Sapphire fibers for use in both optical sensors and structure composites have been manufactured using the edge-defined film-fed growth (EFG) process. A thermocapillary model based on a combined Lagrangian/Eulerian method has been developed to simulate the dynamic characteristics of the EFG process, subject to the pull speed perturbations. The meniscus behavior is governed by the Young-Laplace equation subject to a specified contact condition at the trijunction point. Two models have been investigated at the trijunction point, including a conventionally adopted static model which fixes the contact angle, and a dynamic model which regulates the contact angle according to the speed and direction of the instantaneous movement of the trijunction point. It has been predicted, and observed experimentally, that the fiber diameter responds to the pull speed perturbation at the corresponding frequency, but the sensitivity of the response decays as the frequency increases. While both the static and dynamic models at trijunction points cause the crystal to vary in size in response to the external fluctuations, their effects are noticeably different, indicating that the conventional models are not adequate to yield accurate predictions in the solidification characteristics dynamically.