EXPONENTIAL FORMULA FOR COMPUTING EFFECTIVE VISCOSITY.pdfVIP

THIS PAPER SHOULD BE CITED AS Cheng, N. S., and Law, A. W. K. (2003). “Exponential formula for computing effective viscosity.” Powder Technology. 129(1-3), 156– 160. EXPONENTIAL FORMULA FOR COMPUTING EFFECTIVE VISCOSITY 1 2 Nian-Sheng Cheng and Adrian Wing-Keung Law ABSTRACT : An exponential model is proposed in this paper for evaluating the effective viscosity of a particle-fluid mixture. First, the theoretical consideration is restricted to the dilute condition without the effects of dynamic particle interactions and fluid turbulence. This leads to a power series expressed in terms of particle concentration, which can be viewed as an extension of the Einstein’s formula. The derived expression is then modified by including indirectly effects of inter-particle collisions, fluid turbulence and random motion of the particles, which can cause the effective viscosity to be increased significantly with increasing particle fraction in the mixture. Finally comparisons are made between the present study and various theoretical and empirical results available in the literature and satisfactory agreement is observed. Keywords: effective viscosity, concentration of particles, suspension, two-phase flow, particle interaction, dilute suspension INTRODUCTION The phenomenon of solid particles suspended in fluid is of key interest in hydraulic engineering such as sediment transport in rivers and slurry transport in pipelines. Similar two-phase suspensions can also be found in industrial applications such as the processing of cement, composite materials and foodstuffs. As an important macroscopic property of these suspensions, the effective viscosity is usually requir