Universal Validity of Einstein Relation and Size-Dependent Viscosity and Surface-Active Characteristics of Nanofluids

Abstract

In this report, the general validity of the Einstein viscosity relation, [Formula: see text], [Formula: see text], ratio of solution to solvent viscosity), is examined in nanofluids where monodisperse spherical nanoparticles (polystyrene latex spheres) of size 50–400[Formula: see text]nm were dispersed in water at room temperature, 25[Formula: see text]C. In addition to viscosity, we also measured contact angle, [Formula: see text], and surface free-energy, [Formula: see text], as function of particle concentration and observed that the universal relation [Formula: see text], [Formula: see text], remained valid, where [Formula: see text] may be relative viscosity, contact angle or surface free-energy and [Formula: see text] is a shape-dependent constant and is 2.5 in the Einstein limit. Thus, the Einstein relation has a wider validity than is generally thought encompassing both bulk and surface properties of nanofluids. Furthermore, we extend the study to establish an empirical relation between intrinsic viscosity [[Formula: see text]] and Huggins interaction parameter [Formula: see text], with particle size [Formula: see text], which obeyed: [Formula: see text] or [Formula: see text], where [Formula: see text] is in nm, [[Formula: see text]] is in cc/g, [Formula: see text] is in (g/cc)2 and [Formula: see text], [Formula: see text] and [Formula: see text] are constants of particle size. Identical expressions could be established for contact angle and surface free energy. These remarkable observations have not been reported hitherto.