Effects of Electric Field on Shear Viscosity in 3D Dusty Plasmas

In this study, we present a theoretical analysis of the shear viscosity ( η ) in three‐dimensional dusty plasmas (DPs) through molecular dynamics simulations under the influence of an external electric field ( E ). The Green‐Kubo formula is applied to compute η across various values of E , Coulomb coupling, and screening parameters. The simulation results of η at zero E (= 0.0) are compared with existing data and discuss the applicability of the Green‐Kubo formula. It is found that this method provides overestimations but is still applicable to approximation investigations of η in cooled liquid states of DPs. Further, our investigations reveal that η is anisotropic when applied to E . The results of anisotropic η in DP liquids identify three distinct regimes. The first is a slight decrease in η , indicating the presence of repulsive interactions at low E values. The second is a rapid increase, suggesting strong, attractive interactions at intermediate E values. The third shows relatively stable behavior, indicating saturation at high E values. The obtained values of η as a function of normalized temperature follow the temperature scaling law. Furthermore, dust particles align along the z ‐axis and form clusters; the number and size of the clusters depend on the strength of the E . We show that using the Green‐Kubo relation with a wake potential in DPs provides reliable and accurate predictions of E impact on η . These results enhance understanding of the anisotropic η and electrorheological properties of DPs, offering valuable insights into structural transitions influenced by the E .