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.