Multiphase flows viscosity ratio

The major forces controlling multiphase flow pafferns are capillary forces, viscous forces, and buoyancy forces. These forces are often compared using three key dimensionless numbers the ratio of the displaced to the invading fluid viscosities. 

Abstract Among the noncontinuum-based computational techniques, the lattice Boltzman method (LBM) has received considerable attention recently. In this chapter, we will briefly present the main elements of the LBM, which has evolved as a minimal kinetic method for fluid dynamics, focusing in particular, on multiphase flow modeling. We will then discuss some of its recent developments based on the multiple-relaxation-time formulation and consistent discretizatirai strategies for enhanced numerical stability, high viscosity contrasts, and density ratios for simulation of interfacial instabilities and multiphase flow problems. As examples, numerical investigations of drop collisions, jet break-up, and drop impact on walls will be presented. We will also outline some future directions for further development of the LBM for applications related to interfacial instabilities and sprays. 

In this chapter, we have provided a brief introduction to the LBM for computation of multiphase flows of relevance to atomization and sprays. Since its inception, the LBM has come a long way, especially in overcoming some of the early challenges. In particular, the use of MRT formulation for multiphase flows has been a major step in maintaining numerical stability at lower viscosities or higher Reynolds numbers the use of consistent discretization approaches in the LBM has enabled simulation of high density ratio problems. During the last few years. 

Ranking the importance of different forces helps in categorizing the increasing number of experimental studies with the ultimate goal to predid multiphase flow behavior in microchannel networks and formulate guidelines for their design. Multiphase microflows are charaderized by the ratio of viscous to surface forces, the capillary number (Co) and by the ratio of fluid viscosities ... 

Rheology is a part of continuum mechanics that assumes continuity, homogeneity and isotropy. In multiphase systems, there is a discontinuity of material properties across the interface, a concentration gradient, and inter-dependence between the flow field and morphology. The flow behavior of blends is complex, caused by viscoelasticity of the phases, the viscosity ratio, A (that varies over a wide range), as well as diverse and variable morphology. To understand the flow behavior of polymer blends, it is beneficial to refer to simpler models — for miscible blends to solutions and mixtures of fractions, while for immiscible systems to emulsions, block copolymers, and suspensions [1,24]. 

---