Abstract
A theory was proposed to predict the process of unidirectional filling of a uniformly elongated flat cavity with a thickness, 2Y, and a width, 2Z, by a non-crystallizable thermoplastic at a constant temperature, TI, under a constant injection pressure, PI. The filled length, Λ, was related to the filling time, t, by an equation, Λ=ΛKJ(t/tK), where tK=tE/M and ΛK=(tKDINK)1/(n+1)Y. J(σ) evolved from a set of equations, J(σ)=∫σσI=0j(σI)dσI, and (j(σ))-1/n=γ(σ)+eσ∫σσI=0e-σIj(σI)dσI. In the scheme: tE=ρωY2/4κ, where ρ, ω, or κ is the density, the specific heat, or the thermal conductivity, respectively, of the cooling layer of the thermoplastic in the cavity; M=2(n+2)θ2/n where θ=(TII-TM)/(TI-TM); n or Ψ(T) is the non-Newtonian index or the fluidity, respectively, of the melt, where T specifies the temperature; TII is the temperature at which Ψ(TII)=EFF. Ψ(TI), where EFF is a constant (≤1) taken somewhat arbitrarily to be 0.5 for schematic division of the thermoplastic in the cavity into the flowing layer and the solidified layer; TM is the temperature of the wall of the cavity; DI=D0Ψ(TI)(PD/τ0)n, provided D0 or τ0 is a unit shear rate or a unit shear stress, respectively, for expression of the power law, D=εD0Ψ(T)(ετ/τ0)n, relating the shear rate of the melt, D, with the shear stress, τ, where ε=-1 for τ<0 and +1 for τ>0; PD=PI-PM, where. PM is the atmospheric pressure; NK=Nγn+2 where N=(n+2)-1 and γ=(1/2) exp (1/2); and γ(σ)≡(QM(σtK)/QK)-1/n provided that QK=2Z.2Y.ΛK/tK, where QM(t) is the flow rate through the channels preceding the cavity when the end be opened freely into the air without the cavity. If all the channels preceding the cavity are isothermal, γ(σ)≡a constant, γi, which vanishes if the melt enters from the cylinder directly into the cavity. Law of R. L. Ballman et al. of exponential decrease in speed of flow front is proven for the case where γ(σ)≡γi≤(n+1)1/(n+1), giving the time constant, B, equal to tK/n(1-n(γin+1/(n+1)n+1)1/n). Calculated fill-outs and calculated time constants agree with the experimental results of H. L. Toor et al. The present theory presupposed that the thermoplastic in the cavity can be divided into the inner layer, in which the temperature is TI, and the outer layer, in which the temperature falls down to TM following such a linear profile like that in the case of stationary conduction. The thickness of the inner layer, 2YI, was equated, by a set of assumptions, to (1-(tU/tE)1/2)
