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A novel analytical model development and simulation of melt-electrospinning process is presented. Unconstrained equations of motion for the description of a discretized melt-electrospun fiber are formulated using Kane's method. The motions of the spinneret and the collector plate are also incorporated into the kinematics formulation to simulate direct writing and three-dimensional printing scenarios. Constraints describing viscoelastic joints in the system and the phenomenon of the melt-electrospun fiber adhering to the collector plate are implemented using the Udwadia Kalaba method. Rotational viscoelastic elements are introduced to mimic the dampening of the whipping motion observed in the unstable region. A novel algorithm is devised to continuously run the simulation with no limit on the total duration and phase transitions. System responses such as fiber diameter, collection size, fiber elongations, and jet speeds are monitored for changes in control parameters including applied voltage, collector distance, and flowrate. The results demonstrate close agreement with experimental observations in the literature. The jet starts relatively straight on the onset of its trajectory and develops subtle whipping motion as it advances toward the collector plate. Reduction in the amplitude of the whipping motion is observed once the free end of the fiber adhered to the collector plate.

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