Fluid flow surrounds us. From the flow of water from a faucet and blood in our veins to the processing of most materials, we are both blessed and frustrated with the flow of material. People have developed a great intuition for fluids that experience a linear strain in the presence of a stress; however, most biological and industrial fluids exhibit a nonlinear response to deformation. This nonlinear response can be a hindrance when trying to get ketchup out of a glass bottle, or it can be a benefit when spreading paint on a vertical wall. These everyday examples illustrate that complex fluids can be difficult to process, yet when exploited, this complexity can also be desirable.
The addition of multiple phases to flow systems drastically increases the complexity of the flow physics. These complexities reveal themselves on both the macroscopic and microscopic length scales and can involve solids as well as immiscible and miscible fluids. Complexities such as the presence of polymers, surfactants, colloids, and particulates to flow systems create complex fluids or soft materials that respond in a nonlinear way to stress. Interfacial interactions between miscible systems are further complicated by the presence of gradients in the chemical potential that vary in space and time. These gradients distinguish miscible systems from immiscible systems, which approximate these gradients as discontinuities. A vast number of manufacturing practices and biological materials involve multiphase systems that are highly structured and rheologically complex.