Rheology of Multiphase Systems: Emulsions, Suspensions and Foams

This chapter gives a survey on the rheology of multiphase systems. The topic is of the utmost practical relevance, as flows of multiphase systems, e.g., solids in liquid, liquid-liquid or gas-liquid systems are encountered in a very wide range of applications. It is then evident the difficult task of gathering together sparse results while also unifying concepts and interpretations. We were thus forced to make a severe selection of main topics, and to leave out many arguments which, though interesting, appear to be of less general relevance. We are fully aware that such a selection is certainly biased from our own interests and fields of expertise; although we apologize for this anisotropic point of view, we believe this is unavoidable in any review chapter. The chapter opens with a section devoted to suspensions of solids in liquids. In order to maintain the discussion as simple as possible, we consider the case of identical solid spheres as inclusions, by neglecting inertia and buoyancy. The section progresses from dilute to “dense” suspensions. The second section reports on the rheology of liquid-liquid suspensions, i.e., emulsions. The relevance of the dynamic nature of the interface is stressed throughout, from the disperse to the co-continuous morphology. Deformability of the interface, together with breakup and coalescence phenomena play the central role under flow. The chapter then closes with a rather brief introduction to foams, i.e., the case of gas-liquid systems at very high gas fraction. Whenever theoretical analysis can be profitably used to describe experimental evidences, it has been included in some detail. The reader will notice how theoretical understanding progressively fade out while reaching the end of the chapter, somehow reflecting both the age of the subjects here addressed, and their intrinsic difficulties. Although the topics covered in this chapter are widespread, a unifying tool is often used (if not explicitly reported) for the rheological description, namely, the celebrated stress averaging procedure formalized by Batchelor (1970). Useful limiting behaviors and scaling arguments are presented as well. In the cases where no clear cut understanding can be found, phenomenological arguments and practical rules of thumb are reported to guide the reader.