Interfaces: in fluid mechanics and across disciplines

The dynamics of fluid–fluid interfaces are important in diverse problems that span many disciplines in science and engineering. A series of snapshots is used to illustrate the breadth of applications that can occur in viscous low-Reynolds-number flows and I highlight theoretical and modelling ideas that are broadly useful for these, as well as other, problems. By way of illustration of unifying quantitative ideas we discuss briefly (i) the use of the Reciprocal Theorem in low-Reynolds-number flows, (ii) the use of the lubrication approximation for characterizing thin-film coating flows sometimes referred to as Landau–Levich–Derjaguin–Bretherton problems and (iii) nearly two-dimensional viscously dominated flows.