The interface between protein solute and aqueous solvent exhibits complex geometries, and can undergo conformational changes by combined influences from electrostatic force, surface tension, and hydrodynamic force. To understand the role of solvent Stokes flow in this process, we develop a Dynamic Implicit Solvent Model (DISM). Based on this model, we first analytically study the linear stability of a cylindrical solute-solvent interface, where the asymptotic dispersion relation reveals a power law. Moreover, we develop a computational method to simulate the solvent Stokes flow and the interface motion. The key components of our fluid solver are a virtual node method, a pressure Poisson equation, a specially designed boundary condition, the Schur complement method and the least square technique. Level set method is used for the interface motion. We present some 3D numerical results to demonstrate the accuracy and convergence of our method, and show interesting dynamics of protein conformational change.