A Treatise on the Screw Extrusion of Thermoplastics : Part I, Theory of the Screw Extrusion of Non-Newtonian Liquid

Abstract

Theories of the screw extrusion of highly viscous liquid have hitherto been limited to the extrusion of the Newtonian liquid or the Bingham plastic liquid. The present paper advances the theory of extrusion of the Non-Newtonian liquid, of which the viscosity may be represented by the power law D=ατⁿ where D is the shear rate and τ is the shearing stress. The relation of the rate of pressure flow Q_p and the pressure gradient ξ along the screw channel can be obtained by the following two equations. Q_p=K₁BhV/2, hξ=K₂(V/(αh))ⁿ where B=channel width h=channel depth V=relative velocity between barrel and screw K₁=1/(aⁿ⁺¹-bⁿ⁺¹)[n/(n+2)(aⁿ⁺²±bⁿ⁺²)±aⁿ⁺¹b+abⁿ⁺¹] K₂=(n+1/aⁿ⁺¹-bⁿ⁺¹)^1/n a=h₁/h, b=(h-h₁)/h and h₁ is the distance between stress-neutral surface and the barrel. With the aid of K₁∼a curve and K₂∼a curve, which were previously obtained through numerical calculations, one can obtain a Q_p∼ξ curve graphically by means of parameter a.