedby their charge, mass or diameter, or combinations of them. Theability to adapt their charge, called charge regulation, will follow later. Thatwill complicate the situation even more.The colloidal components (’families’) in the system are numbered by theindex i, n is the total number of components. The colloids have a charge−Z i e, gravitational length L i and diameter σ i . The colloid number density15