In recent years, the importance of understanding the behavior of complex fluids has increased due to the high demand from a wide range of industries. In addition, battery slurry, which has the viscoelastic material properties is being studied to promote its efficiency. Extension properties of the multi-component solution are hard to analyse because of its complexity and sensitivity to external factors such as inertia. In this study, we conduct liquid drop simulation for the two-phase flow, viscoelastic fluid represented with various of constitutive equations such as the Oldroyd-B, Giesekus, and Leonov models and air, using Cahn-Hilliard method for the multiphase and LCR (Log Conformation Reformulation) method based on FEM (Finite Element Method). Notably, the LCR method ensures the positive definiteness of conformation tensor can be preserved without any stabilization methods and enables to solve the high Weissenberg number problem. Temporal discretization is accomplished through the application of the trapezoidal rule which is known for its second order accuracy. To gain deeper insights into the extensional properties of viscoelastic fluids, we employ the Dos-CaBER (Dripping onto Substrate Capillary Break-up Extensional Rheometry). This apparatus enables the observation of the time evolution of the bubble drop radius, allowing us to deduce transient extensional viscosity. The experimental validation of our numerical results is a pivotal aspect of our study, and we compare these findings with experimental data obtained from a widely used dispersant in battery slurry – CMC (Carboxy methyl Cellulose) solution.