Melt blowing: General equation development and experimental verification

Abstract

A model has been developed for steady polymer melt blowing. This model includes the dominant effect that the forwarding air has upon the process. Inertial, gravitational and heat transfer effects are also included. The model equations are solved numerically with both Newtonian and viscoelastic (Phan-Thien and Tanner) constitutive equations. The predicted results compare favorably with actual experimental data.

Polysulfone nanofibers prepared by electrospinning and gas/jet-electrospinning

“…Based on this theory, Shambaugh [17] analyzed the mechanics of the deformation of the filament flow during drawing by gas jet as shown in Fig. 3(b).…”

Modeling the melt blowing of viscoelastic materials

“…For the PTT model, these quantities are governed (Uyttendaele and Shambaugh, 1990) by t zz Á exp½eDeðt zz þ2t rr Þ þDe @t zz @t þ v @t zz @z À2t zz @v @z…”

“…We follow Kase and Matsuo (1965) who used g ¼ 0:42 and m¼0.334 for parallel air flow along the spinline in melt spinning. Uyttendaele and Shambaugh (1990) have also adopted the same set of parameters in modeling melt blowing. The relative Reynolds number of the air flow is Re rel ¼ r air v rel D=m air , where r air is the air density, m air is the air viscosity, D is the fiber diameter, and v rel ¼ v air Àv is the relative velocity of the air with respect to the fiber at a given z-location.…”

“…To model the spatial variation of the shear stress on the fiber, we use the following dimensional expression (Uyttendaele and Shambaugh, 1990):…”

“…Tan et al (2010) also presented a mathematical model that was used to help understand the behavior of the mean fiber diameter. The model is based on the slender-jet (onedimensional) approximation, and is similar to models used by others to study melt blowing (Uyttendaele and Shambaugh, 1990;Zachara and Lewandowski, 2008;Jarecki and Ziabicki, 2008;Jarecki and Lewandowski, 2009;Sinha-Ray et al, 2010;Yarin et al, 2010) and the related process of melt spinning Denn, 1976, 1977;Ziabicki, 1961;Ziabicki and Kedzierska, 1960a,b). The model of Tan et al (2010) (UCM) and Phan-Thien/Tanner (PTT) constitutive models, assumes a constant shear stress acting on the fiber surface, and neglects heat transfer effects.…”