Experimental study of drying kinetics of skim milk

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Drying kinetics of skimmilk solution is investigated in thiswork. Dry oven method used to determine the characteristic drying curves. The experiments are carried out at two temperatures of 45Cand 60C and three different initial solid contents. The
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   ull Paper Experimental study of drying kinetics of skim milk M.S.Hatamipour*, A.Rahimi, M.Sadripour Department of Chemical Engineering, Faculty of Engineering, University of Isfahan,P.O. Box 81746-73441, Isfahan, (IRAN)E-mail : hatami@eng.ui.ac.ir  Received: 15  th  August, 2010 ; Accepted: 25  th  August, 2010 CTAIJ 6(1) 2011 [1-5]  An Indian Journal  Trade Science Inc. Volume 6 Issue 1 chemical technologychemical technology  ISSN : 0974 - 7443 KEYWORDS Drying kinetics;Skim milk;Characteristic moisturecontent. ABSTRACT Drying kinetics of skim milk solution is investigated in this work. Dry ovenmethod used to determine the characteristic drying curves. The experi-ments are carried out at two temperatures of 45 ! C and 60 ! C and three differ-ent initial solid contents. The obtained characteristic curves for drying rateare normalized, based on a simple mass transfer model in which the dryingrate is considered as a first order reaction. These normalized curves areindependent of temperature and initial concentration and coincide together.The obtained experimental data are applied to identify a simple mass trans-fer model parameter. Finally a relative humidity factor f, is obtained as afunction of " , characteristic moisture content. This model can be used inCFD modeling of spray dryers for simple and efficient calculations. #   2011 Trade Science Inc. - INDIA INTRODUCTION Dehydration operations are important steps inchemical and food processing industries. Regarding thisfact, drying technologies along with better control andoperational strategies have contributed to a better qual-ity dried products. Spray drying is a well-known methodfor drying that nowadays covers large number of appli-cations for products ranging from food to mineral oresand chemicals. It is the core component of a milk pow-der production plant. The moisture content of milk pow-der is one of the predominant factors for preserving thequality of the product [5] . There is a great need for dry-ing models to describe the drying process which helpsin its optimization and can be useful in effective designof dryers or improve existing drying systems [7] . A dry-ing process can be described completely by using anappropriate drying model, which usually includes dif-ferential equations of heat and mass transfer in the inte-rior of the product and at its inter-phase with the dryingagent [9] . Having mixed a mass transfer model with theknowledge of the drying kinetics, the calculation mightbe simple and efficient.   Drying kinetics of the productsare the most important required data for design andsimulation of air dryers [3] . Also these models can beused in CFD software to reduce calculations andachieve more realistic performance.In fact characteristic drying curve which expressesthe time history of temperature-moisture content couldbe used to propose a mass transfer model [6] . In therecent years, several investigations have been conductedon the drying kinetics of different food and chemicalmaterials. There have been more than 200 drying ki-netics models offered for various foods in the litera-ture, which are formally characterized by two differentphysical and empirical approaches [7] . But the existing   Experimental study of drying kinetics of skim milk 2  ull   Paper CTAIJ, 6(1) 2011  An Indian Journal  chemic l technologyhemic l technology differences among the model formulations can be con-siderable. Chen & Lin [2]  have studied air drying of milk droplet under constant and time-dependent conditions.An attempt has been made to examine two significantmodels in a more comprehensive manner. One modelis the characteristic drying rate curve approach and theother (new) model is the reaction engineering approach.The model predictions are compared against a very widerange of experimental results including isothermal andtime-varying temperature conditions .  Both models pre-dict and cover the experimental results reasonably well.Besides, the results indicated that the reaction engineer-ing approach model is better than the others. The char-acteristic drying rate curve approach assumes before-hand the falling rate in all kinds of conditions for milk droplet drying, whereas the reaction engineering modelsimply reflects the experimental results closely. Zbicinskiet al. [8]  have developed a method for measuring dryingkinetics of different products in a dispersed system. Theyused phase doppler anemometry (PDA) technique todetermine initial spray atomization parameters, the struc-ture of spray during drying, particle size distribution,velocity of the particles and mass concentration of theliquid phase, etc.The main objective of this research is to formulatean accurate model for analyzing the simulated dryingkinetics of skim milk samples based on a good fit onthe corresponding moisture content. This kinetics modelis to be used in CFD modeling of a spray dryer usedfor skim milk drying to reduce computational time andaccurate calculations. For determination of drying ki-netics, the dry oven method is much easier and its du-ration may vary considerably depending on the dryingtemperature. The range of the studied parameters wasnear to those used in industrial spray dryers. THEORY The drying kinetics is greatly affected by air tem-peratures, initial and instant moisture content and airhumidity. A mass-transfer model can be introduced byusing a characteristic drying curve. This approach as-sumes that there is a corresponding specific drying raterelative to the unhindered drying rate in the first dryingperiod on each volume-averaged free moisture contentthat is independent of the external drying conditions [6] .The mass transfer between the gas and droplet couldbe calculated according to the following first order re-action kinetics: )YY(KfA dtam egpp   (1) where in eq. (1) A p  is the surface of mass transfer, e Y   and Y $  are the equilibrium moisture and air humidityrespectively. Also K g  is the mass transfer coefficientthat can be obtained from eq. (2) with suitable coeffi-cient values for % , & , '  and   '  and   f is the relative dryingrate and is defined as eq. (3). $ &'(# ScResh (2) RDDRf  ! (3) where DR is the drying rate and defines in eq. (4), DRis the rate in the first drying period. 1212 ttxxDR   "   (4) where x is the moisture content (kg H2O  /kg dry solid)and t   is drying time between two successive steps. Pa-rameter f takes on the values in Eq. (5) [4] .Unhindered moisture f = 1; )* 1(5) Hindered moisture 0 < f < 1; 0< )  < 1< " , so called characteristic moisture content, and de-fined in terms of critical moisture content [4] . ecre xxxx   " # (6) where, x e  is the equilibrium moisture content and x cr  isthe critical moisture content. A unique relationship be-tween f and "  can be found for any specific material.The drying curve is normalized and at critical point,there is a transition in drying behavior. By definition of correction factor f, a simple lumped-parameter expres-sion for the drying rate can be obtained. MATERIALS AND METHODS Skim milk solutions with three different initial solidcontents of 0.05, 0.1 and 0.15 (w/w) were preparedby adding water to milk powder at 24 ! C for experi-ments. The concentrated milk samples then were pouredinto a glass plate with 6 cm diameter.The experimental set-up was consisted of a dryingoven (Fan Azma Gastar) with On/Off control and digi-   M.S.Hatamipour et al.  3  ull   Paper chemical technology CTAIJ, 6(1) 2011  An Indian Journal  chemic l technology Figure 1 : Drying curves of skim milk solutionsFigure 2 : Effect of drying temperature on drying timeFigure 3 : Drying rate curve at different initial solid contentFigure 4 : Drying rate curve at different initial solid contentFigure 5 : Drying rate curve vs. x for different of initial solidcontentFigure 6 : Drying rate curve vs. x for different of initial solidcontent tal indicator. For each experiment, changes in weight of sample were measured continuously using a digital bal-ance (Sartorius BP 310s model) with an accuracy of  ( 0.001 gr. The balance was kept outside the oven andthe sample was placed on a special sample holder whichwas hung from the balance. The drying oven was cali-brated for temperature using a calibrated thermometer.In order to obtain an accurate and uniform temperatureinside the oven, intensive air ventilation was used. Allthe required data were recorded every 15 min. To de-termine the equilibrium weight at a specified tempera-ture, the samples were kept in the oven until the differ-ence between two successive mass measurements be-came less than 0.02 g.Before putting any sample into the oven the dryingair temperature was fixed. It was assumed that the thick-ness of the milk solution sample is quite thin, so that theconditions of the drying air (temperature and humidity)were kept constant throughout the drying process, whilethe relative humidity in the room condition was 16%.To consider the effect of temperature on the rate of drying the experiments were carried out at similar con-ditions and different temperatures including 45 ºC and 60 ºC. RESULTS AND DISCUSSIONCharacteristic drying curve The drying behavior of skim milk solution as a func-   Experimental study of drying kinetics of skim milk 4   ull   Paper CTAIJ, 6(1) 2011  An Indian Journal  chemic l technologyhemic l technology tion of time is shown in figure 1. It could be seen thatthe drying curve is almost a straight line with a continu-ous decrease of mass by the passage of time for allconcentrations due to the fact of constant drying rateperiod. At final times, a deviation from the straight linecan be observed which may be explained as the fallingdrying rate period. It also becomes obvious that skimmilk solutions with lower initial concentrations have dry-ing rate curves with higher intercepts.Variations of the moisture content with the dryingtime   at different air temperatures and initial concentra-tions are plotted also in figure 2. As a result, an increasein the temperature of the drying air decreases the totaldrying time as a result of increasing the rate of heattransfer. Besides, when the temperature increases from45 ! C to 60 ! C, the total drying time decreases to about40% of that for the solution with drying temperature of 45 ! C. Drying rate curve as a function of time The drying rate (DR) of the solutions during thedrying process could be obtained by using eq. (4). Fig-ure 3 and 4 show the variation of DR, with time for twodifferent operating temperatures. As a result of the mois-ture transfer, the drying rate decreases, with elapse of time. Approximately entire drying process took placein the constant rate period. These figures illustrate thatfor a higher air temperature, the drying rate will be in-creased and drying will take placed at lower times. Drying rate curve as a function of X The drying rate curve for skim milk can be obtainedalso by plotting drying rate vs. moisture content (x).Figure 5 and 6 illustrate drying rate curve vs. x for twotemperature of 45 ! C and 65 ! C and initial solid con-tents of 0.05, 0.1, 0.015 (w/w). These figures showdrying rate curves of the samples at the selected tem-peratures, where about 83-87% of water content wasevaporated at the end of constant rate period of drying,a linear falling rate can be observed at the end of pro-cess which is due to very low thickness of sample lay-ers. It may indicate that the resistance to moisture trans-port is related to the thickness of solution. Prediction of f  Figure 5 and 6 represent drying rate as a functionof X, according to eq. (1). When the characteristic dry-ing curve became normalized, these curves are inde-pendent from the temperature and initial solid content.Figure 7 shows the relative drying rate as a function of  " . In this figure f    is only a function of " . These six curvesat temperature 45 °C and 60°C and initial solid content of 0.05, 0.1 and 0.15 (w/w) approximately coincidetogether.It is possible to find a relation between relative dry-ing rate f vs characteristic moisture content ( " ). Ac-cording to the best fitting of six data series of figure 5and 6, eq. (7) can be obtained with R 2 in the range of (99-94%). f = -0.325 ) 4  + 1.83 ) 3    –   3.752 ) 2  + 3.27 )    –   0.031 (7) CONCLUSION Dry oven method applied for determination of char- Figure 7 : The relative drying rate vs. ) A particle surface area (m 2 ) DR drying rate (s -1 ) f relative drying rate ( - ) K mass transfer coefficient (kg s -1 ) Sh Sherwood number ( - ) t time (s) T temperature ( ! C) X moisture content (kg moisture kg -1 dry solid) Y' gas humidity (kg kg -1 ) "  characteristic moisture content ( - ) Â , ç , æ , î  constant in eq. (3) ( - ) Subscripts cr Critical e Equilibrium G dry bulb, bulk gas Nomenclature   M.S.Hatamipour et al.  5   ull   Paper chemical technology CTAIJ, 6(1) 2011  An Indian Journal  chemic l technology acteristic drying curve of skim milk solution. Dryingcurves have in general two stages after an initial warm-up: constant drying and falling rate periods. Dryingmodels for constant and falling rate period of skim milk solution based on the concept of characteristic dryingrate are proposed, and found a unique relationship be-tween relative drying rate f and characteristic moisturecontent for specific material. This model can be used inCFD software for simple and efficient calculations. Inparticular, the concept of a characteristic drying curvestates that the shape of the drying-rate curve for a givenmaterial is unique and independent of gas temperature,humidity and velocity.Convective drying of skim milk solutions was de-pendent on temperature, and the drying curve showeda constant rate period; only a short falling rate periodwas observed at the end of process. REFERENCES [1] R.B.Bird, W.E.Stewart, E.Lightfoot; Transport Phe-nomena . New York, John Wiley & Sons, (1960) . [2] X.D.Chen, S.Lin, X.Q.i; AIChE J., 51(6) , 1790-1799 (2005) . [3] J.Fontaine, C.Ratti; J.Food Proc.Eng., 22 , 287-305 (1999) . [4] R.B.Keey, M.Suzuki; Int.J.Heat and Mass Trans, 17 , 1455-1464 (1974) . [5] R.J.Knget, H.V.Brink; Int.Dairy J., 8 , 733-738 (1998) . [6] T.A.G.Langrish, T.K.Kockel; Chem.Eng.J., 84 , 69-74 (2001) . [7] B.Yesilata, M.A.Aktacir; Appl.Thermal Eng., 29 ,748-752 (2009) . [8] I.Zbicinski, A.Delag, C.Strumillo, J.Adamiec;Chem.Eng.J., 86 , 207-216 (2002) . [9] V.T.Karathanos; J.Food Eng., 39 , 337-344 (1999) .
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