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In this paper the well-known Chauchy's inequality is applied to prediction of critical length of the straight jet in electrospinning. A critical relationship between radius r of jet and the axial distance z from nozzle is obtained for the straight jet. Critical length number and critical radius number are defined, which might be found potential applications in experiment and apparatus design.
A modified equation for charge conservation in electrospinning is suggested, and a nonlinear relation between the electric current of charged jet and the solution flow rate is obtained.
A mathematical model describing the resistance of conductive polymer is proposed, which is naturally different from that for metal conductors. An allometric scaling law between the resistance and the section area is obtained. In the derivation, He Chengtian's interpolation, which has millennia history, is applied.
Electrospinning is a simple method used in the preparation of polymer fibers, the diameter of the electrospun fibers, varying in large from micrometer to nanometer, mainly depends upon the electrical field applied. The non-linear relation between the current of charged jet and the applied voltage is an intriguing and enduring problem. An allometric scaling relation between the current and voltage...
Polyacrylonitrile(PAN) is used to study the effect of surface charge on electrospinning by adding LiCl. The theoretical analysis shows that the relationship between radius r of jet and the axial distance z from nozzle follows an allometric law in the form r∼z −0.5 in case of full surface charge, and the scaling exponent becomes larger for partly charged fibers in electrospinning.
Governing equations for one-dimensional ionic polymer–metal composites are reviewed and then cast into the framework of a variational statement. Starting from a trial-Lagrangian, a generalized functional is derived through a systematic procedure of the semi-inverse method proposed by Ji-Huan He. All field equations and boundary conditions are cast into Euler equations of the obtained functional, leading...
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