A Novel Theoretical Model Development and Simulation of Melt‐Electrospinning Using Kane's and Udwadia–Kalaba Methods

Abstract

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.

Mesoscopic Simulation of Centrifugal Melt Electrospinning of PPESK

“…Generally, a higher degree of entanglement among molecular chains results in poorer chain orientation during spinning, which consequently leads to larger fiber diameters. [ 45,46 ] Therefore, by simulating PPESK with different chain lengths, the influence of different molecular chain lengths on fiber diameter and yield was analyzed to study the unwinding of the PPESK molecular chain.…”

“…The fiber diameter can indirectly reflect the entanglement of the molecular chain. Generally, a higher degree of entanglement among molecular chains results in poorer chain orientation during spinning, which consequently leads to larger fiber diameters [45,46]. Therefore, by simulating PPESK with different chain lengths, the influence of different molecular chain lengths on fiber diameter and yield was analyzed to study the unwinding of the PPESK molecular chain.By simulating the spinning process of PPESK with different molecular chain lengths, the diameter of fibers falling to the receiving plate was calculated.…”

Adaptive Robust Control for Uncertain Underactuated Mechanical Systems

“…Based on the Udwadia-Kalaba (UK) equation, [23,24] the binding force F c (h, ḣ, Λ, t) of the UMS is obtained as…”

“…Based on the Udwadia–Kalaba (UK) equation, [ 23,24 ] the binding force $${F^\text{c}(h, \dot{h}, \Lambda , t)}$$ of the UMS is obtained as $$$$\begin{align} F^\text{c}(h, \dot{h}, \Lambda , t)= & M^{1 / 2}(h, \Lambda , t){\left(A(h, t) M^{-1 / 2}(h, \Lambda , t)\right)}^{+}{\left[b(h, t)+A(h, t) M^{-1}(h, \Lambda , t)\right.} \nonumber \\ & \times (C(h, \dot{h}, \Lambda , t) \dot{h}+G(h, \Lambda , t))+F(h, \dot{h}, \Lambda , t)] \end{align}$$$$where the constraints force $$F^\text{c}$$ to satisfy both d'Alembert and Gauss' minimum principles.…”

A study on theoretical predictive model and experimental findings of melt‐electrospinning process

“…It builds upon a prior work published by the same authors in which a theoretical predictive model was proposed for MES. 25 The relationships between the input and output parameters are experimentally investigated under the current work to draw a comparison to this theoretical model. In addition, the experimental data is also used to construct predictive regression models to provide a means for equivalent comparisons and objectively assess the predictive performance of the theoretical model.…”