Annotated Bibliography On Food Fat

Journal of Food Engineering 109 (2012) 49–61

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Journal of Food Engineering journal homepage: www.elsevier.com/locate/jfoodeng

A spinning disc study of fouling of cold heat transfer surfaces by gel formation from model food fat solutions
Jen-Yi Huang, Y.M. John Chew, D. Ian Wilson ⇑
Department of Chemical Engineering and Biotechnology, University of Cambridge, New Museums Site, Pembroke Street, Cambridge CB2 3RA, UK
Department of Chemical Engineering, University of Bath, Claverton Down, Bath BA2 7AY, UK

a r t i c l e

i n f o

Article history:
Received 10 August 2011
Received in revised form 19 September
2011
Accepted 29 September 2011
Available online 8 October 2011
Keywords:
Crystallisation
Fats
Fouling
Freezing
Gel
a b s t r a c t
The formation of immobile gels on heat transfer surfaces (‘coring’) caused by cooling fat solutions below their cloud point was studied using a novel spinning disc apparatus (SDA). The SDA features a cooled, removable heat transfer surface with well defined heat and mass transfer characteristics. Measurements of heat flux were combined with computational fluid dynamics simulations to yield reliable estimates of the surface temperature and shear stress. Fouling studies were performed with model solutions of 5 wt.% tripalmitin in a paraffin oil operating in the ‘cold start’ mode, wherein the experiment starts with the surface colder than the steady state, simulating one mode of operating a standard ‘cold finger’ experiment.
Local heat flux measurements allowed the thermal fouling resistance to be monitored: deposit mass coverage and composition were also measured. The cold surface promotes the rapid formation of an initial gel layer, followed by a period of linear fouling, and finally falling rate fouling behaviour. The linear fouling rate was relatively insensitive to temperature and shear rate, while the fouling rate in the falling rate regime was found to depend on the temperature driving force for crystallisation kinetics. The solids fraction within the deposit layer increased over the duration of a 12 h fouling test, indicating rapid ageing.
The rheological properties of the deposits were highly sensitive to solids fraction.
Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction
The accumulation of unwanted solids on process surfaces is a persistent problem. These materials usually have low thermal conductivity, creating significant resistance to heat transfer. This fouling deposition can also cause partial or complete blockage of piping and process equipment, reducing flow rate together with increasing pressure drop. The formation of deposits from liquid fats on cold surfaces can affect both heat exchangers and distribution lines in the food sector. This ‘coring’ of distribution lines can impair product quality by contamination and by harbouring micro-organisms, as well as reducing the performance of trace heating or cooling designed to maintain the fat in a particular state.
Coring is an example of crystallisation fouling, which Epstein
(1983) defined as deposition resulting from solubility differences, such that solids are generated from solution at the heat transfer

Abbreviations: CFD, computational fluid dynamics; DSC, differential scanning calorimeter; NTU, number of turbidity units; PPP, tripalmitin; SDA, scanning disc apparatus. ⇑ Corresponding author at: Department of Chemical Engineering and Biotech nology, University of Cambridge, New Museums Site, Pembroke Street, Cambridge
CB2 3RA, UK. Tel.: [phone]; fax: [phone].
E-mail addresses: [e-mail],[e-mail](D.IanWilson).
0260-8774/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2011.09.034 surface. The fouling layer can form via heterogeneous growth on the surface, as in water scaling, or by crystallisation of the higher melting point components in the solution at the cold interface to yield a viscous, immobile gel which can harden to give a semi-solid deposit over time. The formation of a viscous gel layer is studied here using model solutions of a high melting point fat, tripalmitin
(PPP), in a non-solidifying paraffin solvent.
Food fats are multi-component mixtures and coring shares many features with wax deposition in subsea crude oil pipelines
(Elphingstone et al., 1999; Ribeiro et al., 1997). The major components are triglycerides, with smaller quantities of diglycerides, and these crystallise when the temperature falls below their cloud point, Tc. The cloud point is defined as the temperature at which the solid particles are first detected, and is lower than the equilibrium melting temperature for a given composition, as cooling-driven crystallisation requires the solution to be supersaturated.
Nucleation is a kinetic process, however, and a crystal seed or foreign surface can promote heterogeneous nucleation and growth in this region (Mullin, 1993). The general scenario for crystallisation fouling of food fats is that the solution must firstly reach supersaturation, followed by nucleation and orientation of crystallites, ending up with aggregation and growth of the crystals (Hartel, 2001;
Walstra et al., 2001). Whereas a number of models have been reported for deposition on oil pipelines from waxy crudes

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J.-Y. Huang et al. / Journal of Food Engineering 109 (2012) 49–61

Nomenclature
Roman
a b Cp
D
G
G0
hb
HO
HS
HT
HX
DHfp
kb kf km
K
m n Nd
NPPP
Nu
Nu⁄
Pr q r rd R
Rcw
Rf
Rf⁄
Rw
Relse
Rer
Sc

constant in Eq. (5) constant in Eq. (21) deposit heat capacity, J kgÀ1 KÀ1 diffusivity of solute in solvent, m2 sÀ1 growth rate of deposit thickness, lm sÀ1 elastic modulus in linear region, Pa film heat transfer coefficient in bulk fluid, W mÀ2 KÀ1 combined contribution of HX and HT, J or kJ sensible heat associated with the deposit, J or kJ total heat energy transferred during fouling run, J or kJ latent heat of PPP crystallisation, J or kJ melting enthalpy of PPP, J molÀ1 liquid thermal conductivity, W mÀ1 KÀ1 deposit thermal conductivity, W mÀ1 KÀ1 film mass transfer coefficient of bulk solution, m sÀ1 constant in Eq. (20), lm sÀ1 KÀ1 mass of deposit per unit disc surface, kg mÀ2 constant in Eq. (21) deposition rate, kg mÀ2 sÀ1 mass flux of PPP towards surface, kg mÀ2 sÀ1
Nusselt number, – modified Nusselt number, –
Prandtl number, – heat flux, W mÀ2 radial position, m disc radius, m universal gas constant, J kgÀ1 KÀ1 thermal resistance of coolant side, m2 K WÀ1 fouling resistance, m2 K WÀ1 asymptotic fouling resistance, m2 K WÀ1 thermal resistance of disc wall, m2 K WÀ1 thermal resistance of coolant flow and plates, m2 K WÀ1
Reynolds number of bulk solution, –
Schmidt number, –

(Akbarzadeh and Zougari, 2008; Bidmus and Mehrotra, 2004;
Singh et al., 2000) freezing fouling in food fats has attracted relatively little attention: Fernandez-Torres et al. (2001) presented a fouling regime map of binary fat/solvent solutions based on simple thermodynamic and heat transfer relationships, and developed a heat transfer based model for coring in pipes carrying a laminar flow of fat. The controlling step in deposit growth is largely unknown, and key mechanisms, whether normal growth (Jackson and Chalmers, 1956), two-dimensional nucleation (Hillig, 1966) or screw dislocation (Hillig and Turnbull, 1956), remain to be
identified.
Freezing fouling may occur at rest, such as in a reservoir, or under conditions of high shear rate and large temperature gradients, as in a scraped surface heat exchanger. For this reason, several experimental studies have investigated the effect of thermomechanical history on fouling behaviour. The temperature difference between the bulk liquid and the cold wall is generally regarded as the thermal driving force for deposition. Bidmus and
Mehrotra (2004) reported an increase in wax deposition from oils with an increase in the temperature difference across the deposit layer. Increasing the flow rate may cause deposit removal because of the higher shear force. Other studies (Singh et al., 2000) have shown that under conditions of constant temperature difference between the bulk crude oil and deposit/oil interface, the deposit thickness decreased as the Reynolds number was increased under both laminar and turbulent flow conditions. Most tests employ constant overall temperature difference: as deposit accumulates,

t
t⁄
tF
T⁄
Tb
Tc
Tcw
Tm
Tp m Ts
Tw
DT
U
U0 wX wS wT xb xs XPPP
Y
Greek df lb qb qf sC sEL
/

xd

deposition time, s, min or hr end time of linear fouling rate regime, s characteristic time, s, min or hr surface temperature at the end of linear fouling rate region, oC or K bulk temperature, °C or K cloud point, °C or K coolant temperature, °C or K melting point, °C or K melting point of pure PPP, °C or K deposit surface temperature, °C or K temperature at base plate/deposit interface, °C or K difference between Tm and Ts, K overall heat transfer coefficient, W mÀ2 kÀ1 initial value of U, W mÀ2 KÀ1 solids content in deposit, wt.%
PPP content in the solution entrained in deposit, wt.% total PPP content in deposit, wt.%
PPP concentration in bulk solution, kg mÀ3
PPP concentration at surface, kg mÀ3 mole fraction of PPP in solution, – rheological parameters G’, sC and sEL

deposit thickness, lm apparent viscosity of bulk fluid, kg mÀ1 sÀ1 density of bulk fluid, kg mÀ3 deposit density, kg mÀ3 crossover point of elastic and viscous modulus, Pa the end point of the linear region, Pa solids volume fraction, – can rotational speed, rad sÀ1

the solution-deposit interface temperature rises and the driving force for deposition decreases. Fouling resistance–time (Rf–t) plots usually exhibit falling rate or asymptotic fouling behaviour (Epstein, 1983) and can often be fitted to the Kern and Seaton
(1959) model, even though this model attributes the observed retardation to increased ‘removal’ as the deposit grows rather than temperature effects. Deposit removal by mechanisms such as spalling can occur, as reported by Fitzgerald et al. (2004).
The most commonly used experimental configurations for studying freezing fouling in waxy crude oils are the flow cell loop
(Fitzgerald et al., 2004; Parthasarathi and Mehrotra, 2005) and the coldfinger (Jennings and Weispfennig, 2005). Recently, Nigo et al.
(2009) reported the design and operation of a novel spinning disc apparatus (SDA) featuring a cooled, rotating, vertical cylinder where deposition occurs on the cold, removable base (the sides are insulated). Food fat fouling behaviour is investigated here using a modified version of the SDA reported by Nigo et al. The SDA was fitted with a heat flux sensor which allows the change in local thermal fouling resistance, Rf, to be monitored. Model solutions of
5 wt.% PPP in a paraffin oil, similar to those used by Fitzgerald et al. (2004) and Nigo et al. (2009), were studied and the effects of disc rotation speed, xd, time, and temperature driving force on fouling behaviour were investigated. The thermal performance of the SDA was characterised more fully using computational fluid dynamics (CFD) simulations, so that surface temperature and surface shear stress could be predicted and manipulated readily. The deposit gels formed were analysed to track changes in composition

J.-Y. Huang et al. / Journal of Food Engineering 109 (2012) 49–61

resulting from ageing as reported for wax deposits by Singh et al.
(2001b).
2. Materials and methods
2.1. Spinning disc apparatus (SDA)
Fig. 1(a) shows a schematic of the deposit generation section in the SDA. A detailed description of the apparatus is given in Nigo et al. (2009). The apparatus consists of a cylindrical can partially immersed in a reservoir of test solution. Rotation is provided by a stepper motor. A recirculating water/glycol bath is used to regulate the temperature of the can, Tcw, whilst the temperature of the bulk solution, Tb, is maintained by a water jacket around the reservoir fed by a second, heating, recirculator. The can sides are insulated so that heat transfer occurs primarily through the base. A magnetic stirrer located at the base of the reservoir provides agitation and maintains temperature uniformity in the bulk solution.
The temperature of the bulk solution, coolant and water jacket are monitored by T-type thermocouples connected to a datalogger.
Fig. 1(b) shows the arrangement of the can base, which was used for heat transfer studies and fouling tests. A micro-foil heat flux sensor (Rhopoint, UK, type 27160) is located between a brass block and a removable 316 stainless-steel disc. The sensor was connected to a battery powered solid-state data collection unit located on the top of the can, so that data could be collected without the use of slip rings etc. and downloaded after an experiment. The thermal resistance of the combined plates and heat flux sensor, Rw, approximately 8.2 Â 10À4 m2 K WÀ1, is shown later to be small compared to the other terms.

51

2.2. Heat transfer tests
The surface temperature, Ts, is a key parameter in the fouling mechanism so a series of heat transfer tests were performed to characterize the thermal performance of the system. The same water/glycol mixture was used on the coolant side, in order to maintain coolant flow similarity. Liquid paraffin (the solvent in the fouling tests), 30 wt.% and 78 wt.% water/glycerol mixtures were used as the reservoir (bulk) liquid. These differed primarily in viscosity, so that a range of hydrodynamic conditions could be studied over the range of rotational speeds accessible with the stepper motor. The bulk liquid hydrodynamics were characterised by the Reynolds number, Rer, defined as

Rer ¼

r2 xd qb d lb

ð1Þ

where, rd, xd, lb and qb are the disc radius, the angular velocity of the can, the dynamic viscosity and the density of the bulk solution, respectively. The viscosity was evaluated at the estimated surface temperature, Ts. The experimental conditions and bulk liquid properties are summarized in Table 1.
Heat transfer tests were performed with a charge of 2 L of liquid in the reservoir, as used in fouling tests. The can was initially isolated from the reservoir and coolant circulated to bring it to the required temperature. The data loggers were then activated, the can lowered into the bulk liquid and rotation started. The data reported are the values obtained after steady state was reached.

2.3. Model fat solutions
Test solutions were prepared by dissolving tripalmitin
(PPP, > 85% purity; density, 984 kg mÀ3, Sigma Chemicals, UK) in liquid paraffin at 60 °C to give solutions with composition 2.5, 5, 10,
20 and 50 wt.%. All fouling tests reported here were performed with 5 wt.% solutions. Solution composition was determined by gas chromatography (GC) on samples diluted in n-heptane (Hewlett Packard Agilent 6890 GC equipped with a dimethylpolysiloxane column, 10 m  0.32 mm  0.1 lm, and a flame ionisation detector using helium as the carrier gas). The GC was calibrated and programmed using the BS EN 14105:2003 method.

2.4. Cloud and melting points measurement

Fig. 1. (a) Schematic of the operation of the SDA, (b) construction of the fouling cell plate. Dimensions are in millimeters (not to scale).

The cloud point of PPP solutions was measured under quasi-static conditions, where the only liquid motion was that provided by a magnetic stirrer. The cloud point, Tc, is the onset of spontaneous precipitation and was measured using a turbidity sensor (ODEON meter, NEOTEK-PONSEL, France). The turbidity probe was immersed in the sample held in a 50 mL jacketed beaker (4 cm in diameter and 6 cm in height) and stirred by a Teflon coated magnetic bar at low rotational speed. The sample temperature was measured using a T-type thermocouple and was initially held at
60 °C for 10 min to eliminate any thermal history. The jacket liquid temperature was manipulated to lower the sample temperature at
(i) 0.5 and (ii) 1.5 K minÀ1. Turbidity was recorded at 10 s intervals and Tc taken as the temperature at which a significant and continuous rise in nephelometric turbidity units (NTU) was observed.
The melting point and melting enthalpy of samples was determined using a Perkin–Elmer Pyris 1 differential scanning calorimeter (DSC) fitted with a refrigerated cooling system. Scans were recorded from 0 to 80 °C at heating and cooling rates of 10 K minÀ1.

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J.-Y. Huang et al. / Journal of Food Engineering 109 (2012) 49–61

Table 1
Experimental conditions employed in heat transfer experiments.
30 wt.% water/glycerol
Coolant temperature, Tcw (°C)
Bulk temperature, Tb (°C)
Dynamic viscosity, lb (Pa s)
Reynolds number, Rer
1

78 wt.% water/glycerol

Paraffin1

10.7
34.2–54.3
0.0015–0.006
303–5443

10.6
35.1–60.7
0.01–0.03
47–307

10.6
35.9–61.4
0.03–0.08
11–48

Density at 25 °C, 870 kg/m3, and viscosity 0.166 Pa s at 20 °C; BDH Chemicals, UK.

2.5. Rheological tests
A short rheological study was performed to investigate the effect of shear on the crystallisation of PPP from model solutions undergoing cooling. In the SDA the deposit gels are formed at a cold surface subject to shear. Samples of 5 wt.% PPP solution were tested using serrated parallel plates on a Bohlin CV120 controlled stress rheometer (25 mm diameter, 0.1 mm gap). Temperature control was provided by a Peltier device located beneath the lower plate. The plates were preheated to 55 °C before loading the sample and the sample was initially held at this temperature, at rest, for 10 min. The sample was then subjected to steady shear at a fixed shear stress of 2 Pa while subject to a temperature ramp of steady decrease from 55 to 5 °C at 5 K minÀ1, followed by 10 min at 5 °C. The shear stress was set at 2 Pa in order to avoid shearing any developing microstructure severely while maintaining sufficient measurement accuracy. This shear stress is also representative of the shear stress exerted by the solution on the disc and deposit surfaces in fouling experiments.
2.6. Numerical simulation
Computational fluid dynamics simulation of the flow and temperature fields in the bulk liquid in the SDA were used to generate estimates of film heat transfer coefficient from the bulk liquid and the can base plate and the surface shear stress. These simulations can be performed with reasonable accuracy as the device is operated in the laminar flow regime and yield estimates of surface temperature and shear stress. The commercial finite element method software COMSOL Multiphysics (version 3.5, Chemical Engineering
Module) was used to solve the continuity, Navier–Stokes and the steady state energy equations for a Newtonian liquid. The flow was modelled as being axisymmetric, incompressible, and at steady state. Physical properties, such as density, thermal conductivity and specific heat capacity, were assumed not to change significantly with temperature and were assumed uniform throughout. This study extends the numerical simulation of Nigo et al. (2009), using similar boundary conditions but using modified fouling cell plate and quantitative settings to include a heat flux sensor and different base plate geometry. Moreover, the effect of thermal resistances from the coolant flow and combined plates were taken into consideration to yield more accurate simulation results. The converged solution took approximately 15 min on a desktop PC with a 3.16 GHz dual core processor and 3.33 GB RAM.

ported later show that the transient lasted $60 s. This cold start mode resulted in the formation of an initial gel layer but avoided transients associated with mixing if the PPP charge were added to the solution to start the fouling test. An alternative mode, of warm start, is under development and will be reported in due course. The rotation speeds, xd, employed were 2.2, 3.5, 5.4 and
7.3 rad sÀ1, corresponding to Rer of 26, 41, 64 and 86, respectively.
The cloud point of the 5 wt.% solution was 29.8 °C (at a cooling rate of 0.5 K minÀ1) and coolant temperatures, Tcw, were selected to give a range of precipitation driving forces, namely 9.8 °C (i.e. Tc
À 20), 19.8 °C (Tc À 10), 24.8 °C (Tc À 5) and 29.8 °C (Tc). Fouling tests normally lasted 12 h, but a series of interrupted tests were performed at one condition, for 1, 3, 6, 9 and 12 h, in order to establish reproducibility and to allow stages in deposit growth to be evaluated. The final deposit was removed from the surface using a plastic spatula, weighed and stored for further analysis.
2.8. Deposit analysis
The deposits consisted of gels of PPP crystals in a liquid matrix and contained PPP in the form of solids and entrained solution. The total PPP content, wT, was determined by dissolving samples in a measured excess of n-heptane and measuring PPP content by GC as described above.
The solids content of the deposit, wX, was determined by filtration. About 3 g of deposit was loaded onto a 0.2 lm polytetrafluoroethylene membrane filter paper (Cole-Parmer, USA) and vacuum applied. The filtered solids were washed with hexane (analytical reagent grade, Fisher Scientific, UK) at ambient temperature to remove any entrained paraffin followed by acetone to remove traces of hexane, then allowed to dry at room temperature for an hour before weighing.
The rheology of the deposits was studied using a Bohlin CVO
120 controlled-stress rheometer operating in oscillatory testing mode as reported by Nigo et al. (2009) with the temperature of the bottom (stationary) plate set at 20 °C. Tests were performed using roughened plates (top 25 mm diameter, base 50 mm diameter, gap 1 mm). The oscillating frequency was set at 10 rad sÀ1
(1.59 Hz) and the sample subjected to shear stress from 2.4 Pa to
29.3 kPa in an ascending ramp.
3. Results and discussion
3.1. Crystallisation under quiescent and shear conditions

2.7. Fat deposition studies
Deposition experiments reported here were performed in a
‘cold start’ mode, wherein the test surface and reservoir were initially brought to their respective operating temperatures by circulation of the heat transfer medium before the can was immersed in the bulk liquid and rotation started. This resulted in an initial transient where the test surface temperature increased from one close to that of the coolant liquid to an intermediate value. The transient was studied separately using PPP-free paraffin liquid and data re-

Fig. 2 summarises the melting and cloud point results for the model solutions of PPP in liquid paraffin and can serve as a simple crystallisation map. Both Tm and Tc decrease with decreasing PPP concentration, as expected. The melting point of the PPP melt
(i.e. no paraffin added), at 65.4 °C, compares favourably with the value of 66 °C reported by Sato and Kuroda (1987). The enthalpy of melting, DHfp of the PPP melt was 108 kJ molÀ1, which is lower than that obtained by Kellens et al. (1990), which was attributed to the differences in purity (165 kJ molÀ1, PPP $ 99% pure). The purer

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J.-Y. Huang et al. / Journal of Food Engineering 109 (2012) 49–61

Tc (cooling rate = 1.5 K min-1)

0.7

D

Tm

1e+6

Tc (cooling rate = 0.5 K min-1)

Relative viscosity

PPP mass fraction

1e+7

Tm

0.8

empirical equilibrium curve

0.6
0.5
0.4
0.3

40

1e+5

B

1e+4

30

Tc

1e+3
1e+2

20

A

10
1e+0

0.1

1e-1
25

30

35

40

45

50

55

60

65

70

0
0

2

4

6

8

Tm or Tc [oC]

the sample, higher the enthalpy value as there are more PPP crystals per unit mass.
The Tm data in the figure were fitted to the following solid–liquid equilibrium model for an ideal solution

"
#
DHfp 1
1
À
Tm
R TP m 10

12

14

16

18

20

Time [min]

Fig. 2. Effect of composition and cooling rate on model solution Tm and Tc. Loci drawn through the Tm data show regression fit to ideal solution, Eq. (2). Lines drawn through Tc data sets as a guide to the eye.

ln X PPP ¼

50

C

1e+1

0.2

0.0
20

60

1e+8

0.9

Temperature [oC]

1.0

ð2Þ

where XPPP is the mole fraction of PPP in solution, R is the universal gas constant, and T P is the melting point of the pure component. m The solutions were prepared with set mass fractions (as plotted in
Fig. 2) and the PPP mol fraction was estimated using relative molecular masses for PPP of 807.35 g molÀ1 and 324 g molÀ1 for paraffin
(CnHn+2, where n = 23, from GC analysis). The DHfp value obtained from the data fit, of 211 kJ molÀ1, differs noticeably from the DSC analysis, which can be attributed to impurities in the material and solvent–solute interactions (Davey and Garside, 2000).
The cloud points show a noticeable influence of cooling rate, with lower values observed for slower cooling rates, as discussed by Saiban and Brown (1997). The width of the metastable zone lay between 10 and 21 K of supercooling over the concentration range studied. The simple crystallisation map deduced from the study can serve as a guide to predict the likelihood of crystal formation at a given temperature and concentration. For the cold start operating mode employed in the experiments reported here, immersion of the cold test section in the warm solution at the start of the experiment results in a high initial cooling rate: Fig. 2 indicates that this is likely to promote homogeneous nucleation and gel formation, as observed in the experiments.
An example of crystallisation in the presence of shear is shown in Fig. 3, where a 5 wt.% PPP solution sample was subjected to a steady shear stress of 2 Pa as it was cooled from 55 to 5 °C at
5 K minÀ1. The Tm value for this solution under quiescent conditions was measured at 49.1 °C and the cloud point (at 0.5 K minÀ1) was 29.8 °C. The viscosity was calculated from the measured shear rate and is presented as the relative viscosity, i.e. made dimensionless by division by the viscosity of the paraffin solvent measured under similar conditions. The solution exhibits an initial region, labelled A, in which the relative viscosity is close to unity, indicating the absence of particles.
After about 7.5 min the relative viscosity increases markedly
(region B), corresponding to the appearance of crystals and formation of a suspension: the AB transition marks the ‘mechanical’ cloud point. The sample temperature, at $17 °C, is 12 K lower than the quiescent Tc value. This is partly due to the turbidity meter

Fig. 3. Evolution of viscosity of 5 wt.% PPP solutions while cooling in the rheometer at 5 K minÀ1. Constant shear stress, 2 Pa. Regions A–D separated by vertical dashed lines discussed in text.

detecting the onset of cystallisation, i.e. a low number concentration of particles, whereas the rheometer is sensitive to the formation of a network. The relative viscosity increases by four decades, indicating the formation of a gel, which increases in stiffness across region C as the solution continues to cool. The change in mass of crystals in this region is small (compare the solubilities in Fig. 2), indicating that the change in viscosity is related to gel behaviour.
A high viscosity plateau is reached at $10 °C, where the peaks are indicative of wall slip and a network in the bulk phase. These characteristics were confirmed by tests in a Linkam shear cell, a controlled shear device fitted with observation windows. Similar transitions in fats have been reported previously (De Graef et al.,
2009; Tarabukina et al., 2009; Walstra et al., 2001).
Fig. 3 confirms that as the fat solution cools, once it starts to nucleate, it can quickly form a highly viscous gel. The BC transition could be interpreted as a gelation temperature. Comparing change in relative viscosity in region C with the solids content estimated from the equilibrium locus in Fig. 2 (data not reported) showed the relative viscosity is not a simple function of the final solids content of gel, indicating that the crystallisation under shear condition is under kinetic control. Similar behaviour was observed with other
PPP concentrations. Whilst this test does not replicate the conditions on the SDA exactly, it does confirm that cold start experiments will form gels rapidly, and that the first appearance of crystals is sensitive to shear and cooling conditions.
3.2. Heat transfer
Spinning disc devices are employed in mass transfer studies as the mass flux (and film mass transfer coefficient) does not vary with radial position across the surface. Sparrow and Gregg
(1959) analysed the heat transfer behaviour of spinning discs operating in the laminar regime and showed that the heat flux, q, film heat transfer coefficient, hb, and surface temperature, Ts, are similarly uniform. It should be noted that the laminar regime extends to Reynolds numbers of $100,000. Measurements of the heat flux yield the overall heat transfer coefficient, U, defined as

q ¼ UðT b À T cw Þ ¼ hb ðT b À T s Þ

ð3Þ

Writing U in terms of resistances in series yields

1
1
1
¼ þ Rcw þ Rw ¼ þ Relse
U hb hb ð4Þ

where Rcw and Rw refer to the thermal resistance of the coolant flow and plates, respectively, and are lumped together as Relse. The hb

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J.-Y. Huang et al. / Journal of Food Engineering 109 (2012) 49–61

term is expected to follow a dependency of the form (Sparrow and
Gregg, 1959);

Nu 

hb r d
¼ aRe0:5 Pr1=3 r kb

ð5Þ

where Nu is the Nusselt number based on the disc radius, kb the thermal conductivity of the bulk liquid, Pr the Prandtl number and the parameter a is a constant. Eq. (5) suggests that the data obtained for different liquids should follow similar behaviour when plotted as Nu/Pr1/3 against Rer. The film heat transfer coefficient is not directly accessible, however, and some estimation is required.
An alternative Nusselt number, Nu⁄, can be based on U and its relationship with Nu given by Eq. (6):

Nuà 

Ur d
Nu
¼
1 þ Relse hb kb ð6Þ

Inspection shows that at low Rer, when hb is small and is expected to influence heat transfer strongly, Nu⁄ $ Nu and the dependency on Rer is expected to mirror Eq. (5). At larger values of Rer,
Eq. (6) indicates that Nu⁄ is likely to give a poorer estimate of hb.
This is confirmed by Fig. 4, where the heat transfer dependency on Rer (Eq. (5)) starts to differ from the trend in the data at higher
Rer. Nu⁄ differs noticeably from Nu estimated using Eq. (5) with a = 0.62, indicating that the parameter a required modification, which was achieved by simulation (next section). The above analysis assumes that Relse does not vary strongly with rotation speed, which is considered reasonable because of turbulence in the coolant flow geometry and the influence of constant, conduction contributions. The thermal resistance of coolant side, Rcw, in the SDA system becomes more significant as Rer is increased and this is estimated by difference, as outlined below.
3.3. CFD simulations
The CFD simulations yield predictions of velocity and temperature distributions in the bulk liquid in the heat transfer experiments. The coolant flow is not modelled: its contribution is expressed as a uniform film heat transfer coefficient. Fig. 5 shows the stream functions (contour lines) and the temperature profiles
(coloured background) obtained for one of the sets of conditions employed in deposition tests. Two vortices are evident in the bulk liquid: an upper one driven by the rotation of the disc, and a lower

100

Fig. 5. Flow patterns and temperature profiles in the SDA for paraffin at a disc rotation speed of 5.4 rad sÀ1, Rer = 27. Black arrows are velocity vectors. Colour indicates temperature, dark red = 60 °C (Tb), dark blue = 9.8 °C (Tcw). (For interpretation of references to color in this figure legend, the reader is referred to the web version of this article.)

one induced by the magnetic stirrer acting in the opposite direction. Simulations were run for a set of cases covering the experimental conditions reported in Fig. 4 and values of hb extracted from the simulations. Relse is then estimated from (1/UÀ1/hb) and Rcw, the thermal resistance on the coolant side, is then evaluated from
(RelseÀRw). The static resistance associated with the base plates,
Rw, is assumed to be constant over the range of temperatures considered here. A subset of the results related to deposition testing are presented in Fig. 6. The film resistance 1/hb decreases with increasing Rer, as predicted by the correlation (Eq. (5)), and the simulation values show good agreement with the correlation: fitting the data to a power law trend yielded a power law index of 0.48, in good agreement with the value of 0.50 in Eq. (5). Rcw also decreases with rotation speed, and is consistently smaller than 1/hb, indicating that the dominant resistance to heat transfer lies on the bulk (fat) side.
These results allow Ts to be estimated by combining Eqs. (3) and
(4), viz.

T s ðtÞ ¼ T b À

"
#
q
T b À T cw
1
¼ Tb À hb Rcw þ Rw þ Rf ðtÞ þ h1 hb

ð7Þ

b

where Rf is the thermal resistance of any fouling layer. Assuming that the other resistances do not vary with temperature as fouling develops allows Rf to be evaluated from

0.030

-1/3
Nu* Pr

1

0.1
10

100

1000

10000

Rer
Fig. 4. Effect of xd on Nu⁄ for different test solutions. Symbols: (solid) 30 wt.% glycerol–water solutions, (grey) 78 wt.% glycerol–water solutions, (open) paraffin.
Tb = 50 °C; (triangles)
Tcw = 10.6 °C,
(squares)
Tcw = 10.6 °C,
(diamonds)
Tcw = 10.7 °C, (circles) Tcw = 10.7 °C. Locus shows trend described by Eq. (5) with a = 0.62 (Sparrow and Gregg, 1959).

Thermal resistance [m2 K W -1]

1/U

10

0.025

1/hb

0.020

0.015

y = 0.064x-0.48
R2 = 0.999

0.010

Rcw
0.005

Rw

0.000
0

5

10

15

20

25

30

35

40

45

Rer
Fig. 6. Effect of Rer on the thermal resistances in the SDA: (circle) 1/U, (triangle)
1/hb from simulation, (square) Rcw and (line) Rw. Temperatures as in Fig. 5.

J.-Y. Huang et al. / Journal of Food Engineering 109 (2012) 49–61

Rf ðtÞ ¼

1
1
À
UðtÞ U 0

ð8Þ

where U0 is the initial, clean, overall heat transfer coefficient. Similarly, the temperature at the base plate/deposit interface, Tw (=Ts when Rf = 0) can be evaluated from

T w ðtÞ ¼ T cw þ qðRcw þ Rw Þ

ð9Þ

Fig. 7(a) shows the initial, clean, steady state Ts at over the range of Tcw and xd of interest. The plots show that Ts is more sensitive to
Tcw. A key assumption in these estimates is that the release of enthalpy of crystallisation during deposition is negligible: this is considered further in Section 3.5.
The average shear stress imposed on the disc surface can also be calculated from the simulated velocity field. The shear stress is directly proportional to radial position, r, and Fig. 7(b) shows the average wall shear stress calculated at r from 0 to 0.035 m. The
CFD calculations indicate that the average shear stress is of the order of 0.3–2.3 Pa for the initial clean surface. This compares favourably with the range of surface shear stresses reported by Fitzgerald et al. (2004) using a rectangular duct flow cell of 0.5–4.0 Pa. Larger shear stresses could be obtained in the SDA using a different motor.
Since surface temperature and shear stress are key parameters in freezing fouling, Fig. 7 illustrates the range of surface conditions that can be investigated in deposition studies.
3.4. Fouling profiles

55

ious times. The Rf–t plots in Fig. 8 shows good agreement, with a maximum difference of 3%. Subsequent tests were repeated only when the results were inconsistent with observed trends. These interrupted tests also allowed the evolution of deposit properties to be investigated.
The Rf–t plots obtained in the ‘cold start’ experiments discussed here all showed similar behaviour, exhibiting three stages:
(i) an initial step in Rf,
(ii) a period of linear increase in Rf, followed by
(iii) a falling rate period, where Rf approaches an asymptote.
The initial sharp increase in Rf derives from the cold start mode.
On immersion of the test cell, the warm solution is contacted with the cold surface (below Tc), inducing gel formation. At the same time, the heat flow through the cell is larger than at steady state owing to the transient in heat conduction, resulting in a temporally large heat flux and associated U value. The definition of Rf in Eq. (8) means that there is a transient, with negative Rf values, as shown in
Fig. 9. The figure shows that a thermal steady state was reached within 2 min, by which time a gel layer had been established.
Fig. 9 also shows the transient observed under identical conditions with paraffin alone, in which case no gel is formed and the steady state Rf value is zero. Negative values of Rf associated with roughness enhancing convective heat transfer have been reported by other workers, e.g. Crittenden and Khater (1987), Bansal and

The reproducibility of the fouling test was confirmed by conducting a series of experiments under identical conditions for var-

Fig. 7. (a) Temperature and (b) average shear stress on the disc surface at the radial location from 0 to 0.035 m, extracted from CFD simulations for various Tcw and xd.

Fig. 8. (a) Rf and (b) estimated Ts and Tw during fouling of 5 wt.% PPP solutions at
Tcw = 9.8 °C, xd = 5.4 rad sÀ1. Vertical dashed line in (a) separates linear rate stage from the falling rate stage. Horizontal dashed lines in (b) show salient temperatures for the 5 wt.% solution used.

56

J.-Y. Huang et al. / Journal of Food Engineering 109 (2012) 49–61

0.025
0.020

0.06

Linear rate stage

Transient stage

from Fig. 8 from Fig. 16 from Fig. 18

0.05

2
-1
Rf [m K W ]

-1
2
Rf [m K W ]

0.015
0.010
0.005
0.000
paraffin
PPP solution

-0.005
-0.010
0.0

0.5

1.0

1.5

0.04

0.03

0.02

0.01

0.00

2.0

0

t [min]

1

2

3

4

5

m [kg m-2]

Fig. 9. Initial transients for tests reported in Fig. 8 and for solvent alone.
Fig. 10. Correlation of Rf and m for fouling runs in Figs. 8, 15 and 17.

m
Rf ¼ qf kf

ð10Þ

where qf is the deposit density. The data from experiments reported in this study are plotted in Fig. 10 and show a linear relationship
(R2 = 0.97), in good agreement with Eq. (10). The gradient, of
0.011 m4 K WÀ1 kgÀ1, yields an estimate of qfkf = 91 W kg mÀ4 KÀ1, which is lower than the value expected for the paraffin, of
130.5 W kg mÀ4 KÀ1 (Fitzgerald et al., 2004): qfkf for the PPP solids is expected to be larger again. The difference may be due to the difficulty in collecting all the deposit (affecting m), and any systematic errors in evaluating Rf. The linear relationship does, moreover, indicate that the age of the deposit does not affect heat transfer and that the heat flux measurements provided a reliable monitor of deposit growth. The deposit composition data in Fig. 11 exhibit a noticeable change over the course of the 12 h fouling test. The solids fraction, labelled wX, increased almost linearly to about 15 wt.% over the first 6 h, coinciding with the linear increase in Rf. The subsequent

25

wX

20

wx, ws [wt%]

Müller-Steinhagen (1993), but this transient mechanism is rarely reported, mainly because the experiments start with heat transfer in steady state. The initial step in Rf was reproducible (see
Fig. 8(a)), and decreased as the coolant temperature increased
(Section 3.8).
In the subsequent stages, as deposit accumulates, the depositsolution interface temperature, Ts, increases and the wall temperature, Tw, decreases. The calculated values of Ts and Tw in
Fig. 8(b) show a rapid increase in Ts which slows down following the linear fouling stage and approaches an asymptote, which is close to Tm. Ts is not measured directly, so there is some uncertainty in the estimate. Tests under other conditions showed similar behaviour. Fig. 8(b) shows a moderate decrease in wall temperature over time, which would promote further crystallisation of the gel. It is noteworthy that the end of the linear fouling regime, at a temperature denoted Ts = T⁄ (estimated by eye as the end of the linear region), extends beyond the point where Ts = Tc (here,
Tc = 29.8 °C at 0.5 K minÀ1, reached after $50 min). The controlling mechanism does not, therefore, appear to be crystallisation at the deposit interface, with Ts = Tc, as reported by Singh et al. (2000).
The interrupted tests allow the measured fouling resistance to be compared with the deposit mass, and plots of Rf and deposit mass against time showed that the latter matched the Rf behaviour closely (data not reported), including the transition between linear and falling rate regimes. When deposition is uniform, the relationship between Rf and the mass of deposit per unit disc surface, m, is expected to follow:

15

wS

10

5

bulk concentration
0
0

2

4

6

8

10

12

14

t [hr]
Fig. 11. Evolution of deposit composition for deposits in Fig. 8.

change in wX was less marked, reaching 20 wt.% after 12 h. The composition of the liquid phase within the deposit, wS, is calculated from the measured values of wT (GC) and wX (filtration) via;

wS ¼

wT À wX
1 À wX

ð11Þ

The data in Fig. 11 show wS being similar to that of the bulk liquid, and increasing over time to $10 wt.%. The increase in wS is less marked than that observed in wX, and the enrichment in solution composition (increase in wS) after 6 h was not statistically significant. These data indicate that the deposit undergoes ageing, mainly through increasing solids content. Further crystallisation of PPP from the solution trapped in the deposit as the local temperature decreases (see Fig. 8(b)) would tend to reduce the concentration of PPP in solution. Higher resolution measurements are required to confirm whether the solution is being enriched, which would require diffusion into the deposit from the bulk solution.
One explanation for the increase in solids content is shear-induced hardening. The latter is related to the shear stress imposed on the surface, which is controlled by xd, and liquid properties
(principally Ts). As fouling continues, Ts increases, the viscosity decreases and the solids composition required to form a gel strong enough to resist deformation by the surface shear stress will increase. These competing aspects of temperature have been reported for wax formation in crude oils by Jennings and
Weispfennig (2005). Shear hardening would not require wS to

57

J.-Y. Huang et al. / Journal of Food Engineering 109 (2012) 49–61

increase. However, in these tests, the change in Ts also reduces the shear stress imposed by the bulk liquid. Decoupling these factors and establishing the driving force for ageing is the subject of ongoing work, including imaging of the deposits.

105

HT
-2
HT, HO, HX [kJ m ]

104

3.5. Fouling mechanisms
Rf–t profiles featuring falling rate and asymptotic behaviour are often fitted to the Kern–Seaton model based on competing deposition and removal processes, viz.

Rf ¼ Rà ½1 À expðÀt=tF ފ f HX ¼ mwX DHfp

ð13Þ

where m and wX are the measured deposit mass coverage and solids fraction, respectively, taken from Figs. 10 and 11. The latent heat of crystallisation was taken as 211 kJ molÀ1 (Section 3.1), which is a worst case estimate as the true value is likely to be smaller, nearer
100 kJ molÀ1. The sensible heat associated with the deposit was estimated from



1
HS ¼ mC p T b À ðT s þ T w Þ
2

ð14Þ

This estimate assumes that the deposit has uniform heat capacity, Cp, taken as that of the paraffin, and a linear temperature distribution across the deposit. Fig. 12 shows that HS was initially the dominant contribution, with HX increasing in importance over time, but the combined contribution (HO = HX + HS) was consistently small, at 1–2% of the total amount of thermal energy transferred. Neglecting latent heat effects in estimating Rf therefore appears reasonable.
3.6. Growth rates
The above calculation indicates that heat transfer was not determining the rate of deposit formation. Further insight into the mechanisms involved can be obtained by comparing the ob-

HO
HX

102

101

ð12Þ

where RÃ is the asymptotic fouling resistance and tF is a characterf istic time, which can be related to initial fouling rate via
½dRf =dtŠt¼0 ¼ Rà =t F . This approach has been applied to wax formaf tion from oils by Nazar et al. (2005), Akbarzadeh and Zougari
(2008) and Ramirez-Jaramillo et al. (2010) but is not appropriate here as (a) the initial linear regime is not consistent with the model;
(b) fitting the Rf–t profiles to Eq. (12) gave systematic deviations in fitting; and (c) the asymptotic level, RÃ , is related to Tm, rather than a f removal step. It is noteworthy that no removal was observed in these tests. Fitzgerald et al. (2004) also reported initial, linear fouling behaviour followed by falling rate behaviour but this was interrupted by spalling, which was not observed in these tests. Future work will consider higher rotation rates to see if this can induce spalling in these deposits.
The estimates of Rf, surface and wall temperatures reported here assume that the enthalpy released on forming the deposit,
i.e. from PPP crystallisation, is small compared to the total rate of heat transfer. The heat flux sensor measures the rate of heat transfer to the coolant, so if the rate of latent heat evolution were significant, the rate of convective heat transfer would be less than the measured value: Eq. (3) indicates that a lower q would result in higher Ts. The contribution from latent and sensible heat effects on heat transfer was therefore considered by comparing the enthalpy associated with forming the deposit with the total amount of thermal energy transferred through the heat flux sensor over the course of a 12 h fouling test.
The enthalpy of crystallisation associated with the crystals in the deposit, HX, was estimated from

103

100
0

2

4

6

8

10

12

14

t [hr]
Fig. 12. Comparison of cumulative HT, HO (= HX + HS) and HX for fouling runs in
Fig. 8.

served deposit growth rate with one estimated from the maximum rate of mass transfer of PPP to the surface. The 5 wt.% solutions can be considered dilute (the mole fraction of PPP in the bulk solution is $0.02): the mass flux, NPPP, from the bulk solution with PPP concentration, xb, towards the surface where growth occurs (with local concentration, xs) can be estimated from

NPPP ¼ km ðxb À xs Þ

ð15Þ

where km is the film mass transfer coefficient, and xi is a mass concentration (in kg mÀ3). The maximum flux was estimated by setting the concentration at the surface, xs, to be that in equilibrium with solid PPP at the surface temperature, Ts (i.e. rapid crystallisation).
The rate of deposition, Nd, can then be estimated from the solids content of the layer, wX, via

Nd ¼

km ðxb À xs Þ wX ð16Þ

Gregory and Riddiford (1956) reported the following expression for km for a disc rotating in an infinite Newtonian fluid;

km ¼ 0:62

D 1=2 1=3
Re Sc rd r

ð17Þ

where Sc is the Schmidt number, expressed as;

Sc ¼

lb qb D

ð18Þ

Here D is diffusivity of solute in solvent, which was estimated from the Wilke Sand Chang correlation (2005) to lie in the range of 4–17 Â 10À11 m2 sÀ1 for the PPP/paraffin solutions employed here. Calculation of Nd requires evaluation of the transport parameters and xs, and hence the surface temperature: Ts was calculated at selected times using Eq. (7) and the experimental Rf value.
The actual deposition rate was estimated from the thickness growth rate, G, by Nd = qfG. The thickness growth rate, G, was calculated from the Rf measurements by assuming the deposit thickness, df, to be uniform and kf known, via;

G¼

dd dRf ¼ kf dt dt

ð19Þ

The gradient dRf/dt (and also the surface temperature, Ts) were evaluated by interpolating the Rf and Ts data sets and extracting values at particular points.
Fig. 13 shows the rates calculated for the 12 h fouling experiment in Fig. 8. Over the first 300 min, where linear fouling was observed, the deposition rate calculated from the Rf data was

58

J.-Y. Huang et al. / Journal of Food Engineering 109 (2012) 49–61

The fitted line does not pass through the origin, which is attributed to the systematic uncertainties involved in calculating Ts from the experimental data.
3.7. Effect of velocity

Fig. 13. Comparison of deposition rates estimated from Rf data and maximum rate of PPP mass transfer for 12 h fouling experiment in Fig. 8.

considerably smaller than the maximum PPP mass flux, indicating that fouling was not controlled by mass transfer in this regime. The mechanism remains to be determined, as the subsequent studies of temperature and velocity show the fouling rate to be relatively insensitive to these parameters.
In the falling rate regime the actual deposition rate is close to Nd estimated by this simple mass transfer model. The main reason for the variation in Nd over time in Fig. 13 is the change in (xb À xs) with Ts, and in the falling rate regime this could be attributed to mass transfer or crystallisation effects.
The transition from linear to falling rate fouling behaviour indicates a change in growth mechanism and this section considers the latter phase. No particulates were present in the bulk solution, and inspection of Figs. 8(a) and (b) suggest that the growth rate in this phase is related to the surface temperature and the temperature driving force DT, the latter being defined as the difference between
Tm and the temperature of crystallisation, here Ts. Ts (and thence
DT) in the falling rate stage was estimated by interpolating the Rf and Ts data sets as described above and extracting values at particular points. Fig. 14 shows the results obtained for the runs in Fig. 8.
A linear trend is evident, which is the form expected for normal growth (Borisov et al., 1968):

G ¼ K DT

ð20Þ

The effect of velocity was studied at four rotational speeds, corresponding to average shear stresses on the disc surface of 0.26,
0.52, 1.03 and 1.66 Pa. Fig. 15 presents the Rf–t profiles obtained from experiments performed at Tb = 60 °C and Tcw = 9.8 °C for
12 h. Under these conditions the test section surface temperature increases with xd, since hb is more sensitive to xd than Rcw. The three stages described previously are evident in each case. The initial step increase in Rf decreased as xd increased. This may occur because the incipient gel is relatively weak, and was less able to resist the shear forces imposed on it at higher xd, or because the new, steady state temperature was warmer at higher xd (Eq. (7)).
The linear fouling rate did not change appreciably with xd, varying from 1.21 Â 10À6 to 1.32 Â 10À6 m2 K JÀ1. Inspection of the (estimated) Ts–t plots indicated that the end of the linear fouling stage occurred at similar values of Ts, around 45.7 °C (i.e. Tm –
4.6 K). After this point, the fouling rate exhibited normal growth kinetics with K value of 1–2 Â 10À5lm sÀ1 KÀ1 and Ts approaching
Tm as discussed above.
The fouling resistance, Rf, reached after 12 h decreased with increasing xd. The associated mass of deposit (m, Fig. 16) was similarly reduced, and the plot of Rf against m in Fig. 10 indicates that the deposit properties were similar to those reported above. The deposit composition data in Fig. 16 show no effect of xd on wS: the variation in wS lies within the confidence limits for the hypothesis that the value is the same for all cases. The solids content, wX, however increases noticeably with xd, by a factor of 3–4Âover the range studied. This result is consistent with the formation of a stiffer deposit to withstand the higher shear stress conditions present at its formation. An alternate explanation, given by Jennings and
Weispfennig (2005), is that the thinner gel (smaller df) and higher hb result in a larger temperature gradient across the deposit, creating a higher diffusive flux for hardening. Again, detailed microstructural distribution data are required to elucidate this behaviour. 3.8. Effect of thermal driving force
Fig. 17 shows the effect of thermal driving force for tests performed at xd = 5.4 rad sÀ1 at four different coolant temperatures.
The initial degree of subcooling (TcÀTcw) ranged from 20 K to zero,

10
9
8

-1
G [μm s ]

7
6
5
4
3
2
1
0
0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

ΔT [Tm-Ts, K]
Fig. 14. Growth rate of df in the falling rate stage for fouling runs in Fig. 8 showing linear dependence on DT. Line shows fit to linear trend.

Fig. 15. Effect of xd on fouling behaviour. Conditions: Tcw = 9.8 °C, t = 12 h. T⁄ and t⁄ are end temperature and time of linear rate stage, respectively.

59

J.-Y. Huang et al. / Journal of Food Engineering 109 (2012) 49–61

Rer
30

5

40

50

60

70

80

40
35

m
4

25

3

wX

20

2

15

wS

wx, ws [wt%]

-2 m [kg m ]

30

10

1
5

bulk concentration
0

0
2

3

4

5

6

7

ωd [rad s ]
-1

Fig. 16. Effect of xd on m and deposit composition for the fouling runs for the fouling runs in Fig. 15.

37 K minÀ1, and the true cloud point would thus be raised significantly by the rapid cooling rate.
The amount of deposit also increased with the degree of subcooling, and Fig. 18(a) suggests a strongly linear relationship. This extrapolated locus continues beyond Tc, and suggests that no deposition would occur when Tcw $ 40 °C. Tests with Tcw > Tc were not performed here. Another factor which may play a role is the presence of the stainless steel surface, which could promote monolayer formation (and heterogeneous nucleation and growth) at temperatures above the bulk cloud point (for homogeneous nucleation).
The linear fouling stage was shorter as Tcw increased, which is consistent with less time elapsing before the transition temperature – again, around 46.1 °C – was reached. The linear fouling rates were similar to those reported above, ranging from 1.04 Â 10À6 to
1.21 Â 10À6 m2 K JÀ1. Falling rate fouling could again be described by Eq. (20), with K values of 1–2 Â 10À5 lm sÀ1 KÀ1.
The deposit composition data in Fig. 18(b) again show little effect of subcooling on PPP concentration in the liquid entrained in the deposit. The values are consistently larger than the bulk concentration, but the uncertainty in the measurement increases with reduced subscooling. The solids mass fraction data exhibit a twofold difference over the Tcw range studied, increasing with lower initial subcooling (and most of the growth occurring via normal crystallisation). Visual inspection of the deposits indicated that for this fixed shear rate, those formed under conditions of smaller subcooling were firmer. The deposits formed under high subcooling conditions (and faster initial rate) appear to incorporate more

(a) 4.0
3.5

-2 m [kg m ]

3.0
2.5
2.0
1.5
1.0
0.5

Tm

Tc
0.0
5

10

15

20

25

30

35

40

45

50

Tcw [oC]

(b) 50 wX Fig. 17. Effect of Tcw on (a) fouling behaviour and (b) Ts profile. Conditions: xd = 5.4 rad sÀ1 and t = 12 h.

based on Tc measured at a cooling rate of 0.5 K minÀ1. The Rf–t profiles again exhibit the three stages mentioned above. The initial step increase is larger and the final Rf value higher with increased subcooling (lower Tcw), as expected. It is noteworthy that an initial gel layer is formed at zero subcooling, indicating that the cloud point calculated under quasi-static conditions does not map directly to deposition tendency in these systems. For comparison, the initial cooling rate in the paraffin in Fig. 9 is of the order of

wx, ws [wt%]

40

30

20

wS

10

0
5

10

15

20

25

30

35

Tcw [oC]
Fig. 18. Effect of Tcw on deposit (a) mass and (b) composition of deposit, for the fouling runs in Fig. 17. Vertical lines in (a) indicate the Tc and Tm for the bulk solution. 60

J.-Y. Huang et al. / Journal of Food Engineering 109 (2012) 49–61

solution, which could either be due to a growth occurring via a dendritic front or the effect of higher liquid viscosity at lower temperature. Singh et al. (2001a) also reported higher liquid contents in wax deposit formation at higher subcoolings.

3.9. Deposit rheology
The strength of the gels formed was investigated by oscillatory rheometry. Shear stress sweeps were performed at a frequency of
1.59 Hz. The results obtained for many of the deposits obtained from the fouling tests described above are presented in Fig. 19.
The rheological parameters extracted are those reported by Nigo et al. (2009): the elastic modulus in the linear elastic region, G’, the limit of linearity, sEL, defined as the end of the linear elastic region, where G’ deviated more than 5% from its initial value, and sC, the crossover point of elastic and viscous moduli. It is noteworthy that all the sC values are >2 Pa, the maximum surface shear stress estimated in the SDA tests reported here. Fig. 19 shows that all the parameters increased with solids volume fraction in a strongly non-linear manner, and there is good overlap with the data reported by Nigo et al. (2009) for similar materials.
As a particulate soft solid, the rheological parameters are expected to be strongly determined by the solid volume fraction in the gel, /. The data exhibit power-law behaviour and could be fitted to the form:

Y ¼ b/n

ð21Þ

where Y is the rheological parameter and b and n are positive constants. The gels are then consistent with the fractal model (Tang and
Marangoni, 2007), where b and n are constants related to structural characteristics of the fat crystal network. In that model, the structure of a colloidal network is considered as a collection of fractal flocs, the increase of G’, sEL and sC with / can be explained by the increase in the number of interfloc links with solid fat content
(Marangoni and Rogers, 2003; Shih et al., 1990; Venkatesan et al.,
2005). The results show that the gel quickly developed an appreciable strength, so that it would resist the shear imposed by the fluid over the surface. However, it was not possible here to determine the local solids distribution: this will be investigated using freezing techniques. 6

log G ', log τEL, log τC

5
4

2

G '

τC

1
0

τEL

-1
-2
0 .0 1

The SDA allows one to investigate the heat and mass transfer characteristics of gel formation from model food fat solutions on cold surfaces under well controlled flow conditions. Experimental investigations of the SDA heat transfer performance were combined with CFD simulation studies to generate maps of the temperature and shear stress conditions on the SDA test surface. The results confirmed that the thermal resistance across the disc was small and heat transfer was controlled by the bulk fluid, however, the internal thermal resistances became significant at higher Rer.
A series of laboratory experiments were carried out in the SDA with 5 wt.% PPP in a non-crystallising solvent to investigate the effects of varying deposition time, shear and thermal driving force on the crystallisation fouling behaviour of food fats. Rf–t profiles for these ‘cold start’ experiments exhibited three stages: transient, linear rate and falling rate stage. Rf–t profiles could be generated reliably and reproducibly, indicating that the heat flux measurements provide a reliable monitor of deposit growth. In all cases, the HX contribution in HT is noticeably small, the estimated Ts increased quickly initially and then levelled off to approach the experimentally measured Tm.
The amount of gel formed initially could be related to the subcooling of the cold disc. The linear fouling rate was relatively insensitive to temperature and velocity effects and the rate controlling step is yet to be identified. In the falling rate stage, the observed dependence of G(T) on DT was linear, regardless of the operating conditions, indicating that a normal growth stage controls fouling at these temperatures.
For given values of xd and Tcw, m and wX increased steadily with t, indicating that deposit ageing occurred in the gels over the time scale of the experiments. Ageing did not change the deposit properties in terms of qfkf. The strength of the gel formed, whether described by G’, sEL or sC, increased with solids content and could be related to a fractal model of deposit microstructure.
At the shear and temperature conditions employed in this study, deposition is driven by formation of gels on the heat transfer surface. The composition and structure of the gels reflected the conditions present at their formation. Increasing the amount of shear generally decreased m and increased wX, while decreasing the coolant temperature (and increasing the degree of subcooling) increased m and decreased wX. Spalling was not observed under the moderate shear stress conditions studied here.

References

7

3

4. Conclusions

0 .1

1

φ
Fig. 19. Effect of deposit solids volume fraction on rheological parameters measured at 20 °C. Solid data sets are those reported for similar PPP solutions by
Nigo et al. (2009). Loci indicate power law trend lines (Eq. (21)) fitted to the data sets: G’ = 9 Â 107/3.7; sEL = 2.9 Â 105/4.8 and sC = 2.4 Â 105/2.8.

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Exchangers. Journal of Heat Transfer 115 (3), 584–591.
Bidmus, H.O., Mehrotra, A.K., 2004. Heat-transfer analogy for wax deposition from paraffinic mixtures. Industrial and Engineering Chemistry Research 43 (3), 791–
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