  The lattice Boltzmann (LB) method has gained much success in a variety of
fields involving fluid flow and/or heat transfer. In this method, the
bounce-back scheme is a popular boundary scheme for treating nonslip
boundaries. However, this scheme leads to staircase-shaped boundaries for
curved walls. Therefore many curved boundary schemes have been proposed, but
mostly suffer from mass leakage at the curved boundaries. Several correction
schemes have been suggested for simulating single-phase flows, but very few
discussions or studies have been made for two-phase LB simulations with curved
boundaries. In this paper, the performance of three well-known types of curved
boundary schemes in two-phase LB simulations is investigated through modeling a
droplet resting on a circular cylinder. For all of the investigated schemes,
the results show that the simulated droplet rapidly "evaporates" under the
nonslip and isothermal conditions, owing to the imbalance between the mass
streamed out of the system by the outgoing distribution functions and the mass
streamed into the system by the incoming distribution functions at each
boundary node. Based on the numerical investigation, we formulate two modified
mass-conservative curved boundary schemes for two-phase LB simulations. The
accuracy of the modified curved boundary schemes and their capability of
conserving mass in two-phase LB simulations are numerically demonstrated.
