The Bridgman crystal growth process represents a prime example of a relevant industrial process in which fluid flow and mixing features impact desired process specifications. In particular, we analyze the bulk mixing properties of the melt flow in a vertical Bridgman process through the identification of Lagrangian coherent structures (LCS). The NavierStokes, continuum, and heat transport equations are formulated in a mixed finite-element universal integration scheme to simulate the multiphase problem using the finite-element method. The highly resolved time-varying accurate numerical solution of the velocity field is utilized to identify the transport barriers in terms of finite time Lyapunov exponent (FTLE) ridges whose movements govern the mixing in the melt flow. The ridge structures are dynamically driven materials surfaces which provide the insight into the efficiency of mixing in two distinct operating regimes of the Bridgman crystal growth process.