# Difference between revisions of "Controlling the Fiber Diameter during electrospinning"

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<center><math>h_t\sim\left(\frac{Q}{I}\right)^{2/3}</math></center> | <center><math>h_t\sim\left(\frac{Q}{I}\right)^{2/3}</math></center> | ||

where <math>Q</math> is the flow rate of the polymer solution and <math>I</math> is current (due to the net downward motion of the fiber, which is simultaneously whipping around in circles). Figure 1 shows a log-log plot of <math>Q/I</math> vs. <math>h_t</math>, which we would expect to have a slope of 2/3. | where <math>Q</math> is the flow rate of the polymer solution and <math>I</math> is current (due to the net downward motion of the fiber, which is simultaneously whipping around in circles). Figure 1 shows a log-log plot of <math>Q/I</math> vs. <math>h_t</math>, which we would expect to have a slope of 2/3. | ||

+ | [[Image:Electrospin1.png|thumb|right|200px|Figure 1:]] |

## Revision as of 20:51, 21 April 2009

Zach Wissner-Gross (April 21, 2009)

## Information

Controlling the fiber diameter during electrospinning

Sergey V. Fridrikh, Jian H. Yu, Michael P. Brenner, and Gregory C. Rutledge

Physical Review Letters, **2003**, 90, 144502

## Soft matter keywords

Electrospinning, surface tension, scaling

## Summary

Fridrikh et al. derive an analytical model of the forces involved in electrospinning [1]. In the process of electrospinning, a polymer fiber is created by ejecting the polymer in a solvent between two plates of opposite electric charge. When the plate voltages are high enough, electrostatic forces dominate forces due to surface tension, so that the polymer develops a very high aspect ratio (i.e., becoming a thin fiber) as it streams toward the opposing plate.

Electrospinning is further complicated by the "whipping instability," in which the electrospun fiber coils around itself. In their model, the authors are able to calculate the minimum possible fiber radius (for a thin viscous jet) before the whipping instability breaks the jet up into droplets (as in electrospraying [2]).

Their main result is that this terminal radius <math>h_t</math> scales as:

where <math>Q</math> is the flow rate of the polymer solution and <math>I</math> is current (due to the net downward motion of the fiber, which is simultaneously whipping around in circles). Figure 1 shows a log-log plot of <math>Q/I</math> vs. <math>h_t</math>, which we would expect to have a slope of 2/3.