Universal Nucleation Behavior of Sheared Systems

Using molecular simulations and a modified classical nucleation theory, we study the nucleation, under flow, of a variety of liquids: different water models, Lennard-Jones, and hard sphere colloids. Our approach enables us to analyze a wide range of shear rates inaccessible to brute-force simulations. Our results reveal that the variation of the nucleation rate with shear is universal. A simplified version of the theory successfully captures the nonmonotonic temperature dependence of the nucleation behavior, which is shown to originate from the violation of the Stokes-Einstein relation.

Figure 1

Variation of the normalized nucleation rate with the normalized shear rate, $\dot{\gamma }/{\dot{\gamma }}_{\mathrm{opt}}$ at selected metastabilities, plotted alongside the corresponding parabolic fit. Equation (10) has been denoted by a solid black line, and filled markers symbolize the nucleation rates calculated using shear-CNT for various systems and metastabilities. Black open squares show the data for the mW model estimated by Luo et al. [22], for a supercooling of 67.6 K, using brute-force approaches to calculate and fit to the induction times [90]. Errors associated with $J$ were within 10% [22]. Open turquoise circles depict the data for a sheared two-dimensional Ising model, obtained using forward-flux sampling [91], by Allen et al. [13]. Error bars for $J$ were of the range of 7%–10% [13].

Figure 2

(a) Dependence of $\tau {\dot{\gamma }}_{\mathrm{opt}}$ on the percent supercooling, $[(T_m-T)/T_m)]\times 100\%$, for TIP4P/2005, TIP4P/Ice, mW, and LJ. Filled and open markers represent values calculated using shear-CNT, with input data calculated from simulations and with approximated inputs, respectively. The solid lines denote $\tau {\dot{\gamma }}_{\mathrm{opt}}$ estimated using the simplified theory, Eq. (11). (b) Variation of $B=[(k_{B}T/D_0\eta )(c/v^{\prime })]$ with the percent supercooling. The inset shows $N_0^{*}$ plotted against the percent supercooling. (c) Test of the Stokes-Einstein (SE) relation, according to which $(k_{B}T/D_0\eta )$ should be constant. SE relation is clearly violated for the water models for the supercoolings considered. Data for which the values of $\eta$, $D_0$, $c$ and $v^{\prime }$ were calculated using simulation data are denoted by filled markers, and dashed lines show values calculated using approximations.