Microfluidic flows in viscoelastic fluids

In this chapter we provide an overview of viscoelastic fluid flow at the microscale. We briefly review the rheology of these nonlinear fluids and assess its implications on the flow behavior. In particular, we discuss the appearance of viscoelastic instabilities, which are seen to occur even under creeping flow conditions. The first type of instability changes the flow type from symmetric to asymmetric, while the flow remains steady. The second (andmore frequent) type of instability, which sets in when elastic effects are enhanced, causes theflow to becomeunsteady varying in time periodically. This unsteadiness results in a nearly chaotic flow, bringing about a significant improvement in mixing performance. After a brief introduction to the theme of microfluidics, its basic principles, relevance and applications, this chapter is organized in five additional sections. Section 6.2 provides an overviewof the problemofmixing at themicroscale and of the current methods used to tackle this problem. Section 6.3 presents an introduction to non-Newtonian viscoelastic fluids describing their most relevant rheological properties. Section 6.4 presents the governing equations for Newtonian and nonNewtonian fluid flow, including the constitutive equations that describe the rheology of thefluids. Section 6.5 dealswith passivemixingmethods in viscoelasticfluidflows, whereas in Section 6.6 other forcing methods for promoting viscoelastic fluid flow at the microscale are briefly described.