A universal yield stress equation for electrorheological fluids

Abstract

In this study, we investigate the universality of the yield stress [τyE0, where E0 is electric field strength] for examining electrorheological (ER) fluids both experimentally and theoretically. We found that the published experimental data for the yield stress of ER fluids for various materials and measurement conditions obey a yield stress scaling equation. In other words, the ER yield stress data in the literature collapse onto a universal correlation: τ̂=1.313Ê3/2tanhÊ using scaled variables τ̂≡τyE0/τyEc and Ê≡E0/Ec. Here, Ec is critical electric field strength. Although this expression is attractive for experimentalists, this empirical equation has not been derived from first principles. We introduce a mesoscopic elementary region concept and justify this universal correlation for the first time. We decompose the ER system into a finite number of elementary regions and introduce “glueons,” which adhere to neighboring elementary regions resulting in fibrillary structures. We investigated the limiting case when the elementary region size is reduced to zero (continuum limit) and used a reaction-diffusion model to calculate glueon concentration. In modeling the reaction term (generation of glueons), we used a linear model by recognizing that the electric field activates glueons, i.e., the number of glueons increases as the electric field strength increases. In our preliminary study, we were able to justify a universal correlation by solving the glueon concentration equation using a simple geometry. The novelty of this work is the development of universality for the ER yield stress and derivation of a universal scaling equation.