High-frequency storage and loss moduli estimation for an electromagnetic rheological fluid using Fredholm integral equations of first kind and optimization methods

Abstract

The purpose of the present study was to estimate storage and loss moduli of an electromagnetic rheological (EMR) fluid in frequencies higher than 100 rad/s. In rotational rheometers, the maximum applicable frequency by the rheometer is 100 rad/s. On the other hand, the required frequency range in various applications of EMR is much higher than this frequency. Therefore, it is necessary to determine rheological properties of smart fluids in frequencies higher than 100 rad/s. The used smart fluid is a magneto-rheological (MR) fluid with the commercial name of MRHCCS4-A. First, using a rotational rheometer, storage and loss moduli in frequencies lower than 100 rad/s were measured. Then, Fredholm integral equations of the first kind and Tikhonov regularization were employed to estimate the relaxation spectrum values. Here, three optimization methods, including imperialist competitive algorithm, genetic algorithm, and particle swarm optimization, have been used. Finally, available analytic correlations were used to estimate the storage and loss moduli in frequencies higher than 100 rad/s. To validate the optimization methods, the numerical results of storage and loss moduli (for frequencies lower than 100 rad/s) were compared with the ones of rheology test. Good agreement between numerical and test results was noticed.