## 4 Discussion  
The results of this study highlight several key advancements in the design and performance of artificial muscle fibers with the incorporation of air gaps. The optimization of the air gap width ('w2') at 50 \(\upmu\)m demonstrates a significant improvement in force production compared to traditional designs without air gaps. This enhancement is achieved by balancing manufacturability and performance, ensuring that the selected gap width is practical for real-world applications. Comparative analysis with the non-gap model further underscores the advantages of the gap model.  
In this study, we have introduced a transient modeling approach to enhance the accuracy and physical validity of simulations compared to the static model used in previous works. The static simulations described in previous communications were limited by their assumption of a constant force application on a non-deformed geometry, which does not capture the dynamic interactions between forces and deformations observed in real-world conditions. Our transient model, however, accounts for the time-dependent evolution of forces and their effects on the device geometry, incorporating a feedback loop that updates forces based on the changing geometry. In particular, this approach is crucial for gapped devices, where geometry significantly influences force distribution and the performance of the fluid-structure-interaction Multiphysics module. Future work should use this simulation approach to produce more realistic results, especially for higher-resolution representative designs of the physical prototype.  
Figure 6: Longitudinal array sweep of ‘n2’ (number of devices) for gap models with a 50 \(\upmu\)m gap width (black circles) and non-gap models (empty circles).  
The force density saturation observed in the longitudinal array sweep indicates that both model types achieve higher force densities as 'n2' increases. The gap model outperforms the non-gap model for all values of 'n2'. The air gap design also improves energy efficiency by reducing material density, thereby lowering the capacitance and power consumption needed for actuation. While saturation is not achieved in this study due to computational limitations, the air gap design does improve actuation efficiency.  
The increase in force density due to the gap technique would be useful to any application that can benefit from a high ratio of force to mass, such as exoskeletal locomotion, powered armor, physical augments and prosthetics, and unmanned underwater vehicles (UUVs), which require low-profile actuation with high force production [28].  
These theoretical results must also be viewed in the context of current cutting-edge 3D printing techniques. Recent developments [29; 30; 31; 32] in 3D-printed embedded microfluidics (achieved by using Stratasys PolyJet printers in conjunction with new clearance techniques of sacrificial material) have shown reliable fabrication and successful clearing of embedded microfluidic channels down to a 400 \(\upmu\)m width and, in some cases, down to a 200 \(\upmu\)m width. When these results are compared with our own theoretical results presented herein, the apparent conclusion is that PolyJet-printed devices are only a step or two away from reaching gap widths that would make the gap technique worthwhile in enhancing force density output. Separately, new SLA printers are poised to achieve features at the scale of tens of microns. Even if negative features and embedded channels would require resolution tradeoffs, it is clear that the gap technique described herein would either already or soon will be quite useful in practical applications.