167

MATHEMATICAL MODEL OF RAW HIDE CURING WITH BRINEby

EDUARD HERNANDEZ BALADA l2 , WILLIAM N. MAluviERl*, KAREL KOLOMAZNIK3 , PETER H. Coo 1 AND ROBERT L. DUDLEY'U.S.' Department ofAgriculture, Agricultural Research Service, Eastern Regional Research Center

600 EAST MERMAID LANE, WYNDMOOR, PA 19038 USA'Department of Chemical Engineering, University of Barcelona

MARTI I FRANQUS 1, 08028 BARCELONA, SPAIN3 Tomas Bata University

MOSTNI 5139, 760 01 ZLIN, CZECH REPUBLIC

ABSTRACT

The most common method of preserving raw hidesis brine curing with sodium chloride. However, thisprocess has three important disadvantages: first, thelength of time that it takes, which is a minimum of18 hours; second, the insufficient degree of curingreached in some hides due to an overload andpossibly the low efficiency of the brine raceway; andfinally, the environmental impact associated withthe discharge of large quantities of electrolytes in thesoaking step. Our long term goal is to address allthree issues. Initially, we have carried out a studyof the salt uptake and its diffusion mechanism inorder to attempt a reduction in the curing time. Acontinuous reaction mathematical model of a closedone dimensional system that describes the diffusionof sodium chloride in the hide during the curingprocess was chosen in the search for the optimumbrine curing conditions such as the optimum brineconcentration and percent float. The effect of thesetwo parameters on the values of transport coefficient

was reported. Brine diffusion into the hide wastracked by measurement of the chloride concentrationof the residual brine solution. In addition, a piece ofhide was cured with a fluorescently labeled brinesolution and analyzed by means of epifluorescentmicroscopy for direct visualization of the sodiumlocation within the hide.

RESUMEN

El método más comi.'in para preservar pieles crudases el curado con salmuera. Sin embargo, esteproceso presenta tres desventajas: en primer lugar,el tiempo que requiere, un mIriimo de 18 horas;en segundo lugar, el insuficiente nivel de curadoalcanzado en algunas pieles debido a la sobrecarga ybaja eficiencia del tanque de curado; y finalmente, el

impacto medioambiental asociado con la descarga degrandes cantidades de electrolitos en la operación deremojo. Nuestro objetivo a largo plazo es resolver losmencionados problemas. Inicialmente, estudiamos laabsorción de sal y su mecanismo de difusión a fin dereducir el tiempo de curado. Un modelo matemáticode reacción continua de un sistema unidimensionalcerrado fue escogido Para describir la difusión decloruro de sodio en la pie1 durante el proceso decurado a fin de buscar las óptimas condiciones decurado, tales como la concentración optima desalmuera y el porcentaje óptimo de baflo. El efectode estos dos parámetros en los valores del coeficientede transporte 2 son presentados. La difusión de sal enla pie] fue monitorizada mediante la determinaciOnde concentración de cloruros en la solución residualde salmuera. Además, una muestra de piel fuecurada con una solución de salmuera etiquetadacon una sustancia fluorescente y analizada mediantemicroscopla epifluorescente Para la visualizacióndirecta del sodio en la pie1.

INTRODUCTION

Raw hides and skins are - 60-70% water and - 25-30%protein. In this form the hide is susceptible to bacterialactivity within hours after being removed from the carcass.The autolytic degradation of skins/hides is assumed to be dueto a combined action of tissue enzymes and bacteria, the latterrequiring moisture to be viable.' Curing is the process thatprovides an environment in which bacteria cannot survive.Several curing agents have been reported in the literature, e.g.,potassium chloride , 2 silica gel,'-' boric acid,' and herbal-basedproducts .6 Common salt, in spite of its inherent impact onthe environment and the large amount required, is the mostpopular and inexpensive material used to preserve hides andskins. A suitable improved method would yield savings in salt,shipping and effluent treatment costs as well as a diminishedenvironmental impact. Mathematical modeling has been

* Corresponding Author - Email address: william.marmer@ars.usda.govMention of trade names or commercial products in this article is solely for the purpose of providing specific informationand does not imply recommendation or endorsement by the U.S. Department of Agriculture.Manuscript received November 14, 2007, and accepted for publication November 19, 2007

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MODEL OF RAW HIDE CURING

c(hr)=r'c0(r) V

(O,rj=O \\ c,(r)

I/I

k)L'1j

flesh side OA

b

(1>1'

Figure 1: Mathematical model of the curing process of a raw hide.

reported to be a powerful tool in the optimization of processessuch as soaking of salted cattle hides. 7 '8 Curing has beenmodeled in substrates such as cheese" () and meat", but has notbeen studied for the particular case of raw hides.

The aim of this work is to develop and verify a mathematicalmodel that describes the diffusion of sodium chloride in thehide during the curing process. Upon its verification, themodel is applied in the search of the optimum values of processvariables such as brine concentration, float percentage andcuring time.

THEORY

We propose a continuous reaction model to describe thediffusion of sodium chloride from the bath containing brinesolution to the surface of the solid phase (hide). The modelassumes that salt will further diffuse into the hide's innervolume where it will form a non-stationary concentrationfield (Figure 1). It also assumes that diffusion takes place onlyinto the flesh side and that hide parameters such as thickness,surface and properties of both hair and flesh sides will remainconstant throughout the whole process.

Curing can be considered as a counter diffusion in whichsodium chloride soaks into the skin as water simultaneouslywashes out. Equation (1) describes a non-stationary onedimensional concentration field inside the inner volume of thesolid phase, defined by Fick's second law. Boundary condition(la) assumes that sodium chloride diffuses into the hide fromthe flesh side only. Terms are defined at the end of the paper.

acD.---(x,r)O<x'<b'r>O

(la)Ox

Equation (2) corresponds to a mass balance of a closed systemin which salt flow at the hide surface is equal to accumulationspeed of sodium chloride in the bath. Equations (2a) and(2b) are the initial boundary conditions (t = 0). They assumea null initial content of sodium chloride in the fresh hideand a constant initial value of brine concentration in thebath respectively.

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Figure 2: Dimensionless sodium chloride concentration field within thehide during the curing process.

(2)ax dx

c(x,O) = 0 (2a)

c0(0)=c01,(2b)

Equation (3) is valid under an ideal mass transfer from the bulksolution to the surface of the solid phase.

c(b,x) = £ c, (r) (3)

The introduction of dimensionless parameters (equations 4ato 4e) has been demonstrated to be a useful tool in the modeldevelopment.

C = LC0p (4a)

C,CID

(4b)op

X =' (4c)

xF

D0 =--- (4d)

Na=J2- (4e)

The dimensionless time, also called Fourier's number [F0],assesses the proximity of the process to the equilibrium, i.e.equilibrium is reached when F 0 --- . The dimensionlesssoaking number [Na] expresses the ratio between the volumes ofliquid and solid phases. The replacement of the dimensionlessparameters into the previous model leads to a new dimensionlessmodel (Eq. (5a) to (50).

MODEL OF RAW HIDE CURING 169

N.

N 20-

N10-.--<

C)

02040808112141818

IFigure 3: Dimensional sodium chloride concentration field within the

hide during the curing process.for various soaking numbers.

O<X<l F. >0

Q1, F,) = C O (FO) (5b)

(50ax aFO

(0,F)=Oax

0 (5d)

C(X,O) = 0 (5e)

C'(0) = 1 (50

the analytical solution of which can be obtained by means ofLaplace's transformation:

c(x FNa +2Nacos(Xg,)eT-o g"

e+Na esin(g )E cos(g,,)--g Na'sin(g)91,

(6)Where g0 are the roots of the transcendent equation (7).

Nagtg(g) = -(g0 > 0) (7)

E

The three dimensional concentration field graphiccorresponding to Eq. (6) is shown in Figure 2.

Replacing Eq. (7) into Eq. (6) and rearranging terms (for X = 1),we obtain an equation that illustrates the variation of brineconcentration with time.

-F0 -g

c0( F Nag°'- Na +2Na

Na's+Na+(8)

In addition, integration of Eq. (6) leads to Eq. (9) whichcalculates the optimal time in order to reach a certaincontent of sodium chloride in the skin, C (integral averageconcentration).

-Na F0gaC(F)-2Na2e+Na

(9)Figure 3 shows the curves of the integral average concentrationfor various values of soaking number.

Determination of Diffusion CoefficientsThe value of effective diffusion coefficient of sodium chloridein the hide can be evaluated from experimental data. Crank"suggested an equation for the diffusion coefficients study atshort times:

COP c0(t) =1+Na ,j -c 0 , -c0 (cc)Na

(10)From the mass balance

V0 = C12 V + E CO. V(11)

We getCOP Na

CO =

Na+ c (12)

Transport parameter ? is defined as a ratio of the effectivediffusion coefficient D' to pore half length (a) square.

A D - D'

a 2--- ( 13)

when the factor for the tortuosity of the pores:

(14)

?. is an important value from an engineering point of view sinceit includes two phenomena not considered in the presentedmodel, which are the transport of water from the hide to thebath and the interaction between sodium chloride and watercounter flows during the curing.

EXPERIMENTAL

MaterialsFresh cow hides were purchased from a local abattoir. Theywere soaked for 2 h (with surfactant) and then fleshed.Approximately 6 x 10 in (15 x 25 cm) pieces were cut andstored at -20°C. They were thawed at 4°C just before use.Food grade sodium chloride of purity minimum 99.82% wasobtained from US Salt Corporation (Watkins Glen, NY). Allother chemicals were reagent grade and used as received.

MethodsThawed hide was cut into square pieces of approximately 4 x4 in (10 x 10 cm) with an average weight of .- 100 g. Theywere transferred to a Dose drum (Model PFI 300-34, DoseMaschinenbau GmbH, Lichtenau, Germany), and tumbled at

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- FIesI4h5h24h48h

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MODEL OF RAW HIDE CURING

Figure 4: Epifluorescent microscopic images of a cross section of a hide atdifferent stages of curing. The hide was cured with 30% (w/v)labeled sodium chloride solution.

0.70

0.600.50

0.40

0.300.20

0.10

0.001012

4 4rniuf)

Figure 5: Determination of transport parameter X from experimentaldata. The graph corresponds to cOp = 30% (wlv) and Na = 3.

6 rpm with brine solution for varying time intervals after whichthey were pulled out of the drum, hand-squeezed to wipe excesswater, sealed in plastic bags and placed in the refrigerator. Afraction of the residual brine solution was also collected atdifferent time intervals. Two sets of experiments were carriedout: a constant 300% (v!v) float (volume of brine solution/volume of hide) at different initial salt concentration levels(20%, 25%, 30% and 35% (wlv), which correspond to 64,80, 96 and 100°SAL, respectively) and a constant 30% (wlv)initial salt concentration (weight of NaCl/volume of solution)at different float percentages (300%, 500%, 750% and 1000%v/v). Density of hide was assumed to be - lg/cm3.

AnalysesChloride concentration determinationChloride concentration was determined by classical Mohrtitration.' 3 Residual brine samples were diluted (1:100 v/v)in nano pure water prior to titration. All samples were runin triplicate.

Fluorescence ImagingCoroNaTM Green Sodium Indicator fluorescent dye (Invitrogen,Carlsbad, CA) was used as a probe of sodium ions diffusinginto raw hide from brine solution. A piece of raw hide ofapproximately 1 x 1 in (2.5 x 2.5 cm) was immersed in abeaker containing 500% v/v float of a 30% w/v NaCl solution

and 5pM of the fluorescent dye and gently agitated. A 2-3 mmwide slice of the sample was excised manually with a stainlesssteel razor blade (cutting from flesh surface toward the grain) atregular intervals of incubation time, then mounted onto Petridishes for imaging, using a Leica MZ FUJI stereomicroscope(Leica Microsystems, Bannockburn, IL, USA) equipped forepifluorescence and with a model DC200 color charge coupledevice camera system at 2.5x magnification. Samples wereirradiated with blue (470/40 nm) and UV (360/40 nm) light,and images of the fluorescence were acquired at 0.1 (blue)and 0.44 (UV) seconds of exposure time. Control samples,immersed in 500% v/v nano-pure water and 5pM dye, wereexamined under the same conditions of concentration and timeto assess the penetration of the fluorescent dye in the absence ofsalt, and a blank sample was also examined to evaluate possibleautofluorescence of the untreated raw hide.

RESULTS AND DISCUSSION

Results and Discussion Epifluorescence MicroscopyThe diffusion of labeled sodium ions into the cross sectionof hide samples was followed by means of epi-fluorescentmicroscopy. In Figure 4, increased fluorescence indicatingdiffusion of salt started on the flesh side and gradually movedtoward the hair side. The lack of fluorescence development atthe hair side validated the mathematical assumption describedby Eq. (la); this can be attributed to the existence of a thinprotective barrier of sebaceous oil.i4 The series of imagesdemonstrate the advance of fluorescence due to sodiumions into the cross sections of hide as well as increasesin fluorescence intensity throughout curing time. Signalsaturation in the area near the flesh side, denoted by a verybright fluorescence, was observed after 5 h of curing. Theapparent retrograde movement of the labeled sodium between2 h and 5 h may be due to the shrinking of the hide caused bydehydration. Surprisingly, sodium ions did not seem to reachthe hair side even after 48 h of curing. This could be due tomany factors. In order to determine if the penetrability ofthe dye is a technical factor, a sample of hide incubated in anaqueous solution of dye for 24 hours was examined under themicroscope and then transferred to a beaker with concentratedbrine solution for 24 more hours. The dye did not fluoresce inthe uncured sample but showed a high fluorescence after beingcured for 24 hours (graphs not shown). However, fluorescencewas absent or undetectable in the upper part of the corium,leading to the possibility that the dye may not penetrate intothe tightly-woven and dense structure of the corium, possiblydue to its size (MW = 586 Da). The use of scanning electronmicroscopy with energy dispersive X-Ray spectroscopy (SEM-EDS) and elemental mapping to measure the amount andlocation of salt in a brine-cured hide is an alternative methodto fluorescence imaging and this approach is planned.

Determination of Diffusion CoefficientsThe diffusion of salt in the hide was evaluated by means of thetransport coefficient X, which can be calculated from the slopeof the straight line that results from plotting C 0(t) versus squareroot of time (Eq. 10). Taking into account early published

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MODEL OF RAW HIDE CURING 171

TABLE ITransport Coefficient ? for Various Conditions of Initial Brine Concentration

(c0 ) and Soaking Number (Na)

Na=3 Cop =30%(wlv)

(% w/v)k iO (s')R2 Na ? 10 (s') R2

20 4.2 0.83525 3.8 0.92130 5.3 0.94935 10.7 0.776'

a2 < critical value for a = 0.05.

results 12 and the accuracy of our measurements, the lineardependence holds approximately as far as to the value of C0(t)= 0.6. Figure 5 depicts this correlation for the particular caseof c11 = 30% (w/v) and Na = 3.

As seen in Table 1, all X values, except from that of c0=35%(wlv), are on the order of 10 s. These results are of the sameorder of magnitude as those reported in the mathematicalmodel of soaking 15, which suggests that the diffusion of saltdoes not significantly differ between curing and soaking. Anumerical value of ?. for c11 =35% (wlv) may not be reliable,because the brine was initially supersaturated and the modelwas developed for homogeneous solutions solely. Note thana saturated brine solution holds 31.7g of salt in 100 ml ofsolution, (c0 ) at 25°C.16

A comparison of the individual values of X is not simple, sincethey may be affected by some of the following factors: 1. Thethickness of the hide, which may vary throughout the processand exerts a strong effect on the value of?, as seen in Eq. (13).2. The pore length, which varies among the hides and is hardlymeasurable. 3. The dry matter content of the hide, the variationof which may extensively modify ?.. In fact, ? may drop upto two orders of magnitude between a wet and a dry hide. 15,174. The temperature, which affects the diffusion rate and wassometimes difficult to keep at 25°C during the process. 5. Theinfluence of the error in the measurement, i.e. the difficultyto measure a small chloride concentration diminution withthe Mohr method despite the very low coefficient of variation(CV) found for this technique (< 1%).

Even so, one can draw the conclusion on the effect that both c0and Na exert on the values of?.. Increasing values of c0p yieldedlarger values of ?. as a consequence of an increasing gradientconcentration between the solid phase and the solution, whichis in accordance with Fick's second law of diffusion. This factcorroborates a general practice applied in curing raceways,where solid salt is periodically added to the brine solution tokeep it close to saturation (a 97 'SAL). The float percentagealso exerts a remarkable effect on the values of transportparameter 7. Larger floats yielded faster diffusion of saltinto the hide, even though that effect became less significantfor Na > 5. That experimental observation corroborates the

5.3 0.949

9.0 0.887

7.5

4.1 0.905

10

8.6 0.876

common practice in tanneries, which operate at Na 4 eventhough the generally accepted rule requires a Na ^- 5 in orderfor hides to receive a proper cure) 8 In addition, a large floatwill help maintain an almost constant salt concentration. Theoutstandingly low value of? obtained for Na = 7.5 may be dueto factors inherent to the hide, e.g., poor fleshing, which slowsdown salt penetration, agglutination of the fibers and contentof dry matter.

Determination of Optimum Brine Curing ConditionsAn 85% salt saturation of the water remaining in the hide wasestablished as a minimum standard in order to attain a properdegree of cure. 19 One can calculate the theoretical minimumsoaking number needed to attain this saturation percentage inthe equilibrium, that is, at infinite time, and without furtheradditions of salt into the solution. From Eq. (8), If T— then

F -; thus the second summand can be neglected, giving:

C c oNa

Colls+Na (15)

Replacing C = E Co and rearranging for Na,

Na C=

C I Cop -c (16)

Using C = 0.85 • C c o ,,, a porosity of E = 0.5 and co, = 30 %(wlv), and assuming that all pores are filled up with brinesolution, a soaking number of 4.4 is needed to reach 85%saturation. Solving Eq. (16) for Co. = 20 and 25% (wlv),negative values of Na are obtained, indicating the unfeasibilityto attain 85% saturation. On the other hand, the minimumsoaking number would drop to 2.8 if the cure was startedout with a saturated brine solution (31.7 % (wlv), or100 'SAL). Notice that these values depend on the porosity ofthe hide, which varies from one to another and within itself.21Therefore, slightly different values of minimum Na's would beobtained using another value of porosity.

Working out the value of c0 from Eq. (16) and usingNa = 3, we received a minimum initial brine concentrationof 30.8% (wlv) in order to achieve the target saturation level.

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By means of Eq. (9), the plot of which is depicted in Figure3, one is able to calculate the curing time needed to reach an85% salt saturation in the hide. As just mentioned above,this level cannot be achieved for c0 = 20, 25 and 30% (wlv)and Na = 3. However, a time of 4.2 h is obtained for a 35%(w/v) supersaturated brine and Na = 3. The 85% saturation isalso achieved in 4.9, 7.7 and 3.4 h if the hide is cured with abrine of c0 = 30% (w/v) and Na = 5, 7.5 and 10, respectively.These values are substantially lower than the 18 hours thatusually are required for a full cure in a normal float (Na-5).The calculations of those times contain the parameter ?.,and therefore are affected by the same factors mentioned inthe previous section. In spite of this, it is interesting to notethe decrease of curing time with increasing float percentages,except from the erratic value obtained for Na = 7.5.

CONCLUSIONS

Over 20 millions brine-cured hides were exported by the U.S.in 2006 (U.S. Leather Industry Statistics, 2007). Increasingcommodity prices for sodium chloride over the past few yearstogether with issues associated with water pollution set thealarm off in the leather and meatpacking industries. Thepurpose of research reported in this article was to optimize thebrine curing of hides and skins under specific process conditionsby means of mathematical modeling. The diffusion of salt intothe hide was characterized by the transport coefficient X, whichwas found to be in the order of 10 s'. The usage of saturatedbrine as well as large floats (>500%) yielded higher values of?., therefore higher diffusion rates. From the model it wasalso possible to determine the minimum float and initial brineconcentration needed to attain an 85% salt saturation in thehide. This saturation level was not achieved employing brinesof initial concentration of 20 and 25% (wlv) independently ofthe float percentage used. For 30 and 35% brines, a minimumfloat of - 440% and -280% was found, respectively. Usinga 30% (w/v) brine, the targeted 85% saturation is attainedin shorter times as the % float increases, and one may expectthe same trend for any other initial brine concentration. Theestablished 85% salt saturation in the hide obviously plays acritical role in the search for optimum conditions of curing,and the need to attain this saturation level for a proper cure willbe discussed in our next contribution.

ACKNOWLEDGMENTS

The authors would like to thank Eleanor Brown, LaurelieBumanlag, Gary Di Maio, Rafael Garcia, Michael Kurantz,Joseph Lee, John Phillips, Maryann Taylor and MichaelaUhliffová for their technical support and assistance.

DEFINITION OF TERMS

c: concentration of sodium chloride in the hide moisture, at adistance x from the boundary (t > 0) [mol m3]

co : concentration of sodium chloride in the bath (t > 0) [molm]

Con: concentration of saturated sodium chloride solution at25°C [mol m]

cop: initial concentration of sodium chloride in the bath (t =

0) [mol m3]c. equilibrium concentration of sodium chloride in the bath- [mol m3]C : dimensionless concentration integral average [1]D: diffusion coefficient of sodium chloride in the hide [m 2 s1]D': effective diffusion coefficient of sodium chloride in the

hide [m 2 s1]S: outer surface of the solid phase (skin) [m2]a: pore half length of the skin [m]b: thickness of cured hide [m]Na: soaking number [1]V: volume of skin [m3]V0 : volume of brine solution [m3]F0 : Fourier number/dimensionless time [1]X: dimensionless distance [1]C, Co : dimensionless concentrations [1]Greek symbolsT: time (s)C: porosity of solid state [1]X: transport coefficient [s]

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