Mathematical Model of Gas Exchange for Modified Atmosphere Packaging Containing Pak-choi

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1 Prceedngs f the 17th IAPRI Wrld Cnference n Packagng Mathematcal Mdel f Gas Exchange fr Mdfed Atmsphere Packagng Cntanng Pak-ch CAO Fe Dept. f Prntng Engneerng Tanjn Vcatnal Insttute Tanjn, P. R. Chna Emal: cafe198@16.cm Abstract: Respratn became the dmnant aspects f metablsm after vegetables were harvested. The man factrs affectng respratn are temperature and gas cncentratn f the strage envrnment. It s a majr challenge that hw t chce a plastc flm wth apprprate permeablty ceffcent fr specfc varetes vegetables n specfc temperature. Therefre, t s the key f mdfed atmsphere packagng technlgy f vegetables that t establsh mathematcal mdel f gas exchange fr mdfed atmsphere packagng (MAP. Based n the dynamc equlbrum thery f MAP, the varatn laws f respratn rates were studed wth the dynamc changes f O and CO cncentratn wthn packages at 1 and respectvely. The ptmal smulated functn expressn was establshed. The expermental data were analyzed wth SPSS fr wndws statstcal sftware. The mathematcal mdel f gas exchange wthn clse packages was develped when the mdfed atmsphere packagng fr Pak-ch was desgned. The theretcal bass fr gettng a rght way t chse packagng materals fr MAP and predctng the gas mass cncentratns nsde the packages were prvded.the crrectness f mdel was verfed by MAP experments cntanng Pak-ch. Keywrds: Pak-ch; mdfed atmsphere packagng; respratn rate; gas exchange; mathematcal mdel 1. Intrductn The Pak-ch s a knd f ppular vegetables.it has nutrtnal and cmmercal mprtance n terms f t s specal functnal cmpstn cntent and cnsumptn demand. Hwever,t s very lable t splage under mprper strage cndtns.sme f the mprtant factrs whch nfluence the strage lfe and qualty deterratn f Pak-ch ncludng the lss f water and hgh respratn and metablsm. A mdfed atmsphere packagng(map n cmbnatn wth lw temperature strage s a prmsng and nexpensve way t mprve the shelf lfe f vegetables [1.MAP may create an atmsphere rcher n CO and prer n O whch can reduce the respratn rates and physlgcal changes f fresh prduce [. LDPE, PP flm are the mst wdely used MAP packagng materals, but the permeablty parameters f the same knds f flm s vared based n the flm thckness and the strage temperature. Hw t chse the plastc flm f apprprate permeablty ceffcent fr specfc varetes f vegetables at a partcular temperature s a majr prblem placed n frnt f peple.in realty, the selectns f flm s type and thckness were ften based n the experence and estmatn f wrkers,t wll need a lng expermental perd, hgh csts and the effectn f packng s nt necessarly deal. Therefre, the develpment and establshment f mathematcal mdel f gas exchange wthn clse packages s the key t MAP technlgy. In ths paper,based n the dynamc equlbrum thery f MAP, the varatn laws f respratn rates were studed wth the dynamc changes f O and CO cncentratn wthn packages at 1 and respectvely.the mathematcal mdel f gas exchange wthn clse packages was develped,t wll be helpful n predctng tempral changes f gas cncentratns and ptmzng the desgn f MAP systems.. Materals and methds.1. Fresh prduce fr experment The Pak-ch were prvded by a peasant husehld vegetables farmland n the suburb f Tanjn. Sngle ne has abut 1 slces leaves,request that the Pak-ch were harvested at 4: AM-: AM, havng n yellw leaf and dd nt sak n water, havng n any mrbd harm,havng n bvus mechancal hurts, the clr and luster were fresh... Determnatn f the vlume f vegetables The fresh Pak-ch was put nt a wde muth brwn glass bttle f 33ml sngly, and 1ml water were njected nt the bttle n advance. At the same tme the fresh Pak-ch shuld be wrapped tghtly usng preservatve flm n rder t avd the nfluence f water n the vegetables. The level f water wll be rased, ths part f the vlume f water was measured by a graduated cylnder f 1ml, and the sum f several measurment was the vlume f vegetables [3..3. The experment f the effectns f gas cncentratns n the respratn rates f Pak-ch The fresh vegetables fr experment were dvded nt grup A and grup B. Grup A: 1 cndtn, the Pak-ch whch average weght f 19.g, and vlume ScRes

2 Prceedngs f the 17th IAPRI Wrld Cnference n Packagng f 43ml was placed n a wde muth brwn glass bttle f 33ml, and sealed wth a rubber stpper that has a hle whch aperture s 3mm, and t was sealed by a slcne nsle whch dameter s 8mm. Grup B: cndtn, the Pak-ch whch average weght f 188. g and vlume f 38ml was placed n the same bttle. Fnally, bttles f grup A and grup B were placed n a temperature humdty chamber.the O, CO gas cncentratns were measured at regular ntervals wth a headspace gas analyser CheckMate99 frm PBI Dansensr,Denmark(Fg.1. In grup A and grup B, O cncentratn decreased nn-lnearly wth the grwth f the prcessng tme, but CO cncentratn ncreased nn-lnearly n cntrast, and the change degree at s larger than 1. The fttng curves prcessed usng SPSS fr Wndws sftware f O, CO cncentratns changed wth tme are shwn n Fg. and Fg.3. [O(% t(h [CO(% Fg.1.The CheckMate 99 nstrument Each measurment repeated three tmes, and calculated the average value. Because the cntaners wth dfferent gas vlume and temperature, the duratn f the prcess was dfferent. The data were prcessed usng SPSS fr Wndws sftware, and the fttng curve equatn f [O = f1(t,[co = f(t were abtaned [4[. Respratn rates were calculated by Eqs(1 and Eqs ( [6. [ O [ O ( V VV RO 1 W t (1 ([ CO [ CO ( V VV RCO 1 W t ( Where RO s the vegetable O cnsumptn (ml kg -1 h -1,RCO s the vegetable CO prductn (ml kg -1 h -1, [O O, [CO O are gas mass cncentratns (partal pressures f O and CO n ar respectvely (%,[O,[CO are gas mass cncentratns (partal pressures f O and CO wthn the package respectvely after sealed t hurs(%, V s the vlume f bttle(ml, Vv s the vlume f vegetables (ml, W s the weght f vegetables (kg, t s the clsed tme (h. 3. Results and Dscussn 3.1. The establshment f mathematcal mdel f gas cncentratns as a functn f tme n clsed system t(h Fg.. O, CO cncentratns as a functn f tme (Grup A ο-expermental data, - fttng curve The apprxmatn functns were cnstructed by prcessng the expermental data wth Spss fr wndws statstcal sftware t express the general trends and characterstcs f sample data. The regressn equatns f each ftted curve are gven n Table 1. The results shwed: the varatn laws f O cncentratns changed wth tme can be ftted by a lgarthmc mdel, the [O(% [CO(% t(h t(h Fg.3. O, CO cncentratns as a functn f tme (Grup B ο-expermental data, - fttng curve ScRes

3 Prceedngs f the 17th IAPRI Wrld Cnference n Packagng Table 1. The equatn f O, CO cncentratns (% as a functn f tme t (h O Cncentratn CO Cncentratn Grup (% (% [O A =1.1e -.73t [CO =.+.17t-.1t t 3 (r =.999 (r =.998 [O B =1.1e -.13t [CO =.+.8t-.4t t 3 (r =.999 (r =.996 r:related ceffcent varatn laws f CO cncentratns changed wth tme can be ftted by a cubc plynmal mdel. The least square methd was used n Curve fttng, that s t btan the mdel parameters by cntrastng the mnmal mean squared devatn (MSD f measured value wth fttng value,and then t btan the ptmum functnal equatn [ The establshment f mathematcal mdel f respratn rates as a functn f O cncentratns The O cncentratns are the dmnant factrs f respratn rate f vegetables n strage cndtns. The respratn rates RO, RCO at dfferent tme can be calculated wth dervatng the equatns whch were getted frm slvng the rgressn equatns n Table 1 nt Eqs (1 and ( respectvly. The fttng curves prcessed usng SPSS fr Wndws sftware f respratn rates RO, RCO changed wth O cncentratns are shwn n Fg.4 and Fg.. RO(ml/kg.h RCO(ml/kg.h [O(% RO(ml/kg.h [O(% RCO(ml/kg.h [O(% Fg..RO, RCO as a functn f O cncentratns (Grup B ο-expermental data, - fttng curve Table. The equatn f RO RCO as a functn f O cncentratn Grup RO =f([o RCO =f([o A B RO =-.1+1.[O RCO = [O +.16[O (r =.998 (r =.999 RO = [O +.3[O RCO = [O +.9[O (r =.999 (r =.998 The expermental data were prcessed wth Spss fr wndws statstcal sftware. The results shwed: the respratn rates RO, RCO ncreased wth the grwth f O cncentratns n bth grup A and grup B. In grup A,the varatn laws f respratn rates RO changed wth O cncentratns can be ftted by a lnear mdel, and the varatn laws f respratn rates RCO changed wth O cncentratns can be ftted by a quadratc mdel. In grup B, the varatn laws f respratn rates RO, RCO changed wth O cncentratns can be ftted by a quadratc mdel. The regressn equatns f each ftted curve are gven n Table [O(% Fg.4. RO, RCO as a functn f O cncentratns (Grup A ο-expermental data, - fttng curve 3.4. The establshment f mathematcal mdel f gas exchange fr MAP cntanng Pak-ch The gas exchange n MAP systems can be seen as a dynamc prcess.the gas cncentratns nsde the package are determned by tw man prcesses: O cnsumptn and CO evlutn caused by prduce respratn and permeatn f gases thrugh the plastc flm ScRes 4

4 Prceedngs f the 17th IAPRI Wrld Cnference n Packagng The prcess f gas dffusn thrugh the flm was determned by Fck law. If the package s placed n ar, the transent varatns f the cncentratns f O and CO can be expressed by Eqs (3 and (4 [8 : d [ O R O W PO O [ O p (3 atm d [ CO R CO W PCO CO [ CO p (4 atm Where RO, RCO, W, [O O, [CO O, [O, [CO represent the same meanng and unts f eqs (1 and (, L s the thckness f flm (μm, PO, PCO are flm permeabltes fr O and CO (ml μm/m h bar, A s surface area f packng bag(m, V s the free vlume n packng bag (ml, P atm s atmspherc pressure (P atm = 1. Slvng the rgressn equatns n Table nt Eqs (3 and Eqs (4 respectvly,the mathematcal mdel f gas exchange fr MAP cntanng Pak-ch at l can be descrbed by Eqs ( and (6.The mdel can be establshed by the same way at. d [ O W PO O [ O ( (.11.[ O patm d[ CO W ( [ O.16[ O (6 PCO CO [ CO patm Where the parameters are same as Eqs (3 and (4. If the deal strage cndtns were knwn,the gas exchange mdel culd be helpful n the desgn f MAP systems t evaluate flm permeabltes.the equlbrum cncentratns f O and CO nsde the packages can als be predcted wth Eqs ( and (6 nce the package materals are selected.the desred equlbrum gas cncentratns can be acheved by adjustng the data f flm specfcatn r prduce weght wth the help f the predctve mdel. The crrectness f mdel was verfed by MAP experments cntanng Pak-ch at 1 usng fur knds f flms whch permeabltes were tested at advance (Table 3. Befre the experment, the deal flm permeabltes can be evaluated by the mdel. It was demnstrated wth the calculatn fr O permeablty,the deal equlbrum cncentratns were % fr O and % fr CO,the flm permeabltes culd able be evaluated as the result f PO(e usng Eqs ( under the cndtns A =.6m, W =.8kg,the results shwed n table 3.Cmpared wth PO(e and the real value PO(r,t s fund that the flm O permeablty sutable fr Pak-ch under such cndtn mght be PP. The calculated methd f evaluated fm permeabltes PCO(e s the same as PO(e. Changes f gas cncentratns n dfferent flm packages by experment are shwn n Fg.6,the equlbrum cncentratns f O and CO nsde the PP flms was the nearest t the deal value, the crrectness f mdel was verfed. Table 3. The evaluated fm permeabltes PO(e cmpared wth the real value PO(r (ml μm/m d bar(1 Flm L(µm PO (r PO (e PO (r/po (e LDPE LDPE HDPE PP Gas cncentratns/% Gas cncentratns/% Gas cncentratns/% Gas cncentratns/% Tme/day (a Tme/day (b 1 1 Tme/day (c 1 1 Tme/day (d Fg.6. Changes f gas cncentratns n dfferent flm packages (aldpe1 (bldpe (c HDPE (dpp -O cncentratns - CO cncentratns ScRes

5 Prceedngs f the 17th IAPRI Wrld Cnference n Packagng 4. Cnclusn By usng an apprprate flm at lw temperature strage cndtn,the rat f CO t O wll cntnuusly adjust tself by the nteractn f the Pak-ch respratn and gas dffusn thrugh the packagng flm.the key f applcatn f MAP tecnlgy successfully s t select a flm f sutable permeablty whch can develp an ptmum equlbrum mdfed atmsphere wthn the package n a shrt tme and keep the state fr a lng tme.in ths paper, the mathematcal mdel f gas exchange wthn clse packages was develped n the bass f the characterstcs f respratn when the MAP cntanng Pak-ch was desgned.the theretcal bass fr gettng a rght way t chse packagng materals fr MAP and predctng the gas mass cncentratns nsde the packages were prvded. References [1 Suparlan,Kazuhk ITOH, Cmbned effects f Ht water treatment(hwt and Mdfed atmsphere packagng(map n qualty f tmates, Packagng technlgy and scence, vl. 16, pp , 3. [ Wang Xangyu, L Xa,Wang Juan, Zhu Jyng, Advances f respratn rate n Mdfed Atmsphere Packagng fr fruts and vegetables, Transactns f the Chnese Scety fr Agrcultural Machnery, 8 th ed., vl. 39, pp. 94 1, 8. [3 Le Qa, Xu Wenda. Study n respratry rate and respratry qutent f Brccl,.Acta Agrculture Shangha, 1 st ed., vl., pp , 4. [4 Yam KL, Lee DS, Desgn f mdfed atmsphere packagng fr fresh prduce, Dep.f Fd Scence Rutgers Unversty, pp. 73, [ N.H.Ullesten, M.S. Hedenqvst, A new test methd based n head space analyss t determne permeablty t xygen and carbn dxde f flexble packagng, Plymer Testng, vl., pp. 91 9, 3. [6 Zhang Changfeng, Xu Buqan, Study n Respratn Rates f Bananas Sealed n LDPE Assayed by NM and TSCM Methds fr Cmparsn, Fd Scence, 4 th ed., vl. 4, pp , 3. [7 Lu Wenda, SPSS fr wndws statstcal analyss, Bejng: Publshng huse f electrncs ndustry, 6. [8 Svetlana Fshman, V.Rdv, J.Peretz, S.Ben-Yehshua, Mdel fr Gas exchange Dynamcs n Mdfed Atmsphere Packages f Fruts and Vegetaables, Jurnal f Fd scence, th ed., vl. 6, pp , ScRes 6