Diffusion of Heptane in Polyethylene Vinyl Acetate: Modelisation and Experimentation

Transcription

1 IOSR Journal of Appled hemsry (IOSR-JA) e-issn: Volume 7, Issue 6 Ver. I. (Jun. 4), PP 8-86 Dffuson of Hepane n Polyehylene Vnyl Aceae: odelsaon and Expermenaon Rachd Aman *, Façal oubarak, hammed El Koual, ohammed Talb, Abdlhak El Brouz, SamaYousf, ona Bouamran / Research Laboraory of Analycal hemsry and Physcal hemsry of aerals Scences Faculy Ben 'sk, orocco / Research Laboraory of Physcal hemsry and Elecrochemsry Faculy of Scence and Technology ohammeda. orocco Absrac: Ths arcle descrbes he mass ransfer n food packagng, where he plasc s brough no conac wh food, ceran ransfers mplemened accordng o a complex process. The mehod we used n hs work, we coupled modelng wh expermenaon n order o undersand he packagng plasc ouch nerface ransfers / food. The numercal model akes no accoun he expermenal sudy. The knecs of dffuson ransfer and dffusvy of lqud smulaor were deermned. The analycal and numercal model has been developed whch ams o gve beer nformaon on he concenraon of lqud smulaor nsde he package (PEVA) and smulae a few hours ransfers lasng n realy several monhs. Keywords: Packagng maeral, Dffuson, odelsaon, Fne dfference mehod. I. Inroducon Food conac maerals play an essenal role n he food conservaon and proecon. They have also ncessan markeng funcon and have o be recoverable. When he polymer s n conac wh he packagng, some ransfers ake place, hs conac nfluence on packaged producs as well as on packagng maerals. The goal of hs arcle s o undersand hese ransfers, by couplng modelng wh expermenaon and onsruc a mahemacal model and a numercal model able o descrbe he dffuson process. II. aerals and mehods The sudy he lqud dffuson no a polymer smulaor s based on he followng smplfyng assumpons [3]: The dsrbuon s n accordance wh fck s laws. The dffuson coeffcen s ndependen of concenraon. The dffuson n he sphere s radale. The polymer was sphercal n shape wh a consan radus, as he amoun of ehanol s very small. The chemcal does no evaporae on surface. A. Analycal processng[] [] [5] When he dffuson s radal, Fck s second law expressng he dffuson equaon under ransen condons s n he general form... D r. ( eq) r r r Where s he concenraon a me and a a dsance r from he cener of he sphere. When he dffusvy D s consan, he dffuson equaon akes he form of: D.. ( eq) r r r Analycal soluons can be obaned when he dffusvy s consan. Problems wh a concenraon-dependen dffusvy need numercal mehods. By pung: U. r( eq3) Equaon () becomes: U U D. ( eq4) r 8 Page

2 Dffuson of Hepane n Polyehylene Vnyl Aceae: odelsaon and Expermenaon Equaon (4) s smlar o he equaon obaned for dffuson n one dmenson hrough he plane shee. ase sudy: The nal dsrbuon n he sphere s consan:. In hs case: Inal Boundary r R U (eq5) r U r R U R ( eq 6) The soluon of he equaon of dffuson becomes: n r, R n r n² ²..sn exp Deq7. r n n R R² Ths soluon n hs form canno be used for he cener of he sphere (r ). As he lm of, when Equaon (7) for he cener of he sphere s reduced o: r,. n n² ² R² n.exp D eq8 B- Analycal model The oal amoun of dffusng subsance gong no or leavng he sphere s gven by negrang Fck s frs law accordng o me. By consderng: And: We can oban: 6 n..exp D ( eq) n R Anoher expresson of he soluon of he equaon of dffuson n he sphere (equaon 5) s gven by: r, R n R r n R r. erfc erfc eq r ( D) D The knecs for he maer ranspored s: 6 D nr D. erfc 3 ( eq) R D R ase of shor mes: Equaon (8) s very useful for shor mes because can be reduced o: 6 D R sn x x n 6 4 R 3 ( eq3) 3. D. r x rr. d( eq9) - Numercal model - Fne dfference mehod-[4] [5] Analycal soluons can be obaned when he dffusvy s consan. Problems wh a concenraondependen dffusvy need numercal mehods. In hs case, he problem mus be solved by usng he numercal Fne dfference mehod. ase sudy: The amoun of he remanng ehanol whn he sphere. The prncple of he mehod s as follows: he sphere s dvded no N sphercal membranes of consan hckness r and he maer balance s evaluaed whn each membrane durng he ncremen of me. 83 Page

3 Dffuson of Hepane n Polyehylene Vnyl Aceae: odelsaon and Expermenaon The amoun of chemcal locaed n he sphere a me s obaned by negrang wh respec o space he concenraon of he chemcal a hs me: R 4 r. r,. dr( eq4) Ths expresson can be rewren usng fne dfference mehod r. n n n n n. n ( eq ) D- Expermenal procedure The maeral used s polyehylene vnyl aceae (also known as PEVA) s he copolymer of ehylene and vnyl aceae. And our produc smulaor used s hepane or n-hepane s he sragh-chan alkane wh he chemcal formula H 3 (H ) 5 H 3 or 7H6 and hs densy s:.6795 g ml. Hepane s a colourless lqud and odor s perolc. onacng: The conacng sample of polyehylene vnyl aceae s carred ou wh hepane a 5. Durng he conac, we measured he specfc mass of he sphere each me o sudy he evoluon of he mass sphere. III. Resuls And Dscussons The percenage of hepane mass varaon nsde our plasc sphere (fg.) s gven by he followng equaon: m m m ( eq6) m Effec of The dffuson coeffcen s gven by hs relaon: En cm²/s:. R D 6 6 ( eq7) D 4,4. -6 cm²/s Fgure - shows he varaon of he amoun of hepane n he PEVA wh me, we noe ha he hepane n polyehylene vnyl aceae mass ncreases wh he conac me. Unl equlbrum reached. Fgure 3- show he amoun of hepane n he maeral accordng o smulaon me for each soluon : analycal soluon, numercal soluon and experence. We noce from hs fgure ha hree soluons gve he same varaon n he amoun of hepane absorbed as a funcon of me. So we concluded ha he model s valdaed. Fgure 4 - show he profle of he concenraon of hepane afer every mn. a- The hepane concenraon whn he sphere s low, n conras o surfaces. b- Ths concenraon profle s amed o gve good nformaon on hepane nsde PEVA, s for each pon n our sample we can easly deermne s concenraon. IV. Fgures Fg.- Schema of he crcular cross secon of a sphere of radus R. 84 Page

4 asse m en % Dffuson of Hepane n Polyehylene Vnyl Aceae: odelsaon and Expermenaon emps (mn) Fg.- Varaon of he amoun of hepane n he PEVA Seres Le profl de la dffuson d hepane dans le PEVA 3 x -3 Hsore de la masse dans le maérau.5.5 Soluon numérque Expérence Soluon analyque Temps de smulaon (h) Fg.3- The amoun of hepane n he maeral as a funcon of me for he smulaon of hree soluons. Fg.4- The profle of he concenraon of hepane afer every mn 85 Page

5 Dffuson of Hepane n Polyehylene Vnyl Aceae: odelsaon and Expermenaon V. oncluson Through hs work, we conrbued o he sudy and developmen of new mehods couplng expermens wh modelng o undersand he behavor of plasc packagng n conac wh he food producs. The sudy was conduced by weghed followng he evoluon of he mass ransferred over me. The polyehylene vnyl aceae conac wh hepane (consdered smulang agen) a a emperaure of 5 showed ha he amoun ofhepane n he polymer ncreases wh me. odel valdaon was made by comparng he heorecal resuls wh expermenal resuls. The resulng profle gves beer nformaon on concenraons of hepane nsde he package polyehylene vnyl aceae. Ths model we allow a few hours o smulae mass ransfer n realy lasng several monhs. References []. Tocc, E.; Gugluzza, A.; De Lorenzo, L.; acchone,.; De Luca, G.; Drol, E. J. embr. Sc. 8, 33, []. Hölck, O.; Heuchel,.; Böhnng,.; Hofmann, D. J. Polym. Sc., Par B: Polym. Phys. 8, 46, 59-7.[3]: Vergnaud, «Dffuson of a chemcal hrough he lqud locaed n a polymer: odelng and expermens», polymer esng 3 (994) [3]. ark Geoghegan, 3, «Weng a polymer surfaces and nerfaces» Prog. Polym. Sc. 8,6 3 [4]. ROSA I.D., VERGNAUD J.., 997, «Transfer of conamnan no sold from a bole made of blayer polymers wh a recycled and a vrgn layer - effec of he hcknesses of hese polymer layers», Journal of Appled Polymer Scence, Vol. 66, Page