Theory Mathematical analysis of intermittent dual countercurrent chromatography has been proposed as follows: 1) General Model Retention time of the solute peak for intermittent dual CCC is mathematically analyzed. The method elutes each phase alternately through the opposite ends of the separation column at a given interval and flow rate while the sample solution is charged at the middle portion of the column. At the hydrodynamic equilibrium state established in each elution mode, the separation channel with a cross sectional area Ac is divided into the area occupied by the lower phase, AL, and the upper phase, AU. Here we assume that the two phases are uniformly distributed at a given volume ratio throughout the channel. The lower phase is introduced from the left terminal at a flow rate of FL ml/min and the upper phase from the right terminal at a flow rate of FU ml/min intermittently at given intervals, ti, L and ti, U, respectively. Then, the analysis of the solute peak motion in the channel is divided into two parts, i.e., for the forward (from left to right) elution and the backward (right to left) elution as follows: For lower phase elution, the lower mobile phase is introduced from the left side of the channel at FLml/min flows through the channel at a linear velocity of uL cm/min, uL= (FL/AC)(AU,L+AL,L)/AL,L = (FL/AC)(BL+1) (1) where BL = AU,L/AL,L (volume ratio of two phases when lower phase mobile). Then the solute in the lower phase moves forward through the channel at a rate of uX,L cm/min according to its partition coefficient, K, and the volume ratio of the two phases in the channel, uX,L = (FL/AC)(BL+1)/(1+K BL) (2) where K = concentration of solute in the upper phase divided by that in the lower phase. Similarly in the backward elution, the upper mobile phase introduced from the right end of the channel at FU ml/min flows through the channel at a linear velocity of uU cm/min, uU = (FU/AC)(AU,U+AL,U)/AU,U = (FU/AC)(1+1/BU) (3) where BU = AU,U/AL,U (volume ratio of two phases when upper phase mobile) and the solute in the mobile upper phase moves backward through the channel at a rate of uX,U cm/min according to K (concentration of solute in the upper phase divided by that in the lower phase) and the two-phase volume ratio in the channel, or uX,U = (FU/AC)(1+1/BU)KBU/(1+KBU) = (FU/AC)K(1+BU)/(1+KBU) (4). Then, from Eq (2) and (4) the average linear velocity (uX,i) of the solute peak is given by uX,i = (uX,L ti,L-uX,U ti,U)/(ti,L + ti,U) = (FL/A) ti,L (BL+1)/(1+KBL) - (FU/A) ti,U K(1+BU)/(1+KBU) /(ti,L + ti,U) (5) where ti, L and ti, U indicate the unit programmed time for forward and backward elution, respectively. Therefore, the retention time (tR) of solute at the end of the unit programmed dual elution is computed from the following equation, tR = L/uX,i =0.5 Vc(ti,L + ti,U)/FL ti,L (1+BL)/(1+KBL) - FU ti,U K(1+BU)/(1+KBU) (6) where L is a half length of the channel and Vc, the total capacity of the channel where Vc = 2LAc. When uX,L>uX,U or uX,i>0, the solute peak moves forward and is eluted from the right terminal of the channel, and when uX,L
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