In this dissertation, we deal with how to generate intricate mixing patterns of two miscible liquids when a small drop of one liquid is traveling in the other as observed with an ink drop falling in water. Modeling the liquid drop as a swarm of particles sampled from it, we reduce the problem of miscible liquid mixing to that of liquid-particle interactions. A physics-based method is presented to trace the particles in an initially still surrounding liquid, while reflecting the two-way interactions between the liquid and the particles as well as the interactions among the particles themselves in an implicit manner relying on the Navier-Stokes equations. We model the miscibility of these liquids with the external forces acting on the particles based on Fick`s law of diffusion, and incorporate a vorticity effect of the surrounding liquid due to fast-moving particles to visually reproduce lively liquid mixing patterns. Our method can simulate multiple liquid blobs with different shapes and colors, simultaneously. We also extend it to produce liquid mixing phenomena involving a miscible liquid of large volume. We visually validated this method by comparing our results with real ink-water mixing phenomena.