Effect of water droplet in solvent sublation

Available online at www.sciencedirect.comCHINES E6 ScienceDirectC HEMICALL .ETTERSEL SEVIERChinese Chemical Letters 19 (2008) 623 626www.esever.om/ocate/ccletEffect of water droplet in solvent sublationPeng Yu Bi, Hui Ru Dong *, Nan Nan WangCollege of Science, Beijing University of Chemical Technology, Bejing 10029, ChinaReceived 5 November 2007Abstractof mass transfer, they are always neglected, but they are very important in the investigation of thermodynamic equilibrium. In thispaper, the efeet of water droplet in solvent sublation was discussed in detail, and the previous mathematical model of solventsubaltion was improved. Matlab 6.5 was used to simulate the process of water droplets, and the comparison between the previoushypothesis and the improvement in this paper showed the superiority, especially in the investigation of thermodynamic equilibrium.Moreover, the separation and concentration of the complex compound dithizone-Co(I) from aqueous phase to n-octanol by solventsublation also proved the improved mathematical model was reasonable.C 2008 Hui Ru Dong. Published by Elsevier B.V. on behalf of Chinese Chemical Society. All rights reserved.Keywonds: Solvent sublation; Water droplet; Mathematical modelThe famous mathematical model [1] of solvent sublation considered that there are two predominated transfer routesin the solvent sublation process: (1) transport within and on the surface of bubbles; (2) a diffusive transport between thephases driven by a concentration gradient. At the same time, there are also two additional processes in the solventsublation process [2]: a thin flm of water is dragged into the organic solvent phase and then returmns as water droplets.But, all of the previous mathematical models [1- 4] considered the two additional processes were minor infuence inthe dynamic process of solvent sublation. In fact, they are very important in the investigation of thermodynamicbalance [5], because the liquid -liquid interface mass transport is the only reverse process in the thermodynamicbalance.In this paper, the effect of water droplet in solvent sublation was discussed in detail, and the previous mathematicalmodel of solvent subaltion was improved. Then Matlab 6.5 was used to simulate, and the simulation results werecomparison with previous model and experimental results.1. ExperimentalDithizone, CoCl2, 1-octanol, HCl, NaOH, ethanol etc. were all of analytical grade, and all from Bejjing ChemicalFactory (China). The solvent sublation system was similar as the one mentioned in earlier report [6]. The pH ofsolution was measured with a Mettler Toledo 320-S pH meter Mettler Co, Switzerland), and UV- vis spectra of the●Coresponding author.中国煤化工E-mail address: donghr@ mail.buct.edu.cn (H.R. Dong).MHCNMHG1001-8417/$ - sce front matter ◎2008 Hui Ru Dong. Published by Elsevier B.V. on behalf of Chinese Chemical Society. All rights reserved.doi: 10.016./.cet.2008.03.010624PY. Bi et al./Chinese Chemical Letters 19 (2008) 623. -626sample solution were recorded with a U-3010 UV-vis spectrophotometer (Hitachi, Japan). The real bubble radius inthe process of solvent sublation was determined by Nicon FM10 camera (Nicon, Japan).250 mL of 2.72x 10 4 mol L I Dithizone-Co(I) solution with H3BO3-HCl buffer 10.00 mL (pH 7.68) was .poured into the sublation column, 10.00 mL 1-octanol was spread on the surface of the solution, at the same time thetimer was started. The samples of aqueous phase were taken periodically for analyzing and monitoring the process.The samples were analyzed by a UV-vis spectrophotometer at 540 nm. In the thermodynamic experiment, each pointrepresents an individual experiment.2. Solute concentration in water droplet and the improved mathematical modelIn the thermodynamic equilibrium of solvent sublation, the liquid- liquid interface mass transport (includes waterdroplet and a diffusive transport) is the only way of solute transfer from organic phase to aqueous phase. Because thecontact area between organic phase and aqueous phase is very limit, the water droplet process is the major infuence.So the effect of water droplet should be adequately considered in the thermodynamic equilibrium. In fact, thehypostasis of water droplet effect is also the difusive transport of solute. In the formation process of water droplet,there is a mass transfer process between organic phase and water droplets. The sublate concentation in water dropletsat t, the formation time of water droplet, can be described as followed by:v.dC= -SgK(1)dd(c- s)In Eq. (1),‘一is represent the process of the sublate transfer from water droplets to organic phase; V is the volumeof water droplets just returming to the aqueous phase; c is the sublate concentration in water droplets at t; Sa is theaverage area of mass transfer between organic phase and water droplet in the increasing process of a water droplet; K1is aqueous phase mass transfer coefficient; Co is the sublate concentration in organic phase; Kow is the sublate partitionconstant between the organic phase and aqueous phase.Eq. (1) can be easily integrated by c and t to Eq. (2), where the initial condition is C= Cw at 1=0, and the finalcondition isC= Cs att= tu Cw is the sublate concentration in aqueous phase; Ca is the sublate concentration in waterdroplets just returming to the aqueous phase, ts is the lifetime of water droplets.Cs =e-(S8/VJluCw + (1 -(SsK/Va)4)(2)! KowIn the whole solvent sublation process, there exists an overall sublate mass balance between the aqueous phase andorganic phase.VwCwi- VwCwC。=-(3)V。In Eq. (3), Cwi is the aqueous initial sublate concentration, Vw is the volume of aqueous phase; V。is the volume oforganic phase. On substituting the Eq. (3) into the Eq. (2):Cd=e-(SsK/J)Ja.Vw-(1 -5s/1/1)[)Cw +(1 -6sK/NbH)CwiVw(4)V.KowVoKowIn order to calculate the sublate concentration in water droplets just retuming to the aqueous phase, to, Vs and Ssshould be fixed on. In the real process of solvent sublation, the, formation and rotrminewater droplets can beconsidered as dynamic equilibrium, so ta can be obtained by:中国煤化工YHCNMHGVs= isQsdAj(5)PY Bi et al./Chinese Chemical Lelters 19 (2008) 623 626625c-7.75x10'md 必-m0.03xm.st.-800s-0.943an'K.-500mLA/昌4 -01196m2- 6anL.sA2B0t-之Fig. 1. Curve of Cs vs C. (A)The sublate concentration of this paper in water droplets the sublate concentration in water droplets. (B)The sublateconcentration of the previous papers [3.4] in water droplets the sublate concenration in water droplets. In this work, the sublate concentration inwaler droplets decreases with the poes of solvent sublatin; in the previous work, the sublate concentration in water droplels was supposed inequilibrium with organic phasewater droplets return into the aqueous phase. It is obvious that the previous equilibrium bhypothesis (B)disobeyed the real state (A).In Eq. (5), Q。is the airflow rate at 1 atm; a is the bubble radius crosing the water- organic iterface. On substitutingthe Eq. (5) into the Eq. (4), we obtain:Ca=:(aSxK1/3Q4).Vw_(1 -e-(asK/3Q4N)Cw +(1 -(a/3/.4)CwiVw(6)VKow! V。KowBecause the swinging water droplets do not have regular shape, Ss should be the average area of mass transferbetween organic phase and water droplet in the increasing process of a water droplet.According to Eq. (6), the sublate concentration in the water droplets was simulated using Matlab 6.5, and comparedwith previous work [3] (Fig. 1). It is proved that the sublate concentration in water droplets cannot be in equilibriumwith organic phase when water droplets return into the aqueous phase. The simulation result proved that the sublateconcentration in water droplets cannot be in equilibrium with organic phase, when water droplets return into theaqueous phase. So Q2((3/a)d)CJKow in previous model [3,4] should be replaced by Qe((3/a)d)Ca, and the improvedmodel can be described as followed by:v.LCc-Q。(x+司)c.- mKx(C. )+f{[-aSsK:/3Q,d4)VwCiVw )VoKow(1 -(xs/3,0d1)|Ccw + (1 - e(as/3.c)! VoKow了(7)All of the parameters in the improved mathematical model were same as previous model [3,4], except Ss, theaverage area of mass transfer between organic phase and water droplet in the increasing process of a water droplet.3. Comparison of theory and experiment中国煤化工Under the certain conditions of kinetics, the equilibrium time ofMYH_nt the thermodynamicequilibrium. When the system achieves the equilibrium of solvent. CNM H Graqucous phase is toolow to be determined by UV- -vis spectrophotometer exactly. So the absorbance of organic phase at dfferent fAotationtime were determined for obtaining the equilibrium time of solvent subltion, and the experimental resuts were shown626P.Y. Bi et al./Chinese Chemical Letters 19 (2008) 623- 6260.400-0.300-。0.200-0.100-Time(min)Fig. 2. Comparison of the experimental results and simulation resuts in solvent sublation of Dithizone C(I). The line represents the theoreticalresult (mathematical simulation), and the red points represents the experimental resuts. Cuw=2.72x 10 4 molL-; K。 = 0.01 cm;Q.=0.67mLs ;K=0.001 cms~ ; Kow= 30; Vw =250 mL; Vo= 10 mL; re = 3.2 cm; dh = 0.0001 cm; a= 0.1 cm; Sa= 1.000 cm.in Fig. 2. The equilibrium time obtained by experiment is identical with the simulation results, which shows that theimproved mathematical model can well describe the thermodynamic equilibrium of solvent sublation.4. ConclusionThe solute concentration of water droplet in solvent sublation was exactly described by Eq. (6). Compared with theprevious hypothesis, the new description was better than the previous. Then the improved mathematical model ofsolvent sublation was taken. The results of the mathematical simulation using experimental data of Dithizone ColI),are quite satisfactory, especially in the thermodynamic equllbrium.Reference[I] K.T Valsarnj, LJ. Thibodeaux. Sep. Sci. Technol. 26 (1991) 37.[2] KT Valsaraj, LJ. Thibodeaux, Sep. Sci. Technol. 26 (1991) 367.[3] YJ. Lu, X.H. Zhu, Talanta 57 (2002) 891.[4] YJ. Lu, J.H. Liu, Y. Xiong X.H. Zhu, J. Colloid Interface Sci. 263 (2003) 261.[5] YJ. Lu, X.H. Zhu, Prog, Chem. 13 (2001) 441.[6] H.R. Dong, P.Y. Bi, S.H. Wang, Anal. Lett. 38 (2005) 257.中国煤化工MYHCNMHG