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We study dynamical heterogeneity and growing dynamical length scales in two kinetically constrained models, namely, the one- and two-vacancy assisted triangular lattice gases. One of the models is a strong glassformer and the other is a fragile glassformer. Both exhibit heterogeneous dynamics with broadly distributed timescales as seen in the distribution of persistence times. We show that the Stokes-Einstein relation is violated, to a greater degree in the fragile glassformer, and show how this violation is related to dynamic heterogeneity. Finally, we extract dynamical length scales from structure factors of mobile particles and show, quantitatively, the growth of this lengthscale as density increases. Our results indicate that the one-vacancy assisted lattice gas is in the same universality class as the one-spin facilitated Fredrickson-Andersen model, while the two-vacancy assisted model is in a different universality class. Our findings support the idea that the dynamics of supercooled liquids can be understood from the existence of a zero temperature dynamic critical point

Heterogeneity and growing length scales in the dynamics of kinetically constrained lattice gases in two dimensions