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Theoretical predictions and numerical simulations are used to determine the transition to bubble and conical vortex breakdown in low-Mach-number laminar axisymmetric variable-density swirling jets. A critical value of the swirl number $$S$$ for the onset of the bubble ( $$S^*_B$$ ) and the cone ( $$S^*_C$$ ) is determined as the jet-to-ambient density ratio $$\varLambda$$ is varied, with the temperature dependence of the gas density and viscosity appropriate to that of air. The criterion of failure of the slender quasi-cylindrical approximation predicts $$S^*_B$$ that decreases with increasing values of $$\varLambda$$ for a jet in solid-body rotation emerging sharply into a quiescent atmosphere. In addition, a new criterion for the onset of conical breakdown is derived from divergence of the initial value of the radial spreading rate of the jet occurring at $$S^*_C$$ , found to be independent of $$\varLambda$$ , in an asymptotic analysis for small distances from the inlet plane. To maintain stable flow in the unsteady numerical simulations, an effective Reynolds number $$Re_{eff}$$ , defined employing the geometric mean of the viscosity in the jet and ambient atmosphere, is fixed at $$Re_{eff}=200$$ for all $$\varLambda$$ . Similar to the theoretical predictions, numerical calculations of $$S^*_B$$ decrease monotonically as $$\varLambda$$ is increased. The critical swirl numbers for the cone, $$S^*_C$$ , are found to depend strongly on viscous effects; for $$\varLambda =1/5$$ , the low jet Reynolds number (51) at $$Re_{eff}=200$$ delays the transition to the cone, while for $$\varLambda =5$$ at $$Re_{eff}=200$$ , the large increase in kinematic viscosity in the external fluid produces a similar trend, significantly increasing $$S^*_C$$ .
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Increasing ionic conductivity within thermoplastics via commercial additives results in a dramatic decrease in fiber diameter from melt electrospinning
Polyethylene melt conductivity was increased by adding a commercial anti-static agent, which resulted in a 20× decrease in electrospun fiber diameter and formation of a significant fraction of sub-micron diameter fibers. Two polyethylene formulations and varying additive concentrations were utilized to span the parameter space of conductivity and viscosity. The key role of conductivity in determining the jet radius (which sets the upper limit on the fiber size) is discussed in the context of fluid mechanics theory and previous simulations. Parameters which affect the conversion of the liquid jet to a solid fiber and the pertinent theory are outlined. An “unconfined” experimental configuration is utilized to both avoid potential needle clogging and enable direct observation of important characteristic length scales related to the interaction of the fluid and the applied electric field. In this approach, the fluid spontaneously forms an array of cone perturbations which act as stationary “nozzles” through which the mobile fluid flows to form the jet. The experimental data and theory considerations allow for a holistic discussion of the interaction between flow rate, viscosity, conductivity, and the resultant jet and fiber size. Information about the fluid viscosity and conductivity gained by observing the electrospinning process is highlighted. Schemes for theoretically predicting the cone-jet density, cone size, and flow rate are compared to experimental results.
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- Award ID(s):
- 1635113
- PAR ID:
- 10325783
- Date Published:
- Journal Name:
- Soft Matter
- Volume:
- 17
- Issue:
- 41
- ISSN:
- 1744-683X
- Page Range / eLocation ID:
- 9264 to 9279
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1039/d1sm01101d
