A Mathematical Model of the Removal of Milk Protein Deposit

Transcription

1 efereed Proceedings Heat Exchanger Fouling and Cleaning: Fundaentals and pplications Engineering Conferences International Year 2003 Matheatical Model of the eoval of Milk Protein Deposit Hong Xin The University of uckland Necati Özkan The University of uckland Xiao Dong Chen The University of uckland This paper is posted at ECI Digital rchives.

2 Xin et al.: eoval of Milk Protein Deposit Matheatical Model of the eoval of Milk Protein Deposit Hong Xin, Xiao Dong Chen* and Necati Özkan Departent of Cheical and Materials Engineering, The University of uckland, Private Bag 92019, uckland, New Zealand * Corresponding author; E-ail: d.chen@auckland.ac.nz BSTCT Based on a polyer dissolution controlled cheical cleaning echanis, a atheatical odel has been developed to describe the different stages of the reoval of ilk protein fouling fro a hard surface. Various processes, such as reptation, disengageent, ass transfer through the boundary layer and surface area changes during the decay cleaning stage have been taken into account in the odelling process. The successful prediction of the cleaning process under various conditions indicates that the odel has proposed a rational echanis accounting for the reoval of ilk protein fouling. INTODUCTION Milk fouling on heat transfer surfaces is a serious proble in dairy processing plants, where frequent cleaning is required in order to eet the strict hygienic standards and to aintain the noral production capability. Cleaning is a ultistage process coprising various steps that ay be controlled by echanical action, cheical reactions, and ass transfer. Matheatical odeling plays a significant role in understanding the cleaning process and can be used to optiise the cleaning process. cheical dissolution based ass transfer controlled cleaning echanis has already been suggested by several researchers (Schlussler In the study of the cleaning procedure of ilk fouling, Gallot-avallée and alande (1985 have provided a pseudo-physical cleaning odel. lthough this odel has been widely recognized as one of the best odels for describing the reoval of porous deposits obtained fro the theral treatent of ilk fluid. The definition of the surface concentration has been criticized by various authors for their lack of theoretical or experiental basis (eclercq- Perlat, 1991; Bird The analytical and nuerical odelling curve provided by Bird (1993 gave a reasonable fit of experiental cleaning data. However, the assuption of the tie to reach the axiu cleaning rate depending on the tie required to convert all the deposits to a reovable for is doubtful (Xin The basic structure of ilk protein deposits is ade of aggregated ilk protein olecules and voids. Milk protein olecules have long olecular chains like polyers. The swelling of the protein deposit and the final reoval of this swollen layer are analogous to the dissolution process of polyers when they are treated with suitable solvents. Therefore, the polyer dissolution concept can be applied to reveal the cleaning echanis of the protein deposits. In a recent study (Xin, 2002a, based on ass transfer theory and the polyer dissolution concept, the constant cleaning rates in the unifor stage have been predicted. The successful prediction of the constant cleaning rate under various conditions indicates that the odel has proposed a rational echanis accounting for the reoval of ilk protein fouling. In this study, based on the polyer dissolution controlled cheical cleaning echanis, a atheatical odel that can be used to describe the different stages of the cleaning process will be further developed. MECHNISMS ND MTHEMTIC MODES Polyer Dissolution Based Cleaning Mechaniss dopting the polyer dissolution concept, the essential physical features of the cleaning of ilk protein deposit are depicted in Figure 1. First, the cleaning solution is transported fro bulk solution to the surface of the deposit through a fluid boundary layer. Then the contact of the cleaning solution with the deposit will trigger a series of reactions, generating soe interediate reaction products (certain protein olecules. Further penetration of the cleaning solution into the deposit will build up a reaction zone and for a swollen gel layer. disengageent process is needed before the interediate reaction products can be transferred across the boundary layer into the bulk cleaning solution. The disengageent process of the protein olecules fro the gel-solution interface is very coplicated. In the swollen region, the cleaning solution concentration is high and the protein olecules have a high obility;the oveent of the protein olecules essentially starts fro this region. fter a short reptation tie, the protein olecular chains on the gel side of the gel-solution interface tend to disengage fro the interface and ove into the solution. The long and utually entangled protein chains are inhibited fro entering the liquid phase due to the friction between theselves. The disengageent rate of Published by ECI Digital rchives,

3 Heat Exchanger Fouling and Cleaning: Fundaentals and pplications, rt. 22 [2003] protein olecules is one of the factors controlling the dissolution process. Bulk cleaning solution eaction zone Unreacted zone Fig. 1 scheatic diagra of the whey protein concentrate (WPC gel fil dissolution process. In addition to the disengageent, a ass transfer resistance also exists at the surface. If the disengageent rate is relatively sall, the ass transfer resistance through the external boundary layer ay be ignored. However, if they occur at coparable rates, then the dissolution process can be both disengageent and diffusion liited (anade, With increasing cleaning tie, the disengaged polyer chains will begin to accuulate on the gel-solution interface until a axiu volue fraction is reached. Then, the rate of disengageent fro the interface would be constrained by the rate of ass transfer to the bulk solution. concentration gradient between the interface of the swollen gel and the bulk cleaning solution provides a driving force for the oveent of the disengaged protein olecules. The dissolution rate then reaches the highest value. Matheatical Model of Cleaning Diffusion of cleaning cheical olecules Disengageent Boundary layer Gel-solution interface Swollen gel Protein deposit Stainless steel surface Polyer dissolution odels involving soe coplicated oving boundary layer probles have been established (Peppas, 1994; Parker, lthough these odels have provided insights for the developent of a cleaning odel, they are generally coplex. In this study, we have attepted to capture the key echaniss by using a siple atheatical odel. The diffusion of cleaning solution and the cheical reactions take place very rapidly. fter contact with the cleaning solution, a gel layer on the surface of the deposit can be observed very quickly. The ass transfer of cleaning solution to the deposit is norally quicker than the ass transfer back the dissolved protein chains due to the saller size. In this study, it is assued that the disengageent of protein olecules fro the swollen gel-solution interface and the transfer of these disengaged protein olecules into the bulk cleaning solution are the rate liiting steps for the cleaning process. During the swelling and unifor stage, the cleaning rate ay be calculated in ters of the ass transfer coefficient and the concentration gradient of the disengaged protein olecules in the boundary layer. In the decay stage, an effective surface area ay be used to correlate the cleaning rate. For siplicity, the accuulation of the disengaged protein olecular chains in the boundary layer is neglected. The oving boundary layer proble and the different protein volue fractions within the swollen gel are not considered. Swelling and unifor stage Based on the conventional concept of ass transfer, the cleaning rate (or ass flux of the WPC gel olecules fro the gel-solution interface ay be written as: d = = k ( b (1 dt where is the ass reoved, is the cleaning rate, k is the ass transfer coefficient, is the surface area, is the volue fraction of the disengaged protein olecules at gelsolution interface, b is the volue fraction of the disengaged protein olecules in the bulk cleaning solution. When b is very sall, Eq. (1 becoes d = = k (2 dt The volue fraction of disengaged protein olecular chains accuulated on the interface between the gel and the cleaning solution at any tie has been assued to change according to a first-order reaction echanis: d = k d (3 dt where k d is the disengageent rate constant. The physics of the disengageent process has been elaborated by Devotta et al (1993. The disengageent rate is recognized to be directly proportional to the obility of polyer olecules, whereas the obility of the polyer olecules will depend on its volue fraction. It has been assued that the variation of the obility of polyer chains is a product of a kinetic constant and the extent of the departure fro the axiu obility (Devotta, Based on this assuption, it is assued that the disengageent rate constant of the olecule chains, k d, reduces with increasing, and approaches to zero when the axiu value ( is reached. s a first estiation, k d takes the following for: k d ξ 1 (4 = where ξ is a kinetic constant, is the axiu volue fraction taken up by the disengaged protein olecules. The change of the volue fraction of the disengaged protein olecules in the boundary layer is then expressed by the following equation. 2

4 Xin et al.: eoval of Milk Protein Deposit d dt ξ (1 = (5 Since a polyer chain requires a finite induction tie to disengage fro the gel-solution interface, the disengageent rate is initially zero. This iniu induction tie required for the first few chains to disengage is equivalent to the reptation tie (t r. Thus, it is assued that the following initial condition exists at the gelsolution interface. d = 0, t < tr (6 dt fter the reptation process, fro t = tr to t > tr, the volue fraction of the disengaged protein olecules in the boundary layer can be calculated by integrating Eq. (5: ξ ( t tr e = (7 ξ ( t tr 1+ e 0 where 0 is the volue fraction of the tangling protein chains at the solution side of gel-solution interface at the tie t = tr ( 0 0. We now define a diensionless paraeter ψ as ψ = 0 1 Cobining Eq. (2 and (7, the cleaning rate can be rewritten as follows: (8 ξ ( t tr ( ψ + e = n (11 ξ ( ψ + 1 Decay stage t the end of the unifor stage, the continuous fil of WPC deposit is broken up and only the patches of the deposit fil are left on the stainless steel surface. In the study of the reoval of organic fils in the decay stage, the change of the surface area of the reaining fil has been odelled as a first order process (Beaudoin, dopting this approach, the protein gel reoval in the decay stage is given as: d dt = k (12 where is the surface area covered by the protein fil in the decay stage, k is the first order rate constant for the surface area reduction. This rate constant is expected to be dependent on teperature, echanical properties of deposit, cleaning solution concentration, and flow velocity. The initial condition for Eq. (12 is: = when t = tsu,0 where,0 is the total surface area covered by the protein fil. Integrating Eq.(12 fro t tsu to t tt (the total cleaning tie: ( k ( t t su = e (13,0 ssuing that the cleaning rate during the decay stage depends on the reaining protein fil area, the cleaning rate during this stage can be expressed as: d dt e ψ + e ξ ( t tr = = ξ ( t tr (9 = (14,0 where (the constant cleaning rate during the unifor cleaning stage is defined as = k (10 The aount of ass reoved (under a certain constant cleaning condition with a known teperature, velocity, and concentration of cleaning solution, etc fro the deposit as a function of tie can then be calculated by integrating Eq. (9 fro tie t tr to t tsu (t su is the total cleaning tie during the swelling and unifor stages. Cobining Eq. (13 and (14, gives ( k ( t tsu = e (15 In order to calculate t su and the total cleaning tie t t, a critical protein ass reaining ( c at the start of the decay stage is defined as: = 0 (16 c su where 0 is the original ass of the deposit, su is total ass reoved during the swelling and the unifor stage. su can be calculated fro Eq. (11 with the boundary Published by ECI Digital rchives,

5 Heat Exchanger Fouling and Cleaning: Fundaentals and pplications, rt. 22 [2003] condition at t = t su. Cobining Eq. (11 and (16, the ass reoved during the decay stage can be deterined as: ξ ( t r ( ψ + su t e c = 0 n (17 ξ ( ψ + 1 earranging Eq. (17, t su is given by the following equation: t su 1 = n ( ψ + 1 e ξ ( ξ 0 c ψ + t r (18 The ass loss of the deposit during the decay stage can also be expressed as: d dt e d = = dt ( k ( t t (19 su Integration with the boundary conditions: = 0 and =,, when t = t 0 su (19a = c and = 0, when t = tt (19b The UV absorption data were recorded at ten-second intervals to onitor the whole cleaning process. The detailed inforation about the UV assay and preparation of WPC gel fils are discussed elsewhere (Xin, 2002a; Xin, 2002b. ESUTS ND DISCUSSION The cleaning experients were carried out under various experiental conditions with flow velocities ranging fro 7 (e =2400 to 0.62 /s (e =21000 and teperatures ranging fro 35 to 85 o C using 0.5 wt.% NaOH cleaning solutions. The aount of whey protein concentrate (WPC gel layer on the stainless steel surface ranges fro 205 to 747 g/ 2. typical cleaning rate against tie curve with the descriptions for the three cleaning stages, the reptation tie (t r, the cleaning tie during the swelling and the unifor stage (t su, the constant cleaning rate (, and the critical ass reaining ( c are shown in Figure 3. the c represents the deposit ass reoved during the decay cleaning stage. The slight decrease of the cleaning rate in the unifor stage ight be due to the faster reoval of the inlet region of the gel layer caused by the hydrodynaic disturbance. repeatability study of the experients was conducted and no significant differences were observed fro the cleaning rate curves. Then, c can be expressed as: c = k ( k ( tt tsu ( 1 e (20 earranging the above equation, t t is given by the following equation: 1 ck t t = n + tsu k 1 (21 Cobining Eq. (18 and (21, then the total cleaning tie t t can be deterined as: Heater Coputer agitator Sapling pup WPC gel fil UV spectrophotoeter Test section Floweter NaOH solution reservoir NaOH solution pup t t 1 = n ( ψ + 1 e ξ ( ξ 0 c 1 ψ k EXPEIMENT POCEDUES ck n 1 + t (22 The cleaning syste designed to deterine the cleaning kinetics of WPC gel deposits fro a stainless steel tube is illustrated scheatically in Figure 2. The stainless steel tube (ID=16 and ength=150, were pre-coated with a WPC gel fil using a rotation rig. In the once-through cleaning loop, the cleaning solution (0.5 wt% NaOH, containing the reoved deposits was continuously transported to the UV spectrophotoeter by a saple pup. r Fig. 2 scheatic illustration of the cleaning apparatus. Identification of Model Paraeters Four paraeters (,, ξ, t r and k are used to characterize the cleaning process. The constant cleaning rate was deterined fro the experiental results using the following equation: u = (24 tu 4

6 Xin et al.: eoval of Milk Protein Deposit where, u and t u are the ass reoved and the cleaning tie during the unifor stage, respectively Cleaning ate (g/ 2 s swelling stage t r unifor stage t su (constant cleaning rate c Cleaning Tie (sec decay stage Fig. 3 typical cleaning rate against cleaning tie curve. During the swelling stage, after the cleaning solution contacts with the deposit, a certain delay tie, referred to as the reptation tie, exists before a finite aount of dissolved WPC protein becoe easurable in the cleaning solution. delay before the start of the cleaning process has been observed in previous cleaning studies (Gallot-avallée and alande, 1985; Bird theoretical basis of the reptation tie as a function of flow velocity and teperature is not available. However, at low teperature and low flow velocity, the reptation tie can be observed directly fro the experiental results. For a given polyer-solution pair and polyer olecular weight, it is reasonable to assue a unique value of interfacial polyer volue fraction at the gel-solution interface (Papanu, recent study showed that the interfacial polyer concentration did not vary significantly with tie during the dissolution process (Devotta, During the fouling and cleaning process, the olecular weights of the disengaged proteins are difficult to estiate due to the coplicated cheical reactions. For siplicity, it is assued that the diensionless value ψ is a constant. earranging Eq. (9, a relationship between ψ and the reptation tie can be expressed by the following equation: ψ ln = ( t tr ξ (25 Using the easured reptation ties at various low teperatures, a siple regression ethod was used to ψ identify the value of ψ. plot of ln against tie t d should give a nearly straight line passing through the point ψ where t = t r when ln = 0, providing an appropriate value for ψ was selected (see Figure 5.6. The iniised su of the square deviations was obtained when an average ψ value of 25±5 was chosen. The value of ψ is independent of ξ, and subsequently is used in all the other calculations. fter obtaining the value of ψ, it is also possible to deterine ξ and t r fro the sae plot, especially when t r is too sall to be directly observed fro the experiental results. The tie at which the decay stage coences is given by Eq. (18 and the cleaning rate during this stage is given by Eq. (15. nother two paraeters c and k have been used to odel the cleaning progress during the decay cleaning stage. The ass of the gel layer left at the start of the decay stage is referred to as the critical ass ( c, and can be used to deterine the swelling-unifor cleaning tie t su. The critical ass value can be calculated by the area integration of the cleaning rate curve in the decay stage as shown in Figure 3. k is the rate constant for the surface area reduction in the decay stage. earranging Eq. (15, the following equation is obtained: n = k ( t t su (26 The value of k can be deterined fro the slope of the plot of ln against ( t t su. Effects of Teperature and Velocity on Cleaning The effect of teperature on the cleaning rate has been studied at a constant eynolds nuber at teperatures ranging fro 35 to 75 o C. The experiental results are illustrated in Figure 4. The effect of flow velocity ( /s on the cleaning rate at 65 o C is shown in Figure 5. In the analysis of the odel paraeters, it was found that the critical ass ( c was not uch dependent on teperature and flow velocity, as a result, the critical ass ( c ay be taken as a characteristic constant for a given fouling and cleaning syste. n average critical ass value of 100 g/ 2 was deterined fro the experiental data for the WPC gel deposits used in this study. Figures 4 and 5 show that with increase of the teperature and flow velocity of the cleaning solution, the cleaning rate during the swelling and unifor stages is increased and the cleaning tie in the decay stage is reduced. s a result, the whole cleaning tie is reduced. Published by ECI Digital rchives,

7 Heat Exchanger Fouling and Cleaning: Fundaentals and pplications, rt. 22 [2003] These observations are consistent with the changes of the odel paraeters. Cleaning ate (g/ 2 s Fig. 4 The coparison of the experiental and predicted cleaning results at different teperatures at a constant eynolds nuber (e = Cleaning ate (g/ 2 s e= Cleaning Tie (sec 65 o C 9 /s 0.18 /s 0.25 /s 0.37 /s 0.46 /s odel prediction Cleaning Tie (sec 35 O C ( 0 =310 g/ 2 s 45 O C ( 0 =652 g/ 2 s 55 O C ( 0 =354 g/ 2 s 65 O C ( 0 =635 g/ 2 s 75 O C ( 0 =532 g/ 2 s odel predictions Fig. 5 The coparison of the experiental and predicted cleaning results at different flow velocities at 65 o C. Previous study has shown that the reptation tie gets shorter with increasing teperature (Peppas, It is expected that the values of ξ increase with increasing teperature since the protein chains have higher obility and larger disengageent rates at higher teperatures. Both the increased axiu volue fraction of disengaged protein olecules and the increased ass transfer coefficient should contribute to a larger at higher teperatures. The changes of k with teperature are possibly due to the changes in the icrostructure and the echanical properties of the fouling layer with teperature. The enhanceent of the cleaning with increasing flow velocity would be ainly due to the increasing external ass transfer coefficient. s a result, the transport of the disengaged protein olecules back into the bulk cleaning solution would be ore efficient at higher flow velocities, thus giving higher and k. The disengageent rate would be influenced by the action of the hydrodynaic forces on the polyer chains dangling into the liquid, so it is expected that ξ increases with increasing flow velocity as well. The faster disengageent of polyer chains could contribute a shorter reptation tie. To evaluate the role of teperature in each cleaning stage, the teperature dependent cleaning odel paraeters 1 (,, ξ,, k, and can be described using the rrhenius relationship. t r lthough the effects of eynolds nuber (or flow velocity on the odel paraeters could be very coplex, it was possible to describe the influence of eynolds nuber on the odel paraeters with a siple equation using the analysis results obtained fro Figures 4 and 5. Since the effects of eynolds nuber on the apparent activation energies are not significant during cleaning processes (Gillha, It is assued in this study that the apparent activation energy is independent of eynolds nuber. Thus, the dependence of the odel paraeters on teperature and eynolds nuber can be represented by using the following sei-epirical equation: E = a Y f exp gt (e (27 where Y represents the odel paraeters:,, ξ,, k, and 1/t r, E a is the apparent activation energy (J/ol, g is the olar gas constant, and f(e is a linear function between eynolds nuber and y, which is independent of teperature and defined as: f (e = α + β e (28 where α and β are the constants. The values of α and β can be obtained fro the intercept and slope of the E a y / exp against e plots, respectively (see gt Figure 6. The coparison between experiental results and odel predictions are provided in Figure 4 and 5. The paraeters used in the odel predictions were given in Table 1. In order to confir the validity of the odel provided here, a set of new cleaning experients were perfored at different teperatures ranging fro 45 to

8 Xin et al.: eoval of Milk Protein Deposit.exp(E a /338 k.exp(e a /338 o C at a constant flow velocity of 0.25 /s. Using the sae paraeters provided in Table 1, the cleaning rates are predicted and copared with the experiental results in Figure 7, a good agreeent was observed. E Fig 6 y exp a versus eynolds nuber plots at 65 o C T for (a y=, (b y=ξ, (c y= k, and (d y=1/t r. 4.0x x x x10 6 y = 184.6x + 9.7E05 ( 2 =0.98 Cleaning ate (g/ 2 s 4.0x x x x10 4 eynolds Nuber (a 2.0x10 4 y = x x x x10 3 ( 2 = x x x x10 4 eynolds Nuber (c ξ.exp(e a /338 (1/t r.exp(e a / x10 4 y = 1.43x x x x10 3 ( 2 = x x x x10 4 eynolds Nuber flow velocity=0.25 /s 0 =645 g/ 2 45 o C 55 o C 65 o C 75 o C 85 o C odel prediction Cleaning Tie (sec Fig. 7 The coparison of the experiental and predicted cleaning results at various teperatures at a flow velocity of 0.25 /s. iterature Cleaning esults The cleaning odel proposed here is obtained fro the investigation of a odel syste based on WPC gel fils. Coparing this odel syste with ore realistic experiental systes investigated previously by other (b 6.0x10 12 y=1e9x-2.7e12 ( 2 = x x x x x10 3 eynolds Nuber (d researchers would not only confir the validity of the cleaning odel proposed in this study, but also ake it possible to apply this cleaning odel to realistic protein deposits. Table 1. The odel paraeters used in the odel predictions for the reoval of WPC gel fouling deposits Stage Paraeters α β E a (KJ/ol eptation 1/t r (s E E Swelling ξ (s E E Unifor ( g/ 2 s 1.0E E Decay k ( s E E There are a few systeic studies on the cleaning kinetics using whole ilk fouling (Gallot-avallée and alande, and whey protein fouling (Gillha et al,1999. Using the current odel, the data obtained fro those previous studies were first analysed, and then the influence of teperature and eynolds nuber on odel paraeters were estiated using Eq. (27 and (28. lthough the real fouling and cleaning systes are quite different fro the gel syste, it was found that the apparent activation energies obtained fro this study are still valid for the protein deposits. The effects of eynolds nuber on odel paraeters were then calculated according to the results obtained fro the analyses of the experiental curves. The average critical asses of 34 g/ 2 and 160 g/ 2 were estiated for the experiental results of Gillha and Gallot-avallée, respectively. Due to the shortage of the data at the beginning period of the cleaning process, the reptation tie was taken as zero for all the following predictions. The literature experiental results and odel predictions are copared in Figure 8 and Figure 9. The paraeters used for the odel predictions are suarised in Table 2. Table 2. The paraeters used in odel prediction for the literature cleaning results provided in Figures 8 and 9. uthor Gallot-avallee Gillha et. al. Constant α β α β ξ (s E E E E+00 ( g/ 2 s 1.0E E E E+00 k ( s E E E E+00 note: the sae apparent activation energies as that of WPC gels have been used. Siilar to the WPC gel reoval, all the cleaning results fro previous studies on the whey protein fouling and the whole ilk fouling showed a typical cleaning rate curve with well-defined three stages. The influence of teperature and flow velocity upon the odel paraeters show a siilar Published by ECI Digital rchives,

9 Heat Exchanger Fouling and Cleaning: Fundaentals and pplications, rt. 22 [2003] trend as that of WPC gel, confiring the cleaning echanis developed to be valid in ore coplex and realistic proteinaceous fouling and cleaning systes. The sae value of the critical ass identified fro each fouling and cleaning syste suggests that the critical ass ay be taken as a syste constant. Cleaning ate (g/ 2 s flow velocity 1.1 /s 95 o C (1.9 wt% NaOH 75 o C (1.9 wt% NaOH 55 o C (2.3 wt% NaOH odel analysis Cleaning Tie (sec Fig. 8 The odel predictions together with the experiental results reported by Gallot-avallée and alande (1985. Cleaning rate (g/ 2 s wt.% NaOH o C (e= o C (e= o C (e=3300 odel prediction Cleaning tie (sec Fig. 9 The odel predictions together with the experiental results reported by Gillha et al. (1999. CONCUSIONS Based on the polyer dissolution theory and fundaental ass transfer concept, a cleaning odel was developed for estiating the cleaning rate and cleaning tie for proteinaceous fouling. Various processes, such as reptation, disengageent, ass transfer through the boundary layer and surface area changes have been taken into account in the odelling process. The experiental results and odel predictions support the odelling concepts eployed. The successful use of this odel in literature cleaning results shows that this new atheatical odel can be applied in a real fouling and cleaning process. The current dissolution odel does not take account of the role of shear force in the reoval of large pieces of deposits. However, the odel provides a good foundation for further studies on the cleaning echaniss of protein-based ilk fouling. CKNOWEDGMENTS This work was partially sponsored by the Foundation for esearch, Science and Technology progra, Fonterra Co-operative Group td. NOMENCTUE surface area of deposits, 2 deposit surface area left in decay stage, 2,0 total surface area covered by the protein fil, 2 E a the apparent activation energy, J/ol f( e a linear function between eynolds nuber and odel paraeters (Eq.28 k a reaction rate. k a rate constant for the surface area reduction, s -1 (Eq.12 k d disengageent rate, s -1 (Eq.3 k a ass transfer coefficient, g/ 2 s (Eq.1 ass reoved, g/ 2 c critical ass, g/ 2 u ass reoved during unifor stage, g/ 2 su ass reoved during swelling and unifor stage, g/ 2 g ideal gas constant, J/olK e eynolds nuber constant cleaning rate, g/ 2 s T absolute teperature, K t d cleaning tie in decay stage, s t r reptation tie, s t su sus of cleaning ties in swelling and unifor stage, s t t total cleaning tie, s t u reptation tie in unifor stage, s y sybol of odel paraeters (Eq.27 Greek letters α a constant (Eq.28 β a constant (Eq.28 the volue fraction of the disengaged protein olecules at gel-solution interface (Eq.1 axiu volue fraction of the disengaged protein olecules (Eq.4 0 volue fraction of the tangling protein chains at the solution side of gel-solution interface at the tie t = tr. ξ kinetic constant, s -1 (Eq. 4 ψ diensionless paraeter (Eq.8 8

10 Xin et al.: eoval of Milk Protein Deposit EFEENCES Beaudoin, S. P., Grant, C. S. and Carbonell,. G., 1995, eoval of organic fils fro solid surface using aqueous solutions of nonionic surfactants, Industry Engineering Cheical esearch, Vol. 34, pp Bird, M.., 1993, Cleaning of food process plant, PhD dissertation, University of Cabridge, UK. Devotta, I., ebeskar,. B., Mandhare and Mashelkar,.., 1993, The life tie of a dissolving polyeric particle, Cheical Engineering Science, Vol. 49(5, pp Devotta, I., Badiger, M. V., ajaohanan, P.., Ganapathy, S. and Mashelkar,.., 1995, Unusual retardation and enhanceent in polyer dissolution: role of disengageent dynaics, Cheical Engineering Science, Vol. 50(16, pp Gallot-avallée, T. and alande, M., 1985, echanistic approach of pasteurised ilk deposit cleaning, Fouling and Cleaning in Food Processing, Madison, US, pp Gillha, C.., Fryer, P. J., Hasting,. P. M. and Wilson, D. I., 1999, Cleaning-in-place of whey protein fouling deposits: echaniss controlling cleaning, Food and Bioproducts Processing, Vol. 77(C2, pp eclercq-perlat, M. N. and alande, M., 1991, review on the odeling of the reoval of porous containants deposited on heat transfer surfaces, International Cheical Engineering, Vol. 31(1, pp Papanu, J. S. and Soane, D. S., 1989, Transport odels for swelling and dissolution of thin polyer fils, Journal of pplied Polyer Science, Vol. 38, pp Parker,., Vigouroux, F. and eed, W. F., 2000, Dissolution kinetics of polyer powders, IChE Journal, Vol. 46(7, pp Peppas, N.. and Wu, J. C., 1994, Matheatical odeling and experiental characterization of polyer dissolution, Macroolecules, Vol. 27, pp anade, V. V. and Mashelkar,.., 1995, Convective diffusion fro a dissolving polyeric particle, IChE Journal, Vol. 41(3, pp Schlussler, H. J., 1970, Cleaning of hard surface in the food industry, Milchwissenschaft, Vol. 25(3, pp Xin, H., 2003, study of the echaniss of cheical cleaning of ilk protein fouling using a odel aterial (whey protein concentrate gel, PhD dissertation, University of uckland. Xin, H., Chen, X. D. and Özkan, N., 2002a, Cleaning rate in the unifor cleaning stage for whey protein gel deposits, Trans ICheE, Vol. 80(Part C, pp Xin, H., Chen, X. D. and Özkan, N., 2002b, Whey protein based gel as a odel aterial for studying initial cleaning echaniss of ilk fouling, Journal of Food Science, Vol. 67(7, pp Published by ECI Digital rchives,