Analysis of fluid motion in the field of microfluidics, i.e., the dynamics of fluid flow at the sub-millimeter scale under the influence of relevant physical forces. Contemporary microfluidics is relevant to the scientific study of flows in small geometries, to the design of tools for biology, medicine and energy technologies. Constitutive relations for the stress tensor in a fluid; Conservation equations of mass, momentum, and energy. Capillary and multiphase flow at small scales. Wettability and related surface engineering methods. Interfacial transport phenomena involving thermal, chemical or electrical gradients. Analytical and numerical methods to design microfluidic devices such as pumps, valves, heat exchangers, actuators, dispensers and mixers. Analysis of applications of multiphase microfluidics in engineering and biological structures.