Whey Processing with Nano Chitosan


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1 World Applied Sienes Journl 19 (4): , 2012 ISSN ; IDOSI Pulitions, 2012 DOI: /idosi.wsj Whey Proessing with Nno Chitosn Mzyr Shrifzdeh Bei, Mohmmd Jvd Hosseinzdeh nd Hiollh Younesi 1 Chemil engineering Deprtment, Aytollh Amoli rnh, Islmi Azd University, Amol, Irn 2 Deprtment of Environmentl Siene, Fulty of Nturl Resoures nd Mrine Sienes, Trit Modres University, Imm Rez Street, Noor, Irn Astrt: Sine mlei id is ple of speilly dissolving Chitosn, in this reserh the method of produing wter lurint nnoprtiles in Chitosn solution, sed on mlei id hs een studied. The resulting nnoprtiles hve remrkle ontt surfe with the ordinry Chitosn form in soring metl ions, proteins nd ft existing in Whey. After providing the 0.02, 0.03, 0.05 gr. density of Chitosn nnoprtile nd ordinry Chitosn in 10 Whey with ph 4, 5, 6 were ompred in soring the prtiles nd the results were oserved through (UV) spetrum. Sine mximum sorption ws oserved in ph=6 nd 0.05 gr. density of Chitosn nnoprtiles nd ordinry Chitosn, olloidl sorent in Whey, y tomi sorption nd infrred spetrum were exmined in the rest of the test. An inrese in the sorption of metl ions like led, iron nd opper is mong the signifint points of using this kind of nonoprtiles. The other items exmined in this study re omprison of proteins nd fts sorption fter tretment of Whey in ph=6 nd 0.05gr density of nno Chitosn with ordinry Chitosn in 10 of this mteril. Key words: Nnoprtiles % Chitosn % Ltose % Whey INTRODUCTION proess inludes hemil [2], physil nd iologil methods or integrtion of hemil nd physil methods. Whey is the lrgest derivtive of diry industries Among physil methods we n mention ltose whih uses environmentl pollution nd mirosopi seprtion of Whey using het nd inverse osmosis n orgnisms in these sustnes. The rte of oxygen inside e mentioned. In nother method tht uses lium wter used y B.O.D (iohemil oxygen demnd) ronte with intertion elernt ftors, ltose is miroorgnisms is different in Whey (it is seprted. It ws proposed s hemil method [4]. ppm) nd depending on the proportion of the milk soure Nnotehnology n e defined s the prodution of nd ltose, it n e mong lrgest nd most importnt mterils, prts nd useful systems with ontrol in effetive ftor [1]. The high nutrition vlue of milk nnometer longitudinl sle nd utilizing properties nd depends on onsuming 11 grm ltose dily [1, 2]. new phenomen resulted from suh sle. Ltose hs lso signifint nutrition properties tht n Nnotehnology mke it possile to mnipulte mterils e enumerted here; 1.Effets on nutritive mterils nd up to nno sle nd in this re, the synthesis of minerls sorption [2]. nnoprtiles hve een on fous, espeilly polyshride physil nnoprtiles due to their C Dietry fierlike tivities nd proioti effets [3]. iologil destrution properties, hydrophili nd C Clorifi vlue [3]. ioomptiility. C Glyemi index [3]. In this reserh, ttempt we mde to not only C Sweetness [2]. disuss high vlue of Chitosn nd Chitosn nnoprtiles for etter seprtion of Whey inluding Mny methods for isolting nd purifying ltose s (ft, ltose, metl prtiles protein nd solution solid well s Whey produts nd seprting prtiles of this mterils), ut lso justify the use of this mteril in vlule sustne hve long een estlished; this eonomil plns. Corresponding Author: Mzyr Shrifzdeh Bei, Chemil engineering Deprtment, Aytollh Amoli rnh, Islmi Azd University, Amol, Irn. 530
2 World Appl. Si. J., 19 (4): , 2012 MATERIAL AND METHOD proteiniztion of their mino groups euse of n + inrese in H in idi environment, the sorption Nno Prtiles Prodution: Chitosn is very sensitive proess of the prtiles in question is ultimtely loked. polymer mteril whih is ffeted y het nd hnges in Given these two fts, the rnge of prtiles sorption environmentl ondition. So during the test, ttention nd nd the results of Whey spetrophotometer in ph 4, 5, 6 ury in orret performne is neessry ftor for nd in 0.02, 0.03, 0.05 densities were exmined nd prodution of this mteril. mesured. The results re in figures 205 nd 35. Conerning the omprison of the sorents, it ws Chemil Mterils: Potssium Persulfid (K2S2O 8), Mlei oserved tht the dispersion of numers in As is Aid (HO2CCH2CHOHCO2H), Hydrohlori Aid (HCl) etween Therefore, to hve etter exmintion 37% whih were purhsed from Merk Co. Sodium nd more urte onlusion, stndrd smple with Hydroxide (NOH) nd Chitosn with low moleulr densities lower thn Whey (00.09) ws olleted gin weight (deityltion degree etween 7585%) prepred from shrimp shell purhsed from (SigmAlderih Co.). A Miniture Fourier Trnsform Spetrometer: In order In 100ml distilled wter, 0.003mol Mlei Aid ws to ompre the mount of sored prtiles in the dissolved, then 0.012mol Chitosn ws dded nd the primry smple nd the test (Whey treted with ph: 6 nd smple ws mixed y mixer for 3 hours [5]. After tht, ph 0.5 gr. Nno Chitosn) to reh fixed weight, 10ml of ws djusted y the solution of Hydrohlori Aid nd eh smple wter ws evported in furne with molr Sodium Hydroxide. The smple ws mixed t degree. The resulting sh using solid KBr, the speil room temperture for 8 hours nd nitrogen gs ws lown tlet, is produed nd finlly the resulting hrt of eh onto it over the lst hour. After one hour, s Nitrogen gs smple is evluted. ws lowing, 0.054gr Potssium Persulfid (K2S2O 8) ws dded nd ws Nitrogen gs ws lown onto the smple Sttistil Dt Anlysis: All of the tests were done in in the temperture of 70 entigrde degrees for 2 hours. In three lok plns three times. Anlysis nd evlution the se suspended prtiles ppered, the resulted (ANOVA), using liner model (G.L.M) in SPSS18 with the mixtures were ooled in ie th nd the resulting proility of 5% nd Dnken multirnge test ws done nnoprtiles were eing seprted y the entrifuge with for onfirming the possile differene etween the mens rpm yle for 30 minutes. The otined prtiles were dried y freezedryer nd used for sorption tests Atomi Asorption: After oserving the idel ph [6]. sorption nd the required nno Chitosn mount for the highest mount of seprtion, the reserhers used tomi The Mesurement of Different Vlues of Whey Inluding sorption mhine to mesure the mount of three metls Protein, Ft, Ltose nd Metl Ions: Protein of Cu, Fe nd P with mount of eh in the primry mesurement of Whey through forml titrtion method: smple nd fter sorption. this method is known s formul method whih is very quik test for protein mesurement in food like milk nd RESULTS AND DISCUSSION Whey. Mesurement of ft ontent in Whey ws performed Nnoprtiles Prodution Exmintion: The results of y using grvimetri through the test method. This SEM pitures relted to Chitosn nnoprtiles in weight method is fmous to Rose Gotli. Ltose of Whey ws proportions of 2:1, Mlei Aid/ Chitosn in ph 4, 5 nd mesured y Lori method [4]. Mesurement of sh ws 6. In mole rte of CS/MA=2:1 re showed in (Fig. 1). performed y heting the smple in furne with 550 C Given the ft tht mlei id is doulegent for 30 minutes nd the mount of eh metl element ws id, gent groups proportion is NH 2/COOH=1. done y using tomi sorption. As n e seen in Figure () the prtiles hve smller dimeters nd dimensions ompred to the The Determintion of the Required Amount of Chitosn ones in Figure (). This shows the positive effet of ph=4 Nnoprtiles nd proportion rte of 2:1, mlei id/ Chitosn. The Spetrophotometer: Chitosn nd its nnoprtiles hve Porosity rte in moleulr struture of Figure () is lso tendeny to dhesiveness nd selfssemly in ph more thn tht of Figure (); therefore, the desirility ove 6. Also, in ph lower thn 4, due to the of PH=4 with PH=6 ould e dignosed from the results. 531
3 World Appl. Si. J., 19 (4): , 2012 Fig. 1: Compre of different Nno Chitosn. ) Nno prtile in ph=4 ) Nno prtile in ph=6 ) Nno prtile in ph=4 d) Nno prtile in ph=5 The prodution of Chitosn prtiles out of Chitosn with eletrostti fores of mlei id inrese hene it uses high moleulr weight ws done. It ws oserved tht distention in nnoprtiles nd n inrese in their size distriution of nno Chitosn prtiles size with gr. rte (Fig. 1) shows this ft. Seond, with n inrese in ph, CS/MA=2:1 in ph: 3, 4, 5, 6 re vrious nd different from the soluility of Chitosn is deresed, using n eh other. inrese in the dhesion nd ggregtion of In ph=4, the distriution of prtiles is nrrower thn nnoprtiles. So, with regrds to the studies rried out in ph=3. This shows tht in the sid ph, the prtiles re in the pst, in this study with only two ph, 4 nd 6 re less ssemled nd the mjority of the prtiles re formed tken into ount for produing Chitosn nnoprtiles seprtely. In ph=5, the prtiles re ompletely seprted from Chitosn with low moleulr weight. The results re nd re lrger thn the two previous forms. It is lso the s follows: se in idi ph of the mino Chitosn group nd protonted roxyl id mlei group, in whih se the The Result of Spetrometry: In order to selet the size of nnoprtile is ffeted. Therefore, s ph inreses stndrd smple, first the Whey onentrtions from 0.1 from 3 to 6, the mss of the nnoprtiles too inreses. up to 0.9 were prepred; Fig. 2 () ws oserved, while the There might e two resons for tht. omprison of the resultnt sorptions ws tken into First, with n inrese in ph, the ioniztion ount. The rnge of the oserved figures is etween 0 degree nd lod density of mlei id moleules 0.9 overing the rte of sorption of nnoprtiles in lso inrese; s result, innermoleules repulse Whey. 532
4 World Appl. Si. J., 19 (4): , 2012 Fig. 2: Stnderd solution urve or whey Fig. 3: Effet of nno prile nd Chitosn in sorption ) nno Chitosn ) Chitosn So, for the ske of etter investigtion nd more Figure 3 shows the sorption of the prtiles in urte onlusion, stndrd smple ws olleted question, the rnge of prtiles sorption nd the results gin from pure Whey, with the onentrtions of Whey spetrometry. The effet of ph 4, 5, 6 nd the of 00/0.09. In (Fig. 2) two mtters re illustrted (). visosities of 0.02, 0.03 nd 0.05 on prtiles sorption of Chitosn nd its nnoprtiles tend to ssemle nd Whey. dhere in ph more thn 6 in the ph lower thn 4, result of this tretment will e due to derees in sorent. So in Dt Anlysis for Otining the Conentrtion nd this study to determine effetive sorent doze, whih Optimized ph for Performing Susequent Tests: determines the pity of the sorent, ertin tests Aording to the (Tle 1), the vrine nlysis with were rried out y hitisn nnoprtiles for proility of %95 ws oserved nd investigted. exmining the effet of the sorent mount on the There is signifint differene etween the sorption proess of protein ions nd suspending solid onentrtions nd ph. Performing the omprison test prtiles in Whey. In order the rnge of sorent mount etween the mens in Tle 2, the reserhers oserved ws determined in vrious mounts inluding 0.02, 0.03, tht ph=6 nd the onentrtion 0.05 gr. of nno Chitosn 0.5 gr. on 10 ml. of Whey in ph 4, 5, 6, y using in 10 Whey hs the est sorption. In order to perform spetrophotometer (Fig. 3). the other tests, the sme ph nd onentrtion were used. Tle 1: vrine nlysis of the effet of hnging onentrtions nd ph on sorption used y Nno Chitosn nd Chitosn Chnge Referene Free Rte Totl of Squres The Averge of Squres FVlue Proility Nno Chitosn Chitosn Filure Totl
5 Tle 2: The effet of Nno Chitosn, Chitosn visosities nd ph on prtiles sorption in 10ml Whey onentrtion (ns.s) Asorption of Nno Asorption gr. in 10 ml Whey ph Chitosn (As) y Chitosn World Appl. Si. J., 19 (4): , 2012 Atomi Asorption: In studies rried out y Mukhopdhyy et l. (2006) for isolting metl ions, ft nd protein y using Chitosn gel with deityltion more thn 90% nd high moleulr weight, the rte of metl ions Fe, Cu nd P respetively rehed to 0.001, , gr. in 100 ml. Finlly, the totl of metl ions rehed to 0.1 gr. in 100 ml [17], ut when nnoprtiles were used with low moleulr weight nd lower deityltion ( ) through the reserh, its rte rehed the lowest mount. The results of eh metl n e seen in Fig. 3, Fig. 4 nd The Study of Metl Ions Asorption: Metl ions The mens hving similr letters in olumn hve no signifint differene sorption ours y one or omintion of ion sed on Dnken test with 95% proility. exhnge mehnisms, helting nd eletrostti sorption [7]. Mny studies hve shown tht the most Tle 3: The rte of sorption nd ooper onentrtion in Whey nd Whey treted with nnoprtiles importnt prmeter for hevy metl sorption y No. Test Mteril Conentrtion (pp) Asorption sorent is the ph primry solution tht hs high 1 Distilled Wter impt on metlsoring spots on the sorents 2 Stndrd surfe nd hemil struture of metl in wter [8]. In this 3 Stndrd study, the effet of primry ph solution, within the rnge 4 Stndrd of 46, on the rtio of metl ion sorption of P, Cu nd 5 Whey Fe ws onsidered. In ph less thn 3, Chitosn 6 Treted Whey nnoprtiles re solved nd in ph more thn 7, metl ion preipittion ours s metl hydroxide. Metl ion Tle 4: The rte of sorption nd Iron onentrtion in Whey nd Whey sorption is highly depends on protontion nd nonprotontion of mino groups nd roxyltes exists in treted with nnoprtiles No. Test Mteril onentrtion (pp) Asorption Chitosn nnoprtiles [9]. 1 Distilled Wter As the ph of solution inreses, mino groups in the 2 Stndrd Stndrd ompound of Chitosn nnoprtiles eome protonted 4 Stndrd in different degrees; onsequently, essile spots for 5 Whey helting metl ions re redued, leding to eletrostti 6 Treted Whey removl of metl tions [10]. In low ph, euse of the + + ompetition mong H ions nd metl tion, H ion Tle 5: The rte of sorption nd density of led in Whey 1 nd Whey treted with nnoprtiles domintes on sorption ples nd the essiility of tions over these spots is limited, leding to redution No. Test Mteril Density (pp) Asorption of sorption perentge [10]. In ft, the effet of ph on 1 Distilled wter 0 0 sorption effiieny relted to lignd protontion nd 2 Stndrd metl ion in solution. Theoretilly, metl ions in solution 3 Stndrd exist in vrious types tht depend on the solution s ph. 4 Stndrd Whey 1 101/ In low ph mounts, the mjority of metl ion vrieties re 6 Treted Whey 0 0 tions, while metl hydroxide vrieties hve high mounts of ph. In ddition, euse in low ph min Tle 6: Mesuring metl ions in pure Whey nd Whey treted with NnoChitosn groups re protonted, thus the pility for mking protonted lignd links with metl tions is less thn the Different vlues Whey treted in pility for mking nonprotonted moleule links with of metl ions Pure Whey NnoChitosn (pp) metl hydroxide in high ph mounts. On the other hnd, P 101/968 0 in low ph, protons with metl tions ompete with mino Fe 181/ groups for intertion, whih leds to the formtion of Cu 0/ RNH nd positive lod on the sorent surfe [11]. 534
6 World Appl. Si. J., 19 (4): , 2012 Trnsmittne Vvelene Fig. 4: Infrred spetrosopy of Whey in nturl ph Trnsmittne Vvelene Fig. 5: Infrred spetrosopy of Nno prtiles fter sorption in different ph ) ph=4 ) ph=5 ) ph=6 Tle 7: In the following tle, the mount of eh prmeter is fter filtrtion Type of used Chitosn for sorption in Whey Protein (in100ml Whey) Ft (in100ml Whey) Ash (in100ml Whey) Ltose (in100ml Whey) pure Whey 0.26gr 0.1gr 0.56r 4.4r Chitosn prtiles 0.18gr 0.08gr 0.28gr 4.2gr Nno Chitosn prtiles 0.08gr gr * Fe = * Cu = * P =0 Pp* 4.2gr But in higher ph, the existing lignds in the sorents Infrred Spetrosopy: Fig. 4 nd Fig. 5 show results from  like COO, inrese the density of negtive lod on lignds infrred spetrosopy nd two digrms of treted nd surfe, s result of whih, eletrostti ttrtion of pure Whey. Considering the digrm, we n ontend tht positively loded metl ions inreses on lignd surfe nno Chitosn prtiles n sor metl, ft nd protein nd the perentge of sorption will e inresed. As ph prtiles. inreses due to ompression of OHions, the preipittion of metl ions pper s hydroxide nd Asorption nd Tension Exmintion of Protein Groups: redues sorption perentge [12]. In (Tle 6), the As stted ove, the spetrum is relted to the sorption perentge of mounts resulted from metls is existene of protein groups nd singlepity nd summrized. doulepity mide proteins with wvelength 535
7 World Appl. Si. J., 19 (4): , ( ) CM. Thus, in (Figure 4), the wvelength in In ph higher thn 7, nnoprtiles egin to ssimilte question, the existene of this dispther in nnoprtiles nd onnet with eh other nd the points with nd lso extending the rnge of relted to onnetivity derese. In phs lower thn 6, the onneted proteins tension in Chitosn nnoprtiles (Figure 5, groups mong nnoprtiles mines nd tripoly prt **) is onfirmed. Therefore, sed on (Figure 5), the phosphori groups in proteins led to deproteiniztion, so existene of proteins in nnoprtiles in ll ph is proven, the sorption of the prtiles dereses in this sitution ut if we oserve the rte of sorption on vertil xis, [13]. the gretest mount of sorption is in density 0.05 gr. Milk ft gloule memrne frgments (MFGM) exits Nno Chitosn in 10. Whey with ph=6. This n e euse of the negtive hrge in phosphte groups nd proof for exmining optimum ph nd gives n pproprite in phospholipids memrne of Whey ft ells. Given the density. ft tht the positively hrged mine groups re in Chitosn nnoprtiles strutures, in idi ph soring Asorption nd Tension Exmintion of Fts nd Ft nno Chitosn mine groups y phospholipids groups of Aids: The spetrum is relted to the existene of ft id ftty nd protonted ells led to floules nd isoltion 1 groups (CH) nd fts with wvelength CM. of ft from the liquid phse [14]. The mount the sh of As n e seen in (Figure 4), in exmining wvelength Chitosn nd nno prtile smples is deresed (***) the existene of this dispther onfirms ompred to tht of pure Whey euse of the sorption nnoprtiles nd extending the rnge of slts nd minerls y the nnoprtiles. relted to the tension of ft ids in Chitosn nnoprtiles (Figure 5) prt ***). Thus, ording to Ltose Isoltion: After the exmintion of sorption (Figure 5), the existene of fts in nnoprtiles in ll ph rte nd the effet of Chitosn nd its nnoprtiles on is proven, ut if we oserve the rte of sorption on different prmeters of onentrtion nd ph, the vertil xis, the gretest mount of sorption is in ph=6. mounts of protein, metl ions, ft nd sh re mesured Thus, it gives us nother proof for hoosing the most gin for eh of them y ertin methods nd finlly the optimum ph s well s sorption of prtiles in Nno perentge of existing ltose is lulted with high Chitosn network. purity. The moleules of ltose re nonioni surftnts, so it is not ffeted y ph. Thus, hrged prtiles of Asorption nd Tension Exmintion of Amino Chitosn nd nnoprtiles do not hve ny effet on it. 3+ Groups: The ple of tension virtions of NH is in The deresing mount of ltose in omprison to mg (these vlues re for solid stte nd the primry stte is euse of fermenttion during the wide spetrum) nd the intensity of sorption strips retions fter the exmintion of the effet of Chitosn in this ple is more medium nd the virtion is nd Chitosn nnoprtiles on Whey while there is no tensionl. (Figure 5) shows the tension virtion of onnetion with nnoprtiles. So, high purity of ltose mino groups in Chitosn nnoprtiles in omprison is euse of Chitosn nd Chitosn nnoprtiles effet with pure Whey (****). Asorption strips re on the sorption of other mterils forming Whey usully in (ut not lwys). Bending inluding protein, fts, metl ions nd hrged prtiles 3+ virtions innh group re sorption strips hving the suspended in Whey. The verge of dt resulting from wvelength of with the sorption strip prtiles sorption efore the tretment of smples nd intensity of S (strong). fter Whey ws treted with norml Chitosn nd its nnoprtiles (Tle 7). Asorption Exmintion in Proteins, Ft nd Ash in Whey y Nnoprtiles: Amino ids in idi CONCLUSION environment nd high density of hydrogen ion re dominnt tions nd in lkline environment re In this reserh, the effet of prmeters suh s ph dominte in n nion stte. In speil rnge of ph, mino nd grm rtio of Chitosn nd mlei id on the size nd ids exist s zwitterions nd lled isoeletri points. morphology of nnoprtiles ws exmined. The results Isoeletri point of most proteins is 5/5. Protein show tht synthesis of nnoprtiles with the mole rtio sorption through eletro stti reltions in ph=6 nd of 2:1 of mlei id to Chitosn in ph=4 yielded more protein eletronegtive in ph helps in sorption nd pproprite ondition ompred to other prtiles. Also, ogultion proess. the tivity of prmeters suh s solution ph, the 536
8 World Appl. Si. J., 19 (4): , 2012 mount of sorent on metl ions sorption, proteins 6. De Mour, M.R., F.A. Aoud nd L.H.C. Mttoso, nd impurities used y Chitosn nd its prtiles were Preprtion of hitosn nnoprtiles exmined nd the results show tht with ph inrese using methryli id. J. Colloid Interfe Si., from 4 to 6, the sorption pity too inreses. Also, 321: s the sorent mount inreses from 0.02 to 0.05 gr on 7. Ghorni, F., H. Younesi, S.M. Ghsempouri, 10 of the smple, the pity of sorption inreses. A.A. Zintizdeh, M. Amini nd A. Dneshi, 2008 The results of spetrophotometer show tht if ph=6 nd Applition of response surfe methodology for the mount 0.05gr of Chitosn nnoprtiles is used for optimiztion of dmium iosorption in n queous sorption, in omprison with the other rtios, it n e solution y Shromyes erevisie. Chem. Eng. J. more effetive. Also, with sme mount under sme 145: onditions with norml Chitosn, the pity of 8. Amini, M., H. Younesi, N. Bhrmifr, sorption is out two times greter. Any derese in A.A.Z. Lorestni, F. Ghorni, A. Dneshi nd sh is due to derese in metl ions nd proteins used M. Shrifzdeh, Applition of response y nnoprtiles. Croxyli nnoprtiles mke surfe methodology for optimiztion of led signifint onnetion for mino groups with proteins, ft iosorption in n queous solution y Aspergillus nd metl ions, thus they hve speil pility ginst niger. J. Hzrd. Mter, 154: Chitosn. A derese in the mount of ft is used y 9. Sreejlekshmi, K.G., K.A. Krishnn nd floultion nd pereption whih re resulted from T.S. Anirudhn, Adsorption of P(II) nd inding nnoprtile with the memrne of ft gloule. P(II)itri id on swdust tivted ron: Considering the findings of the reserh, the Chitosn Kineti nd equilirium isotherm studies. J. Hzrd. nnoprtiles re suitle sorents for removing Mter., 161: impurities, hevy metls, fts nd existing protein in 10. Chu, K.H., Removl of opper from queous Whey. They n turn into ltose with high purity fter solution y hitosn in prwn shell: dsorption these prtiles re isolted. Finlly, they n e used in equilirium nd kinetis. J. Hzrd. Mter, 90: food nd drug onsumptions. 11. Punngm, M. nd F. Uno, Preprtion nd use of hemilly modified MCM41 nd sili gel s REFERENCES seletive dsorents for Hg (II) ions. J. Hzrd. Mter., 154: Rupk mukhopdhyy nd dip tlukdr, Crist, R.H., K. Oerholser, N. Shnk nd N. Ming, Whey proessing with hitosn nd isoltion of Nture of onding etween metlli ions nd ltose. J proess iohemistry, pp: lgl ell wlls. Environ. Si. Tehnol., 15: Homn, P.G., Review of proesses nd 13. Montill An nd Csl En, Isoltion of ovine produts for utiliztion of ltose in deprotonted BLtogoloolin from omplexes with hitosn Diry milk serum. J. Diry Siene, 70: interntionl, pp: Y ng ST, Silv em (1979). Novel produts nd new 14. Hwng, D. nd S. Dmodrn, Seletive tehnologies for use of fmilir rohydrte, milk Preipittion nd Removl of Lipids from Cheese ltose's Diry siene, 78: Whey Using Chitosn. J. Agri. Food Chem., 4. Nikerson, T.A., Ltose hemistry. J. Agri. 43(1): food Chem., 27: Bodnr, M., J.F. Hrtmnn nd J. Borely, Preprtion nd Chrteriztion of ChitosnBsed Nnoprtiles. Biomromoleules, 6:
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Computing dt with spredsheets Exmple: Computing tringulr numers nd their squre roots. Rell, we showed 1 ` 2 ` `n npn ` 1q{2. Enter the following into the orresponding ells: A1: n B1: tringle C1: sqrt A2:
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