Abstract
The effective dynamic bulk modulus and density are presented for random media consisting of particles in a viscous host fluid, using a core-shell, self-consistent effective medium model, under the large compressional wavelength assumption. These properties are relevant to acoustic or dynamic processes in nano- and micro-particle fluids including particle density determination, resonant acoustic mixing, and acoustic characterisation. Analytical expressions are obtained for the effective bulk modulus and mass density, incorporating the viscous nature of the fluid host into the core-shell model through wave mode conversion phenomena. The effective density is derived in terms of particle concentration, particle and host densities, particle size, and the acoustic and shear wavenumbers of the liquid host. The analytical expressions obtained agree with prior known results in the limit of both static and inviscid cases; the ratio of the effective bulk modulus to that of the fluid is found to be quasi-static. Numerical calculations demonstrate the dependence of the effective mass density on frequency, particle size (from nano- to micro-regime), and concentration. Herein it is demonstrated both theoretically and numerically that the viscosity, often neglected in the literature, indeed plays a significant role in the effective properties of nanofluids.
Highlights
Estimating the effective properties of complex media is of interest from both a theoretical and experimental point of view owing to their numerous applications; these include the mechanical properties of solid composite structures, the soundabsorbing properties of porous materials, and the dynamic properties of fluid-suspended particle systems
The current work is directed towards the determination of dynamic effective properties for acoustic propagation in complex fluids consisting of solid nanoparticles in a viscous liquid; previous investigations have studied mainly inviscid fluid hosts
Since MSTs are limited to low volume concentrations, Yang and Mal combined the GSCM with the MST of Waterman and Truell in order to obtain a dynamic generalised self-consistent method (DGSCM),46 whereby they calculated the effective wavenumber of a fibre-reinforced composite (a 2D cylindrical problem) in a self-consistent manner; they showed that the effective wave speed calculated was in good agreement with experimental data
Summary
Estimating the effective properties of complex media is of interest from both a theoretical and experimental point of view owing to their numerous applications; these include the mechanical properties of solid composite structures, the soundabsorbing properties of porous materials, and the dynamic properties of fluid-suspended particle systems. Since MSTs are limited to low volume concentrations, Yang and Mal combined the GSCM with the MST of Waterman and Truell in order to obtain a dynamic generalised self-consistent method (DGSCM), whereby they calculated the effective wavenumber of a fibre-reinforced composite (a 2D cylindrical problem) in a self-consistent manner; they showed that the effective wave speed calculated was in good agreement with experimental data. Other workers have combined the two approaches, to determine effective properties at higher concentrations, but retaining the wave-nature of the problem; McClements et al applied this approach for thermal interactions, and Hipp combined the two methods for a thermal-viscous-acoustic system of spherical particles assumptions were made regarding effective properties rather than deriving them.. III, numerical predictions of the model are presented, and their physical interpretation discussed
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have