Concentration Gradient in a Continuous Countercurrent Extraction Column with Longitudinal Back-Mixing

Abstract

The following relations have been derived by the authors for the variation of concentration in a continuous countercurrent extraction column in which there is longitudinal back-mixing of the continuous phase, on the assumption that the diffusivity of the back-mixing and liquid velocity are constant and the solutions are dilute : When 1+β>0 Cc-α/Cc₀-α = (1+√1+β)e²ᵞ√¹⁺ᵝ⁽¹⁻ˣ/ᴸ⁾-(1-√1+β)

2√1+βeᵞ⁽¹⁺√¹⁺ᵝ⁾⁽¹⁻ˣ/ᴸ⁾ and when 1+β<0 Cc-α/Cc₀-α = i√1+β cos[γi√1+β(1-x/L)]+sin[γi√1+β(1-x/L)]

i√1+βeᵞ⁽¹⁻ˣ/ᴸ⁾ where : α = C*c₀-(mFc/Fd)Cc₀

1-(mFc/Fd), β = 2MN/(M+NQ)², γ = M+NQ, M = Luc/2EcHc, N = Kcα′(1- mFc/Fd)(LHc/uc), Q = 1/2 1/(Fd/mFc)-1. The applicability of these equations is discussed, and the performance of an extraction column is analyzed.