Research Article Modelling of Rehydration of Freeze-dried Dumpling Wrapper

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1 Rsarch Joural of Applid Scics, Egirig ad Tchology 1(5): , 16 DOI:1.196/rjas ISSN: ; -ISSN: axwll Sciific Publicaio Corp. Submid: Spmbr 1, 15 Accpd: Ocobr 3, 15 Publishd: arch 5, 16 Rsarch Aricl odllig of Rhydraio of Frz-drid Dumplig Wrappr War Ch, Hua Li, Xigli Jiao ad Xuwi Cui School of Chmical Egirig ad Ergy, Zhgzhou Uivrsiy, No.1 Scic Road, Zhgzhou, Ha, 451, Chia Absrac: I was aimd o assss h impac of rhydraio procss of frz-drid dumplig wrappr o hir propry ad ra of rhydraio, i is cssary o sudy h mpraur ffc; hrfor h rhydraio kiic of frz-drid dumplig wrappr was ivsigad a mpraur of 38, 343 ad 373 K, rspcivly. Fick Diffusio hory, Plg modl ad Wibull modl wr usd o dscrib rhydraio procss. Th rsuls show ha: h prdicios wih Plg modl ad Wibull modl ar i good agrm wih xprimal daa. Th sudy o rhydraio procss will hlp udrsad rhydraio characrisics ad rhydraio mchaism of dry foodsuff ad provid horical guidac for h frz-drid food. Kywords: Dumplig wrappr, Fick diffusio, mass rasfr, plg, rhydraio, vacuum frz-dryig, Wibull INTRODUCTION Drid foodsuffs of d o b rhydrad bfor hy ar cosumd. I is dsirabl for h drid foodsuffs o hydra as fas as possibl ad show adqua srucural ad chmical characrisics. Iformaio abou war absorpio as a fucio of mpraur of hos marials is criical imporac o hir shlf lif ad produc usag. Rhydraio of food marials also has a impora impac o hir rhydraio ra, uriioal ad ssorial propris. A umbr of sudis hav b rpord o modl h hydraio kiics of food ad diffr yps of modls hav b usd. odls usd o dscrib h rlaio bw moisur co ad im durig rhydraio is commoly classifid io wo cagoris: horical os ad mpirical os. Fick Diffusio odl is a horical modl, ypically ad frquly usd. I spi ha h modl is complicad, rivial compuaio ad may of assumpios wr a variac wih ral sysm, y, his modl is basd o Fick s Firs ad Scod Laws of Diffusio, which ca accuraly rflc h ssc of mass rasfr, so Fick Diffusio odl is widly applid i food ad chmical girig. Amog mpirical modls, Plg modl ad Wibull modl ar of usd. Plg modl has b provd fi o modl h rhydraio of milk powdr ad whol graham flour (Hug al., 1993). As i is a popular mpirical o xpoial modl ad asy o calcula, Plg modl is of usd o dscrib rhydraio of various foodsuffs. Aohr widly applid modl is Wibull modl, by which zymaic or microbiological procss dgradaio ca b dpicd xacly. Du o is simpliciy ad flxibiliy i h simaio of wo paramrs, Wibull modl is also xsivly applid i food idusry. Th objciv of his sudy is o assss h impac of rhydraio procss of frz-drid dumplig wrappr o hir propry ad rhydraio ra. I paricular, h ffc of mpraur is modld. Rhydraio bhavior of dumplig wrappr a various mpraurs is ivsigad. Thr modls ar proposd o modl h rhydraio procss ad prdicios of modl wr compard, i was foud ha Plg modl ad Wibull modl ar i good agrm wih xprimal daa. EXPERIENTS arial ad apparaus: Wha flour is producd by Huaxu Grai ad Oil Procssig Co., Ld. Th vacuum frzig dryr LGJ-1S is producd by Huaxig Tchology Dvlopm Co., Ld. Sogyua Bijig cor. JY sris fucio lcroic balac is producd by Shaghai dical Dvic Facory. Elcric-had hrmosaic war bah is producd by Shaghai Balacr Facory. Exprimal procsss: Wigh frz-drid dumplig wrappr of abou 1 g ad immrs io 3 ml disilld war a a crai mpraur wih hrmosa war bah. Th mpraurs ar 35, 7 ad 1 C, rspcivly. Durig rhydraio, h dumplig wrappr Corrspodig Auhor: Hua Li, School of Chmical Egirig ad Ergy, Zhgzhou Uivrsiy, No.1 Scic Road, Zhgzhou, Ha, 451, Chia, Fax: This work is licsd udr a Craiv Commos Aribuio 4. Iraioal Lics (URL: hp://craivcommos.org/licss/by/4./). 556

2 Rs. J. App. Sci. Eg. Tchol., 1(5): , 16 d o wigh vry ow ad h ad war o h surfac is rmovd by filr papr. Wh h dviaio of mass for wo ims is lss ha 1 g, moisur co has rachd quilibrium ad rhydraio procss is fiishd. odls: Fick diffusio law: Fick s Scod Law was applid o obai diffusio coffici i his sudy ad h formula ca b xprssd by Eq. (1). Th quaio is udr hs assumpios (Crak, 1975; García al., 6): iiial moisur co is sam, hr s o shrikag, diffusio coffici is a cosa a a crai mpraur: 8 Dw ( ) xp( ) (1) 4L whr,, ad is h iiial moisur co, moisur co a im ad quilibrium moisur co (g H O/g dry marial); D w is diffusio coffici; L is h hickss of sampl. Saisical aalyss: Th modl was valuad by Roo a Squar Dviaio (RSD), SSE (Sum of Squar Error) ad RAD (Rlaiv Avrag Dviaio), which ar dfid as (Sopad al., 199): RSD 1 ( i ci ) (5) i1 i1 SSE 1 ( i ci ) (6) 1 i ci RAD (7) i1 i RESULTS AND DISCUSSION Fick diffusio: Tak h logarihm ram o boh sids of Eq. (5), h Eq. (9) was obaid: 8 Dw l( ) l (8) L 4 Plg modl: Th xprssio of Plg modl is as follow (Plg, 1988): () k k 1 whr, ad rfr o h iiial moisur co ad moisur co a im (g H O/g dry marial); k 1 (s/% ) ad k (% -1 ) ar wo paramrs for Plg modl. As rhydraio procss is ulik dhydraio procss, quilibrium moisur co cao b masurd. Bsids, h log soakig im will brig may chags i h srucurs ad propris of foodsuffs, so i is vry hard o sablish quilibrium. Equilibrium moisur co is xprssd by Eq. (3): 1 (3) k Wibull modl: Th xprssio of Wibull modl is show as follow (achado al., 1999): ( )xp[ ( ) ] (4) whr,, ad rfrs o h iiial moisur co, moisur co a im ad quilibrium moisur co (g H O/g dry marial); α β ar wo paramrs for Wibull modl which ar calld shap paramr ad scal paramr, rspcivly. A plo of l[( - )/( - )]vrs yilds a sraigh li wih slop big -D w π /4L from which D w ca b calculad. Th plo of l[( - )/( - )]~ was show i Fig. 1. I ca b foud from Fig. 1 ha hr ar wo sags i ach rhydraio curv, idicaig ha rhydraio procss is maily composd of wo diffr sags, amly iiial sag ad fial sag, ach of which has a ffciv diffusio coffici show i Tabl 1. From Tabl 1, ffciv diffusio cofficis D 1, D icrasd as mpraur icrasd a h iiial sag ad fial sag. orovr, D 1 is largr ha D obviously a cosa mpraur, implyig h war absorpio ra a h iiial sag is quickr ha ha of las sag. Accordig o diffusio hory, h diffusio of liquid ad gas i porous marials dpds o molcular rasiio. Ad diffusio coffici ca b xprssd by Eq. (1) (Crak ad Park, 1968): 1 6 D (9) whr, δ : To rasiio disac from o cll o adjac cll i h solid Φ : as h umbr of molculs ha diffus i ui im wihi δ D : Diffusio coffici Th frqucy of molcul rasiio Φ dpds o h diffusio rgy, which is drmid by is mpraur. Nvrhlss, as hr is o quaio o xprss h rlaioship bw frqucy of molcul 557

3 Rs. J. App. Sci. Eg. Tchol., 1(5): , 16 l(x -X )/(X -X ) im/s Fig. 1: Plo of l[( - )/( - )] vrsa a diffr mpraurs, 38 K;, 343 K;, 373 K Tabl 1: Effciv diffusio cofficis of frz-drid dumplig wrappr a diffr mpraurs Tmpraur/k Tim/s D 1 /m s -1 R Tim/s D /m s -1 R 38 ~ ~ ~ ~ ~ ~ Tabl : Paramrs of Plg modl for frz-drid dumplig wrappr a diffr mpraurs Tmpraur/k K 1 /s K R war/g d m X /g Tabl 3: Paramrs of Wibull modl for frz-drid dumplig wrappr a diffr mpraurs X /g war / Tmpraur/k Α Β/s g d m R rasiio Φ ad mpraur, so oly qualiaiv mhod is availabl for h dscripio of rlaioship bw hm. From Eq. (1), as mpraur icrass, war molculs obai mor rgy from surroudigs ad mov much fircly, ladig o h icras of Φ ad diffusio coffici. Th posiiv corrlaio bw ffciv diffusio coffici ad mpraur has b cofirmd by may rfrcs (Sajuá al., 1; Doymaz, 4; Kapso al., 8). Plg modl: Plg modl paramrs for frz-drid dumplig wrappr a diffr mpraurs wr show i Tabl. Tabl, k 1 dcrasd wih h icras of mpraur. As k 1 is rlad wih mass rasfr ra, h smallr k 1 is, h highr war upak ra is, which is i accordac wih h fac ha rhydraio ra a highr mpraur is highr oo. A h sam im, k was foud o b a fucio of mpraur, dcrasig as mpraur icrasd. As k is rlad wih war holdig capaciy of marial show i Eq. (3), h miimum valu of k mas h srogs war holdig capaciy ad vic vrsa (Solomo, 7). I also ca b s from Eq. (3) ha h dcy of quilibrium moisur co wih mpraur is h sam as k. As k 1, k boh showd a crai rlaioship wih mpraur from Tabl, wo quaios wr applid o illusra h corrlaios, show i Eq. (1, 13). k 1, k wr subsiud io Eq. () ad a w quaio was proposd ha ca dscrib h rlaioship bw moisur co, im ad mpraur, xprssd by Eq. (11). Sic k 1, k ar iflucd by marials irisic characrisic ad xral codiios, Eq. (11) is oly suiabl for h xprim sysm i his sudy. Ay chag i variy of dhydrad producs or rhydraio codiios will brig Eq. (11) modra rvisio. ( T ) ( 46T ) (1) k 1 = T (11) k = -46T (1) Wibull modl: Wibull modl paramrs for frzdrid dumplig wrappr a diffr mpraurs wr show i Tabl 3. I Wibull modl, α is calld shap paramr, which icrasd wih h icras of mpraur show i Tabl 3. As a shap paramr, diffr shaps of foodsuff will lad o diffr valus of α. I his sudy, 558

4 Rs. J. App. Sci. Eg. Tchol., 1(5): , 16 / g war /g d m /s Fig. : Plg cosas k 1, k vrsa a diffr rhydraio mpraurs, k1;, k /g war /g d m.4. Fig. 3: Exprimal ad prdicd moisur co by Fick Diffusio Law for rhydraio of dumplig wrappr a diffr mpraurs,, 38 K;,343 K;,373 K; -prdicd daa sic h shap of dumplig wrappr is cosa ad diffr valus of α a diffr rhydraio mpraurs idica a co-rlaioship bw α ad mpraur. Y, i was cosidrd hr was o rlaioship bw h paramr ad mpraur. Thrfor, i is worh ohig v hough h wo paramrs show a posiiv corrlaio ad hus α ca b rgardd as a cosa idpd of mpraur (Abu-Ghaam ad cka, 1997). Thrfor, i is blivd ha i his sudy apar from h facor of foodsuff shap, α migh also b iflucd by h xprimal codiios lik mpraur. Bsids, α o oly rflcs marial shap, bu also migh b rlad wih war upak ra durig rhydraio. awhil β i Tabl 3 dcrasd wih icrasig mpraur. Is rciprocal is similar o ffciv diffusio coffici i Fick Diffusio Law, which /s rprss kiics paramr i Wibull modl ad masurs h difficuly or faciliy dgr of marial o rhydra. β is h im by which 63% of procss has b carrid ou (Saguy al., 5). Th smallr β is, h highr rhydraio ra is. From Tabl 3, i ca b s ha β dcrasd as mpraur icrasd, idicaig war upak ra a highr mpraur is largr ha a lowr mpraur. Also from Fig. 5, i is vry obvious ha rhydraio ra a 373 K is largr ha 38 K ad 343 K. Saisical aalyss: Th ma valus of RSD RAD ad SSE i Eq. (5, 7 ad 6) for ach modl a diffr mpraurs wr lisd i Tabl 4 ad compariso bw horical valus ad xprimal valus was show i Fig. o 5.

5 Rs. J. App. Sci. Eg. Tchol., 1(5): , 16 / g war /g d m /s Fig. 4: Exprimal ad prdicd moisur co by Plg modl for rhydraio of dumplig wrappr a diffr mpraurs, 38 K;, 343 K;,373 K; -prdicd daa /g war /g d m.4. Fig. 5: Exprimal ad prdicd moisur co by Wibull modl for rhydraio of dumplig wrappr a diffr mpraurs, 38 K;,343 K;,373 K; -prdicd daa Tabl 4: Saisical aalysis for ach modl as of saisical ss Fick diffusio modl Plg modl Wibull modl RSD RAD SSE I gral, ach modl ca fi h rhydraio daa approprialy, amog which Plg modl ad Wibull modl show br fiig accuracy ha Fick Diffusio Law, idicaig ha h mass rasfr mchaism durig rhydraio of frz-drid dumplig wrappr is o Fick Diffusio Law. This migh b bcaus frzdrid foodsuffs hav pliful micro pors brough by h paricular dryig mhod ad h mass rasfr mchaism of rhydraio is capillary imbibiio isad of Fick Diffusio Law whil h mchaism for air-drid producs is Fick Diffusio Law (arabi al., 3) /s Th rhydraio kiics a diffr mpraurs wih diffr modls was showd i Fig. 3 o 5 ad h diffrc bw xprimal ad prdicd daa ca b s from hs figurs, oo. Though Fick Diffusio Law i Fig. 3 ca prdic h quilibrium moisur co, y h diffrc bw xprimal ad prdicd daa is much largr, which suggss h mass rasfr mchaism is o govrd by Fick Diffusio Law from aohr poi of viw. CONCLUSION Rhydraio bhavior of dumplig wrappr a various mpraurs is ivsigad; rhydraio of food is graly iflucd by mpraur. Fick Diffusio Law, Plg modl ad Wibull modl wr applid o modl rhydraio procss ad prdicd 56

6 Rs. J. App. Sci. Eg. Tchol., 1(5): , 16 quilibrium war co. Comparig wih modl prdicios, i is foud ha Plg modl ad Wibull modl ar i good agrm wih xprimal daa, which is hlpful o udrsad h rasfr mchaism durig rhydraio procss. REFERENCES Abu-Ghaam, N. ad B. cka, Th applicaio of Plg s quaio o modl war absorpio durig h soakig of rd kidy bas (Phasolus vulgaris L.). J. Food Eg., 3(4): 39l-41. hp:// aricl/pii/s Crak, J., Th ahmaics of Diffusio. Oxford Uivrsiy Prss, Lodo. Crak, J. ad G.S. Park, Diffusio i Polymrs. Acadmic Prss, Lodo ad Nw York. olilibrary.wily.com/doi/1.1/app /absrac. Doymaz, I., 4. Covciv air dryig characrisics of hi layr carros. J. Food Eg., 61(3): hp:// García, P.P., N. Sajuá, R. lis ad A. ul, 6. orchlla Escula (morl) rhydraio procss modlig. J. Food Eg., 7(4): hp:// Hug, T.V., L.H. Liu, R.G. Black ad.a. Trwhlla, War absorpio i chickpa (C. ariium) ad fild pa (P. saivum) culivars usig h Plg modl. J. Food Sci., 58(4): hp://olilibrary.wily.com/doi/ /j b9374.x/absrac. Kapso, K.G., Y.N. Njiag, A.E. Komk, J. Houhouiga, J. Schr ad C..F. bofug, 8. Physical propris ad rhydraio kiics of wo variis of cowpa (Viga uguiculaa) ad bambara groudus (Voadzia subrraa) sds. J. Food Eg., 86(1): hp://www. scicdirc.com/scic/aricl/pii/s X. achado,.f., F.A. Olivira ad L.. Cuha, Effc of milk fa ad oal solids cocraio o h kiics of moisur upak by rady-o-a brakfas cral. I. J. Food Sci. Tch., 34(1): hp://olilibrary.wily.com/doi/1.146/ j x/absrac. arabi, A., S. Livigs,. Jacobso ad I.S. Saguy, 3. Normalizd Wibull disribuio for modlig rhydraio of food pariculas. Eur. Food Rs. Tchol., 17(4): Plg,., A mpirical modl for h dscripio of moisur sorpio curvs. J. Food Sci., 53(4): hp://olilibrary.wily.com/doi/ /j b13565.x/absrac. Saguy, S., A. arabi ad R. Wallach, 5. Nw approach o modl rhydraio of dry food pariculas uilizig pricipls of liquid raspor i porous mdia. Trds Food Sci. Tchol., 16(11): hp:// scic/aricl/pii/s Sajuá, N., J.A. Cárcl, G. Clm ad A. ul, 1. odllig of h rhydraio procss of brocolli flors. Eur. Food Rs. Tchol., 1(4): hp://lik.sprigr.com/aricl/1.17/ s1777#pag-1. Solomo, W.K., 7. Hydraio kiics of lupi (Lupius Albus) sds. J. Food Procss Eg., 3(1): hp://olilibrary.wily.com/doi/ /j x/absrac. Sopad, P.A., E.S. Ajisgiri ad.h. Badau, 199. Th us of Plg s quaio o modl war absorpio i som cral grais durig soakig. J. Food Eg., 15(4): hp://www. scicdirc.com/scic/aricl/pii/