  In this paper we analyze the curvature corrections to the surface tension in
the context of the Shan-Chen (SC) multi-component Lattice Boltzmann method
(LBM). We demonstrate that the same techniques recently applied in the context
of the Shan-Chen multi-phase model can be applied to multi-component mixtures.
We implement, as a new application, the calculation of the surface of tension
radius $R_s$ through the minimization of the generalized surface tension
$\sigma[R]$. In turn we are able to estimate the Tolman length, i.e. the first
order coefficient of the curvature expansion of the surface tension
$\sigma(R)$, as well as the higher order corrections, i.e. the curvature- and
the Gaussian-rigidity coefficients. The SC multi-component model allows to
model both fully-symmetric as well as asymmetric interactions among the
components. By performing an extensive set of simulations we present a first
example of tunable Tolman length in the mesoscopic model, being zero for
symmetric interactions and different from zero otherwise. This result paves the
way for controlling such interface properties which are paramount in presence
of thermal fluctuations. All reported results can be independently reproduced
through the "idea.deploy" framework available at
https://github.com/lullimat/idea.deploy.
