Shear viscosity of strongly coupled Yukawa liquids

We present molecular-dynamics calculations of the shear viscosity of three-dimensional strongly coupled Yukawa liquids which are frequently used as a model system of complex plasmas. The results obtained using two independent nonequilibrium simulation methods are critically compared with each other and with earlier published data for a wide range of plasma coupling $\left(\Gamma \right)$ and screening $\left(\kappa \right)$ parameters. The non-Newtonian behavior of the liquid, manifested as a descrease of the shear viscosity with increasing shear rate (shear thinning), and the validity of the Stokes-Einstein relation at high coupling strength are also demonstrated.

Figure 1

(Color online) (a) Shear viscosity of the Coulomb OCP. DN: Donkó and Nyíri [18] using 1024 and 8192 particles; WB: Wallenborn and Baus [16]; VH: Vieillefosse and Hansen [14]; BV: Bernu et al. [17]; B: Bastea [19]. The dashed line (D: Daligault [11]) represents an Arrhenius-type behavior at high $\Gamma$ values; this curve has been scaled to match the minimum value of $\eta$. Additional data for YOCP with small screening coefficent: SC: Salin and Caillol [20]; SH: Saigo and Hamaguchi [15]. (b) Shear viscosity of the Yukawa OCP at $\kappa =2$. M: Murillo [22]; SM: Sanbonmatsu and Murillo [24]; FM: viscosity obtained from mapping with effective hard-sphere system by Faussurier and Murillo [23]; SC and SH: see (a).

Figure 2

Simulation methods for shear viscosity calculation. (a) Equilibrium MD: uses phase-space trajectories to compute $\eta$. (b) Transient perturbation technique: the decay time of an artificial velocity profile modulation is monitored. (c) Reverse molecular dynamics: an exchange of particles’ momenta between cells A and B results in a velocity profile. (d) Homogeneous shear algorithm using sliding periodic boundary conditions. The figures show 2D faces of the 3D computational boxes. For more details about the different methods, see text.

Figure 3

(Color online) (a) Shear viscosity of the Yukawa liquid at $\kappa =1$. SM: Sanbonmatsu and Murillo [24]; SH: Saigo and Hamaguchi [15]; SC: Salin and Caillol [20]; present: results obtained with the homogeneous shear algorithm (HSA) using $N=8000$ particles and a normalized shear rate $\overline{\gamma }=0.05$. Left scale: viscosity values normalized by the plasma frequency $\left({\eta }^{\prime }\right)$; right scale: viscosity values normalized by the Einstein frequency $\left({\eta }^{*}\right)$. (b) Comparison of the results obtained by using different methods in the present work [HSA: homogeneous shear algorithm, with number of particles $\left(N\right)$ and at reduced shear rates $\left(\overline{\gamma }\right)$ indicated; RMD: reverse molecular dynamics with number of particles $\left(N\right)$ indicated] and with viscosity values obtained in previous works (SH and SC, see above). The present data shown in (a) have been taken as reference data, ${\eta }_{\mathrm{REF}}^{\prime }$. The shaded region represents $\pm 5\%$ deviation from the reference data.

Figure 4

(Color online) Shear viscosity of the Yukawa liquid at $\kappa =2$. For details, see the caption of Fig. 3.

Figure 5

(Color online) Shear viscosity of the Yukawa liquid at $\kappa =3$. For details, see the caption of Fig. 3.

Figure 6

(Color online) (a) Dependence of the (“TOT”) shear viscosity on the normalized shear rate $\overline{\gamma }$ as obtained from HSA calculations, at $\Gamma =10$, 50, and 300, $\kappa =2$. (b) Potential (“POT”) and kinetic (“KIN”) contributions of the viscosity.

Figure 7

(Color online) $D^{*}{\eta }^{*}∕T^{*}$ as a function of normalized temperature of the system $T^{*}$. The proximity of the data points to the horizontal dashed line indicates the fulfillment of the Stokes-Einstein relation in the $T^{*}\lesssim 12$ domain. The inset shows the connection between $T^{*}$ and $\Gamma$ for the different $\kappa$ values studied.