Electrostatics in liquids: From electrolytes and suspensions towards emulsions and patchy surfaces

These lecture notes describe ionic screening of liquid-immersed charged surfaces within the linear and the nonlinear Poisson–Boltzmann theory. The classic Gouy–Chapman description of a single charged planar surface is extensively described, as well as its linearised version and the connection with charge renormalisation. We also consider effective ion-mediated electrostatic interactions between suspended colloidal particles in some detail, and in addition we study Debye–Hückel theory for bulk electrolytes. We argue that relatively straightforward extensions of these basic notions can be used to describe systems of recent interest, e.g. patchy surfaces, oil–water interfaces, and Pickering emulsions. A number of references to recent literature is included.