Effects of strangeness on the chiral pseudocritical line

Within a 2+1 flavor Nambu\textendash Jona-Lasinio model, we calculate the curvature coefficients and check them against available lattice QCD estimations. With the observation that the flavor mixing due to the `t Hooft determinant term significantly affects the $\kappa_{2}^{S}$, we explore the effect of $\mu_{S}$ on the $T-\mu_{B}$ crossover lines. With the novel determination of negative $\kappa_{2}^{B}$ at large $\mu_{S}$, we advocate the importance of studying the same in lattice QCD.