There is a need for an efficient actuator that consumes less power and produces large displacements for microrobotic applications. The electrostatic zipper actuators have the potential to drive microrobots; however, these actuators received less attention whose dynamics is not fully understood. Through first-principles mathematical models, we describe the actuator dynamics over a broad range, three orders of magnitude of viscosity and two orders of magnitude of relative permittivity of the media. Our electrostatic zipper actuator comprises of a complaint beam electrode to deliver the generated force displacement strokes, and a set of curved electrodes to pull the beam electrode in the forward direction. The beam electrode is clamped on both sides and is reinforced with a reinforcing beam, while the curved electrode is an immovable rigid member with shape profile. In this work, we model the actuator dynamics using Galerkin and mode superposition methods, solve using Python function ODEINT for a set of initial conditions, and validate with experiment data for different actuation voltages. In this work, we report two main observations: (1) the actuator response near the vicinity of the "pull-in" instability region is sensitive to electrostatic and viscous damping forces; and (2) the high dynamic viscosity of the media increases the response time by up to one order of magnitude. Our model predicts that the actuator achieves large displacements (up to 10 microns) at low actuation voltages (up to 8 Volts) in viscus dielectric media, namely water, methanol, and air.