高分子溶融体のバラス効果について

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Barus effect means a phenomenon in which the diameter of fluid becomes larger than the diameter of a nozzle at its exit when the fluid is extruded through the nozzle. Roughly there are 4 causes of this Barus effect. The first is the elastic flow-in effect, the second is normal stress produced by shear deformation and the third is the molecular orientation, in which the molecules, which have been oriented in the flow direction in the nozzle become non-oriented as they stop receiving shear stress. The first and third causes must be treated mathematically in the same manner as in the case of the second cause. The method by Metzner et al. which seeks to obtain normal stress that is the cause of Barus effect from the measured value of swelling, is effective. However, even if the swelling index is the same, there are substances, whose behavior during the swelling process differ. So it is necessary to know more about the profile change of swelling phenomenon. In view of this, velocity distribution and swelling index were determined kinematically and dynamically. In applying the equation of motion, the model of linear viscoelasticity was used as the rheological equation of state. And the concept of relaxation distance is introduced in place of relaxation time. At present the concept of relaxation time was not applied to the polymer melt becaure of the complexity of mathematical treatment. So simple relaxation function is assumed. P_<ij>=∫^z_<-∞>φ*e_<ij>dx_i φ_0 exp (-z/λ) P_<ij>:stress tensor. *e_<ij>:rate of shear tensor φ,φ_0:relaxation function, x_i,z:coordinate. λ:relaxation distance. First the relation between the swelling index and the velocity profile is calculated. It is assumed that the velocity profile at the nozzle exit has been fully developed and it conforms to the power law. And the velocity profile in the extrudate becomes as follows: w=a(ζ)+b(ζ)S^<n+1>+c(ζ)s^<2n+2> w:velocity in the axial direction n:power ζs: dimentionless co-ordinate in the axial and radial direction respectively. Here the unknown functions a(ζ),b(ζ) and c(ζ) are determined by the law of conservation of mass and consideration of stream line. And the result is a(ζ)=A δ^<-2>, b(ζ)=-2Kδ^<-n-3>, c(ζ)=Kδ^<-2n-4>, δ:swelling index. A,K: function of n alone. Next, it is necessary to obtain the relation between the swelling index and the distance of axial direction. The equation of motion of the axial direction is applied to the axis of the flow. In the extrudate the change of hydrostatic pressure is neglected. And the integral limit of the rheological equation is devided into two at the exit of the nozzle. In case the relaxation distance is large, the relation between the swelling index and the axial distance is obtained as follow; δ=[E+{G+F(1-exp(-Rζ/λ))}]^<-1/2> E.F.G: constant determined from material and flow condition. R: radius of nozzle. It may follow from this equation, (1) that swelling occurs when the material has the property of relaxation, and (2) that swelling index becomes larger according to the increase of relaxation.
社団法人日本材料学会の論文
1967-07-15

高分子溶融体のバラス効果について

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