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Rheological characterization and electrokinetic phenomena of charged whey protein dispersions of defined sizes
ARTICLE IN PRESS
LWT 39 (2006) 206–215 www.elsevier.com/locate/lwt
Rheological characterization and electrokinetic phenomena of charged whey protein dispersions of defined sizes Christopher R. Daubert, Heather M. Hudson1, E. Allen Foegeding, P. Prabhasankar Department of Food Science, North Carolina State University, 130 Withers Hall, Campus Box 7624, Raleigh, NC 27695-7624, USA Received 25 October 2004; received in revised form 22 December 2004; accepted 23 December 2004
Abstract A multi-step processing technique produced large colloidal particles from whey proteins, prompting instantaneous thickening upon hydration. Analysis of the rheological characteristics and zeta potential of the modified whey suspensions of defined particle sizes allowed investigation into the role of size on ingredient functionality. Preliminarily, the modified protein powders were sieved to achieve three size ranges, and analyzes were conducted on each of the three distributions and the non-sieved fractions. Following hydration, steady and oscillatory shear analyzes were performed using a controlled stress rheometer to determine rheological characteristics. Intrinsic viscosity was determined with a capillary viscometer and application of the Huggins equation. Zeta potential was calculated from colloidal electrophoretic mobility, measured with a ZetaPALS analyser. After thorough hydration, particle-size analysis revealed a size increase of 41.3 times for each fraction. When analysed on a protein basis, increasing particle size yielded an increase to intrinsic viscosity, flow behavior index, zero shear viscosity, and a decreased zeta potential and consistency coefficient. Knowledge of the interrelationship between zeta potential, rheological properties, and particle size of the modified whey ingredient will further advance an understanding of the functionality of this protein ingredient. r 2005 Swiss Society of Food Science and Technology. Published by Elsevier Ltd. All rights reserved. Keywords: Whey protein; Rheology; Dispersion; Zeta potential; Particle size
1. Introduction Whey proteins are important to many food products, providing essential amino acids and impacting a broad range of functional characteristics including gel formation, foaming, and emulsification. These ingredients have been developed over the past few decades, often with specific application. The demand for dairy-based ingredients to mimic the functionality of hydrocolloids, starches, or gelatin in dairy systems has provoked much research into instantaneous whey protein thickeners and cold-set gelation (Barbut & Foegeding, 1993; Corresponding author. Tel.: +1 919 513 2092; fax: +1 919 515 7124. E-mail address: [email protected] (C.R. Daubert). 1 Present address: Kraft Foods, 801 Waukegan Road, Glenview, IL 60025, USA.
McClements & Keogh, 1995; Elofsson, Dejmek, Paulsson, & Burling, 1997; Hongsprabhas & Barbut, 1998; Vardhanabhuti & Foegeding, 1999; Bryant & McClements, 2000). Earlier research developed a process to modify whey protein isolate (mWPI) into an instantaneous, temperature, and pH stable thickening agent composed of charged colloidal particles with a porous structure and large size distribution (Hudson, Daubert, & Foegeding, 2000; Resch, 2004). The protein colloids are not soluble, and therefore create dispersions when reconstituted in water. A colloidal dispersion has particles much larger than molecules of the dispersed medium, but are small enough for Brownian motion not to be overwhelmed by the force of gravity (Dickinson & Stainsby, 1982). The size and size distribution of colloidal particles are important characteristics governing suspension
0023-6438/$30.00 r 2005 Swiss Society of Food Science and Technology. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.lwt.2004.12.013
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ac g_ K n z fE r Dh Dd
Nomenclature Zrel Zs Z0 Z; Za [Z] Zsp Zsp Zr
relative viscosity, Pa s pure solvent viscosity, Pa s zero shear viscosity, Pa s apparent viscosity, Pa s intrinsic viscosity, Pa s specific viscosity, Pa s specific viscosity, Pa s reduced viscosity, Pa s
behavior, as flow properties, rate of settling, aggregation, and stability are all influenced (Hunter, 1993). When shear or electric fields are applied to systems of charged particles, electrokinetic phenomena arise from a disturbance of the equilibrium double layer. Electrostatic and Brownian forces attempt to restore equilibrium by moving ions relative to the fluid, thereby dissipating energy (Russell, 1978). Electroviscous effects are electrokinetic phenomena associated with the additional stress required to deform particles with diffuse charge clouds, inducing an increased viscous response in the liquid (Russell, Saville, & Schowalter, 1989). There are three such electroviscous effects, stemming from both inter- and intra-particle phenomena, which alter many rheological properties of suspensions. Einstein found the intrinsic viscosity for rigid spheres in a Newtonian medium is precisely 5/2, independent of particle size. According to Einstein, the relative viscosity Zrel of a very dilute suspension (f51) of rigid, spherical particles in a continuous dilute liquid medium is given by Zrel ¼ 1 þ 2:5f,
(1)
where f is the volume fraction and Zrel is the ratio of the suspension viscosity (Z) to that of the pure solvent (Zs ) (Dickinson & Stainsby, 1982). Einstein’s law of viscosity has two major assumptions: the particles are solid spheres, and they are far enough apart to be treated independently (Hiemenz, 1977). The primary electroviscous effect skews viscosity values away from Einstein’s prediction, as the symmetry of the ionic atmosphere around each particle is distorted by shear flow yielding higher viscosity values than for noncharged particles of similar size (Dickinson & Stainsby, 1982). Even at high dilution, such as those used in intrinsic viscosity measurements, the interaction of the ion and its atmosphere augments energy dissipation, thereby increasing the intrinsic viscosity (Krieger, 1985). More importantly for non-dilute dispersions is the effect of electrostatic repulsive forces to increasing the effective collision diameter of charged particles in shear
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time constant, dimensionless shear rate, s1 consistency coefficient, Pa sn flow behavior index, dimensionless dielectric constant, dimensionless zeta potential, mV effective volume fraction, dimensionless density, g/ml hydrated particle diameter, mm dry particle diameter, mm
flow, the secondary electroviscous effect. As two charged spheres approach one another due to shear flow, the trajectories are altered due to repulsive forces originating from the charged ionic cloud surrounding the particles. This secondary electroviscous effect gives an additional source of energy dissipation, and hence higher viscosity than for an equivalent suspension of uncharged particles (Krieger & Eguiluz, 1976). This effect is greatly diminished by adding electrolytes or increasing the shear forces acting on the colloidal dispersion. The tertiary electroviscous effect describes changes in dimensions of the charged layers on colloids due to changes in the valency, pH, or dielectric constant. At low ionic strength, the repulsion between like charges on the same molecule leads to expansion of the polyelectrolyte chain, which may affect the bulk rheology and the effective interactions between particles. In food dispersions containing protein or charged polysaccharides, the tertiary effect usually dominates. All of these factors influence the electrostatic repulsion between charged groups and will hence control the conformation and thickness of the double layer (Goodwin, 1987, Chapter 10). The objective of this research was to expand the understanding of the interdependence of particle size, zeta potential, and rheological properties in modified whey protein dispersions. Another goal of this research was to study the influence of particle size on the rheological characteristics of the modified whey protein dispersions.
2. Materials and methods 2.1. Materials A commercial whey protein isolate (WPI) powder (lot # JE057-7-420), containing approximately 91.2 g/100 protein (N 6.38, micro-Kjeldahl, AOAC, 1984) was used (Bipro, produced by Davisco International Inc., Le Sueur, MN, USA). All chemicals were purchased from Fisher Scientific Company (Norcross, GA, USA).
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2.2. Preparation of protein dispersions and gels WPI powder was hydrated (12 g/100 ml) in deionized (DI) water, pH adjusted with 6 mol/l HCl to 3.357.02, and thermally gelled at 80 1C for 3 h according to the procedure of Hudson et al. (2000). Gels were subsequently frozen, freeze-dried, and ground into a powder. Modified whey protein powders were then sieved to obtain three particle-size ranges: 75–125, 45–74 and 20–44 mm. The sieves had mesh sizes of 120, 200, 325 and 635 (W.S. Tyler, Mentor, OH) and yielded a wide distribution of sizes: 2.53% of 4125 mm fraction; 41.58% of 75–125 mm fraction; 37.25% of 74–45 mm fraction; 12.62% of 20–44 mm fraction, and 6.02% of 6.02 mm fraction. 2.3. Particle-size analysis Powders were suspended in silicone oil or deionized water for 24 h, and particle size and size distribution was determined via a Centrifugal Particle Size Analyzer SACP4 (V1.0) (Shimadzu Corporation, Tokyo, Japan). 2.4. Density determination Dry powder and solution densities were determined at 25 1C on a Micromeritics Multivolume Pycnometer 1305 (Norcross, GA). Sample weights were measured (70.001 g), and instrumentation readings provided volume. Tests were performed in triplicate. 2.5. Dielectric constants Powder dielectric constants were measured on a Hewlett Packard (HP) 8753E Network Analyzer attached to a HP 85070B Dielectric Probe utilizing HP Dielectric Probe Software (Rev. 01.05) (Palo Alto, CA, USA). Tests were performed at 25 1C in triplicate. 2.6. Rheological measurements Steady and small amplitude shear tests were performed on a Reologica StressTech controlled stress rheometer (ReoLogica Instruments AB, Lund, Sweden) at 25 1C. All samples (10 g/100 protein) were hydrated in deionized water during gentle agitation (o100 rpm) for 5 h at 25 1C; samples were then stored at 5 1C for X24 h. Prior to rheological analysis, samples were equilibrated to ambient temperature. Once the bob (37.9 mm high and 2.5 mm diameter) was immersed in the cup (27.0 mm diameter), a thin layer of mineral oil coated the sample surfaces to prevent moisture loss, followed by a preshear at 15/s for 30/s. The same lot of modified whey powders was sieved to achieve the three narrow particlesize ranges. For all rheological testing, suspension pH and ionic strengths were constant, and only average particle diameter was varied.
2.6.1. Zero shear Zero shear viscosity (Z0 ) was determined for five protein concentrations (6.0, 6.5, 7.0, 7.5 and 8.0 g/100) by subjecting the dispersions to stress ramps from 0.05 to 25.0 Pa, and recording viscosity and the corresponding shear rate. Apparent viscosity (Za ) was modeled via a modified cross model, Z0 Za ¼ , (2) 1 þ ðac g_ Þm where ac is a time constant, g_ is shear rate, and m is a dimensionless exponent. Equation constants were assessed using non-linear regression statistical techniques. 2.6.2. Steady shear rheology Shear rate ramps (1.0–100.0/s) were performed and viscosity was modeled using a power-law equation to determine sample consistency coefficient (K) and flow behavior index (n). Za ¼ K g_ n1 .
(3)
2.6.3. Oscillatory rheology To ascertain viscoelastic properties, mechanical spectra were conducted at a stress of 1.0 Pa as frequency was oscillated from 0.1 to 20.0 Hz. Analysis was conducted in the identified linear viscoelastic region. 2.6.4. Intrinsic viscosity Intrinsic viscosity [Z] was measured with a Cannon– Fenske capillary viscometer submerged in a water bath maintained at 25.070.1 1C. Five concentrations between 0.548 and 2.74 mg protein/ml were measured, and specific viscosity Zsp was calculated as Zsp ¼
ðt t0 Þ , t0
(4)
where t0 be the efflux time of DI water and t is the efflux time of the sample. The intrinsic viscosity was determined using the Huggins equation Zr ¼ Zsp =c ¼ ½Z þ k½Z2 c,
(5)
where c is protein concentration (g/mL); Zsp ¼ Zrel 1; Zrel is the relative viscosity and Zr ¼ Zsp =c is the reduced viscosity. 2.7. Electrokinetic analysis Electrophoretic mobility was measured on a ZetaPALS Analyzer (Brookhaven Instruments Corp., Holtsville, NY, USA), and zeta potential was calculated using the Smoluchowski equation mE ¼
z , Z
(6)
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where mE is electrophoretic mobility, is dielectric constant, z is zeta potential, and Z is the apparent viscosity of the suspending medium.
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less structural rigidity. Therefore a greater proportion of the smaller particle sizes may possess greater porosity yielding greater swelling capacities. 3.2. Volume fraction
3. Results and discussion
Many colloidal calculations and discussions are conducted on a volume fraction (f) basis, defined as
3.1. Particle-size analysis
f¼
A median particle size for 75–125, 45–74 and 20–44 mm sieved fractions and non-sieved mWPI was determined in oil to approximate a dry particle size and in DI water after a 24 h hydration period. Dry and fully hydrated diameter values are provided in Table 1. Comparison of the two particle-size data series clearly depicts the swelling capacity of these colloids, with the 20–44 mm sieved fraction swelling approximately 1.8 times its dry particle size after hydration, and all remaining fractions swelling at least 1.3 times. Deviations in the swelling capacities of the various sieved fractions may elucidate some structural characteristics of the powders influenced by size. For example, the smaller particles may possess enhanced swelling ability due to fewer structural networks or linkages between proteins within the colloid, thereby producing a more porous structure. This structure therefore may allow more water to imbibe into the colloid, increasing the particle volume and measured diameter. Walbridge (1987) found softer titanium dioxide crystals to yield finer particle fragments during milling. Hence, powder with fewer networks may mill into smaller pieces due to
Volume of particles . Volume of particles þ Volume of dispersant
(7)
Determination of particle volume fraction was necessary for dispersed colloidal systems as viscosity depends strongly on the amount of the dispersed phase, especially at high volume fractions (Dickinson & Stainsby, 1982). This experiment however based all analyzes on a percent hydrated (swollen) protein and not percent powder. Therefore, a hydrated particle or effective volume fraction (fE ) was determined for all protein concentrations. Due to significant particle swelling, incorporation of a swelling capacity ratio (Dh/Dd) into the calculation was required ½protein Dh 3 , (8) fE rpowder Dd where r is density, Dh is hydrated particle diameter, and Dd is dry particle diameter. Conversions from weight percent to an effective volume fraction for all concentrations are given in Table 2. A basis for the incorporation of swelling capacity into the calculation of volume fraction is well established for starch systems (Bagley &
Table 1 Physical and electrical properties of powdersa Sample
Density r (g/ml)
Dry diameter Dd (mm)
Hydrated diameter Dh (mm)
Zeta potential z (mV)
Dielectric constantb
WPI mWPI 75–125 mm 74–45 mm 20–44 mm
1.1570.01 1.3270.01 1.3170.00 1.3370.02 1.3270.02
N/A 25.372.7 100.9715.7 56.574.8 35.173.5
N/A 36.378.2 133.6724.1 87.4711.8 64.0 710.3
44.671.6 35.570.9 52.172.9 34.470.5 31.771.3
1.8970.04 2.0970.03 1.9070.01 1.9170.02 1.6970.02
a
Averages7standard error Dielectric constants measured at 1 Hz.
b
Table 2 Conversion of protein weight percent to effective volume fraction (fE ) Protein weight percents (g/100)
mWPI 75–125 mm 45–74 mm 20–44 mm
0.05
0.10
0.15
0.20
0.25
6.00
6.50
7.00
7.50
8.00
10.00
0.0012 0.0001 0.0015 0.0025
0.0024 0.0019 0.0030 0.0050
0.0036 0.0029 0.0045 0.0074
0.0048 0.0038 0.0060 0.0099
0.0060 0.0048 0.0075 0.0124
0.1533 0.1222 0.1926 0.3171
0.1670 0.1331 0.2097 0.3452
0.1808 0.1441 0.2271 0.3737
0.1948 0.1553 0.2447 0.4027
0.2088 0.1665 0.2623 0.4317
0.2610 0.2081 0.3278 0.5396
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Christianson, 1982; Christianson & Bagley, 1983; Steeneken, 1989). Modified powders have similar behaviors to starch in solution (significant water holding and swelling capacities), and therefore it was not surprising that for accurate volume fraction determination, both necessitate the integration of similar parameters. 3.3. Zeta potential Dispersion electrophoretic mobility depends upon the shape and size of the particle, the properties of the electrolyte solution in which it is dispersed, and the potential at the shear plane (Dickinson & Stainsby, 1982). The modified protein (0.1 g/100) colloidal suspensions tested were acidic (pHE3.7) and well below the isoelectric points of the major whey proteins, commonly given as 5.4 for b-lactoglobulin and 4.3 for a-lactalbumin (Morr, 1989, Chapter 7). Therefore, the modified whey colloids were positively charged whereas the native whey proteins (pH 6.8) had negative charges, as do many proteins in biological systems at native pH (de Wit, 1989). A direct relationship between zeta potential and colloidal diameter was observed, with the 74–125 mm fraction exhibiting a 1.6 times larger potential than the 20–44 mm fraction. The impact of zeta potential on the rheological behaviors and physical properties of the dispersions will be addressed throughout the remaining sections. 3.4. Rheological analysis Much research on colloidal dispersions has been conducted on monodisperse, hard sphere systems (Mellema, de Kruif, Blom, & Vrij, 1987; Buscall, 1991; Foss & Brady, 2000), providing a framework from which to draw upon when studying the complex dispersed colloidal systems typically seen in food. This research attempted to assimilate colloidal theory into the explanation of the rheological and functionality characteristics exhibited by the mWPI dispersions. 3.4.1. Zero shear Almost all colloidal dispersions are shear thinning; therefore, apparent viscosity will decay with increasing shear rate, and Newtonian behavior may only exist at very low rates. This situation corresponds to the horizontal Newtonian plateau (zero shear viscosity) in the viscosity shear rate plots shown in Figs. 1a–d. Increasing weight percent induced lower zero shear plateaus for each fraction (Figs. 1a–d). As the degree of colloidal interaction increased, the freedom of movement of the individual colloids was progressively restricted. Consequently, the time required to form new interactions to replace those disrupted by deformation increased. Thus, the shear rate at which Newtonian
behavior was lost moved to ever-decreasing values as concentration increased (Morris, Cutler, Ross-Murphy, Rees, & Price, 1981). Therefore, the shear rate duration at which Newtonian plateaus were present decreased with increasing weight percent for all particle sizes. This characteristic was due to the polymer dispersions becoming increasingly non-Newtonian as concentration increased (Krieger, 1985). Additionally, the magnitude of the Newtonian viscosity plateau (Z0 ) at each weight percent increased with decreasing particle size (Figs. 1a–d). The rheological dependence upon particle size was qualified by the recognition that as particle size decreases the number of particles in a given volume increases, resulting in a decrease in the average distance between particles (Russell, 1978). Therefore, the smallest fraction (20–44 mm) had the highest number of particles in solution at a given weight percent. As a result, the larger viscosity for the smallest diameter was most likely due to a concentration effect and not electroviscous in nature. This hypothesis was reinforced by the electrokinetic analysis that yielded smaller zeta potentials for smaller particles, and this fraction would be less apt to exhibit secondary electroviscous effects during zero shear analysis. Zero shear viscosities were plotted on a volume fraction basis and presented in Fig. 1e. Clearly, lower effective volume fractions achieved higher plateaus for the larger diameter colloids. Additionally, the log Z0 verses fE relationship for each fraction followed the same trend. For a dispersion of 20–44 mm particles to produce an analogous zero shear viscosity to a dispersion of 75–125 mm dispersions, effective volume fraction would need to be increased approximately 2.6 times that of the larger particles. This response was expected, as increasing particle diameter resulted in larger zeta potentials, and these particles may therefore exhibit higher secondary electroviscous behaviors (Russell, 1978). 3.4.2. Steady shear rheology The shear-thinning behavior observed in mWPI suspensions was not surprising, as many suspensions display pseudoplasticity. The proposed mechanism responsible for this behavior is layering of the colloids during increasing shear, allowing the particles to slip easily over one another resulting in a diminished viscosity (Ackerson, 1990). A clear influence of particle size on the rheology of samples during steady shear analysis was observed, with the suspensions composed of the smaller diameter particles possessing the highest viscosity (Fig. 2). When analysing the curves via the power-law model, a clear relationship between consistency coefficient (K) and particle size was evident, with K decreasing with increasing particle diameter (Fig. 3). The inverse relationship between suspension viscosity
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211
10.00
Viscosity (Pa s)
Viscosity (Pa s)
10.00
1.00
1.00
0.10
0.10
0.01 1.00
(a)
10.00 Shear rate (s-1)
0.01 1.00
100.00
10.00
(b)
100.00
Shear rate (s-1)
10.00
1.00
0.10
0.01 1.00
(c)
Viscosity (Pa s)
Viscosity (Pa s)
10.00
0.10
0.01 1.000
100.00
10.00 Shear rate (s-1)
1.00
10.000
(d)
100.000
Shear rate (s-1)
10
η (Pa s)
1
0.1
0.01 0
0.1
0.2
(e)
0.3 φE
0.4
0.5
0.6
Fig. 1. (a). Zero shear viscosity ramp of mWPI at five concentrations (6.0% (J), 6.5% (E), 7.0% (n), 7.5% (K) and 8.0% (&) protein w/w). (b). Zero shear viscosity ramp of sieved fraction 75–125 mm at five concentrations (6.0% (J), 6.5% (E), 7.0%(n), 7.5% (K) and 8.0% (&) protein w/w). (c) Zero shear viscosity ramp of sieved fraction 45–74 mm at five concentrations (6.0% (J), 6.5% (E), 7.0% (D), 7.5% (K) and 8.0% (&) protein w/ w). (d). Zero shear viscosity ramp of sieved fraction 20–44 mm at five concentrations (6.0% (J), 6.5% (E), 7.0% (n), 7.5% (K) and 8.0% (&) protein w/w). (e) Plot of Newtonian viscosity verses effective volume fraction for mWPI (n), and 75–125 mm (m), 45–74 mm (K), 20-44 mm (J) sieved fractions.
and particle size was contrary to the findings of Rao and Tattiyakul (1999), who found K to increase with increasing tapioca starch diameter. However, Yoo and Rao (1994) found smaller diameter tomato products to have larger viscosities than tomato products of larger diameters. The increasing viscosity with decreasing colloid diameter observed in the Yoo and Rao (1994) study and in this research may be a phenomenon
resulting from colloidal charge, not evident in the Rao and Tattiyakul (1999) study at any pH because starch is not charged. Previous research established that decreasing particle size increased dispersion viscosity, caused by an increase in the overlapping area of the electric double layer around each particle (Ogawa, Yamada, Matsuda, Okajima, & Doi, 1997). Thus, at a constant weight percent, there were more smaller particles present,
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212
Viscosity (Pa s)
100
10
1
0 0
20
40
60
80
100
120
140
Shear rate (s-1)
Fig. 2. Shear rate ramp (1–100/s) for mWPI (n), and 75–125 mm (&), 45–74 mm (K), 20–44 mm (~) sieved fractions.
Consistency Coefficient (K) (Pa sn)
110 100
20-44 µm
90 45-74 µm
80 70 60 mWPI
75-125 µm
50 40
0
50
100
150
200
Hydrated Diameter (µm)
Fig. 3. Consistency coefficient (K) verses hydrated particle diameter for sieved and non-sieved mWPI fractions.
allowing the electric double layer around each particle to overlap more strongly than for larger colloids. The interpartical potential (the potential acting between the particles) increased with decreasing particle diameter, and therefore so may the secondary electroviscous effects. Hence, with a decrease in charged particle diameter, the repulsive interaction between dispersed particles increased with viscosity, as observed in this study. It should be noted that consistency coefficient was additionally analysed on an effective volume fraction instead of a weight percent basis, and increasing K with decreasing diameters was still observed. A decrease in the flow behavior index (n) was observed with decreasing whey dispersion particle diameter (Table 3). Ogawa and colleagues (1997) however observed decreased pseudoplasticity with decreased particle size in a synthetic system of charged colloids (Ogawa et al., 1997). This discrepancy in behaviors was attributed to the fact that measurements in this research were conducted on a 10 g/100 weight basis in lieu of volume fraction whereas the results of
Ogawa et al. (1997) were conducted at a set volume fraction of 0.30. Therefore for comparative purposes the flow behavior indices derived in this study were analysed with respect to calculated effective volume fraction (fE ). The increasing n with decreasing particle diameter trend was observed when power-law properties were evaluated in this manner. The reduction in the magnitude of the secondary electroviscous effect at the higher shear rates tested may also be responsible for a portion of the decreased flow behavior indices seen in the colloidal dispersions. It is well established that viscous forces tend to decrease with shear rate, while electrostatic forces remain constant. Thus, the particle displacement due to charge and viscosity decreases with increasing shear rate (Russell, 1978). This decreased displacement caused a drop in the measured viscosity of dispersions. 3.4.3. Oscillatory rheology A deviation in the trend of smaller-sized particles showing superior rheological properties (on a weight percent basis) was evident in the small strain analysis. The mechanical spectra revealed a larger complex modulus (G*), and therefore stronger viscoelastic properties for the 75–125 mm sample; while all other sample fractions, regardless of size, exhibited analogous viscoelastic fluid properties (Fig. 4). For comparative purposes, the effective volume fractions (fE ) for dispersions of protein (10 g/100) are presented in Table 2. Clearly, the 75–125 mm sample achieved higher moduli values on a weight percent and fE basis. Quite possibly, higher zeta potentials and the minute shearing placed upon samples during oscillation may culminate in large electroviscous effects, thereby increasing viscosity. 3.4.4. Intrinsic viscosity At high dilution the behavior of a colloidal dispersion is described by a quantity known as intrinsic viscosity, [Z]. Because [Z] represents the hydrodynamic or sweep volume of a colloid and is related to the molecular weight and the radius of gyration, it reflects important molecular characteristics (Rao, 1999, Chapter 1). Intrinsic viscosities of mWPI and the sieved fractions are given in Fig. 5, and increased [Z] was noted with increasing particle diameter. Macromolecules that possess a large number of ionisable groups are called polyelectrolytes. When these groups dissociate in aqueous media, the result is counterions and a macroion, where the charge groups have no independent mobility because they are attached to the chain (Launay, Doublier, & Cuvelier, 1986, Chapter 1). Intrinsic viscosities for many polyelectrolytes demonstrate a peculiar behavior, increasing reduced viscosity with decreasing polyelectrolyte concentration (Frollini, Reed, Milas, & Rinaudo,
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Table 3 Steady shear flow behavior indicesa, consistency coefficients, and apparent viscosities of 10 g/100 protein solutions Sample
K (Pa sn)
n
R2
b
75–125 mm 74–45 mm 20–44 mm mWPI
50.4971.78 80.9672.16 97.9772.43 53.8071.09
0.2870.01 0.1870.01 0.1870.01 0.2070.01
0.93 0.97 0.91 0.93
Za,25 c (Pa s)
Za,75
4.53 6.82 8.72 4.15
2.40 2.39 2.84 1.85
d
(Pa s)
a
Averages7standard error. Regression coefficient for power-law model fit. c Apparent viscosity at a shear rate of 25 s1 and 25 1C. d Apparent viscosity at a shear rate of 75 s1 and 25 1C. b
10000
1.180 1.160 1.140
η/η0
G* (Pa)
1.120 1000
slope = 14.1 slope = 24.3 slope = 7.3
1.100 1.080 1.060 1.040 1.020
100 0.01
0.10
1.00
10.00
100.00
1.000 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 φE
Frequency (Hz)
Fig. 4. Frequency sweep of mWPI (n), and the three sieved fractions: 75–125 mm ( ), 45–74 mm (K), and 20–44 mm (~).
[η] 90
♦
∆ 71.39
76.75
0.0015
0.0020
O 80.32
84.57
80 70 ηred (mL /g)
60 50 40 30 20 10 0 0.0000
0.0005
0.0010
0.0025
0.0030
Protein Concentration (g/mL)
Fig. 5. Reduced viscosity plot of mWPI (D), and the three sieved fractions: 75–125 mm (&), 45–74 mm (J), and 20–44 mm (~).
1995), in contrast to the linear plots obtained for standard polymers. Polymerized whey protein preparations have also been shown to exhibit this behavior, attributed to a decrease in the ionic strength at high dilution, permitting polymer unfolding and yielding
Fig. 6. Verification of Einstein’s viscosity equation for a suspension of spheres using suspensions of the three sieved fractions: 75–125 mm (m), 45–74 mm (&), and 20–44 mm (~).
(increased Zr ) at lower concentrations (Vardhanabhuti & Foegeding, 1999). As represented in Fig. 5, polyelectrolytic behavior was noted for the modified whey colloids of all size fractions and was credited to the expansion of the colloidal particle due to reduced electrolytic concentrations upon dilution. The close proximity of groups carrying like charges caused the polymer expansion by electrostatic repulsion, the tertiary electroviscous effect. This effect is due to changes in the chemical environment such as valency, pH, and electrolytic concentration (Launay et al., 1986, Chapter 1) as in this case. The thickness of the double layer is inversely proportional to the square root of the electrolytic concentration in the continuous medium (Hill, 1998), and the diminished mineral content allowed heightened electroviscous effects due to ionic cloud expansion in the dispersions. The intrinsic viscosity of suspensions differs from the Einstein value of 5/2. Some of the factors shown to influence [Z] are the surface properties of the particles (due to the effects of concentration, pH, ionic strength, and adsorbed layer thickness), aggregation, non-Newtonian behavior of the continuous phase, and particle size (when in the Brownian motion size regime) (Bagley, 1992, Chapter 13). A plot of Zrel verses effective volume
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fraction was created to test Einstein’s law of viscosity for derivitized whey colloids (Fig. 6). The slope of the regression lines should yield the predicted 5/2-viscosity value, however significant deviations were observed for each of the fractions.
4. Conclusion Obtaining mWPI dispersions of defined sizes permits enhanced control of powder functionality, as rheological and electrokinetic behaviors were significantly impacted by particle size. The increase of dispersed particle diameter resulted in increased zeta potential, flow behavior index, intrinsic viscosity, and deviation from Einstein’s viscosity law. Whereas decreased consistency coefficients, zero shear plateaus and swelling capacities were witnessed with increasing particle size. Therefore, many rheological properties can essentially be controlled and conclusively manipulated through selection of mWPI dispersions of specific sizes and distribution.
Acknowledgements Paper No. FSR-01-30 of the Journal Series of the Department of Food Science, N.C. State University, Raleigh, NC 27695-7624. Support from the North Carolina Agricultural Research Service is gratefully acknowledged. Mention of a trademark or proprietary product does not constitute a guarantee or warranty of the product by the North Carolina Agricultural Research Service, nor does it imply approval to the exclusion of other products that may be suitable. The authors would like to thank Tim Seaboch, Heather Stewart, and Dr. John Miller (GlaxoWellcome) for generously donating their time and assistance with the instrumentation used in this research. Davisco Foods International, Inc. kindly donated all proteins used in the experimentation. References Ackerson, B. J. (1990). Shear induced order and shear processing of model hard sphere suspensions. Journal of Rheology, 34, 553–590. AOAC. (1984). Official methods of analysis (14th ed). Arlington, VA: Association of Official Analytical Chemists. Bagley, E. B. (1992). Mechanistic basis of rheological behavior of foods. In H. G. Schwartzberg, & R. W. Hartel (Eds.), Physical chemistry of foods. New York: Marcel Dekker, Inc. Bagley, E. B., & Christianson, D. D. (1982). Swelling capacity of starch and its relationship to suspension viscosity—effect of cooking time, temperature and concentration. Journal of Textural Studies, 13, 115–126. Barbut, S., & Foegeding, E. A. (1993). Ca+2-induced gelation of preheated whey protein isolate. Journal of Food Science, 58, 867–871.
Bryant, C. M., & McClements, D. J. (2000). Influence of NaCl and CaCl2 on cold-set gelation of heat-denatured whey protein. Journal of Food Science, 65, 801–804. Buscall, R. (1991). Effect of long-range repulsive forces on the viscosity of concentrated lattices: comparison of experimental data with an effective hard-sphere model. Journal of the Chemical Society Faraday Transactions, 87, 1365–1370. Christianson, D. D., & Bagley, E. B. (1983). Apparent viscosities of dispersions of swollen cornstarch granules. Cereal Chemistry, 60, 116–121. de Wit, J. N. (1989). Functional properties of whey proteins. In P. F. Fox (Ed.), Developments in dairy chemistry 4. New York: Elsevier Applied Science. Dickinson, E., & Stainsby, G. (1982). Colloids in foods (pp. 33–66). New York: Applied Science Publishers. Elofsson, C., Dejmek, P., Paulsson, M., & Burling, H. (1997). Characteristics of a cold-gelling whey protein concentrate. International Dairy Journal, 7, 601–608. Foss, D. R., & Brady, J. F. (2000). Brownian dynamics simulation of hard-sphere colloidal dispersions. Journal of Rheology, 44, 629–651. Frollini, E., Reed, W. F., Milas, M., & Rinaudo, M. (1995). Polyelectrolytes from polysaccharides: selective oxidation of guar gum—a revisited reaction. Carbohydrate Polymers, 27, 129–135. Goodwin, J. W. (1987). The rheology of colloidal dispersions. In T. F. Tadros (Ed.), Solid/liquid dispersions. New York: Academic Press. Hiemenz, P. C. (1977). Principles of colloid and surface chemistry (pp. 1–41 & 453–491). New York: Marcel Dekker, Inc. Hill, S. E. (1998). Emulsions and foams. In S. E. Hill, D. A. Ledward, & J. R. Mitchell (Eds.), Functional properties of food macromolecules, (2nd ed.) (pp. 302–334). New York: Aspen Publishing. Hongsprabhas, P., & Barbut, S. (1998). Structure-forming processes in Ca+2-induced whey protein isolate cold gelation. International Dairy Journal, 7, 827–834. Hudson, H. M., Daubert, C. R., & Foegeding, E. A. (2000). Rheological and physical properties of derivatized whey protein isolate powders. Journal of Agriculture and Food Chemistry, 48, 3112–3119. Hunter, R. J. (1993). Introduction to modern colloid science (pp. 57–96). New York: Oxford University Press. Krieger, I. M. (1985). Rheology of polymer colloids. In R. Buscall, T. Corner, & J. F. Stageman (Eds.), Polymer colloids (pp. 219–246). New York: Elsevier Applied Science Publishers. Krieger, I. M., & Eguiluz, M. (1976). The second electroviscous effect in polymer latices. Transaction of the Society of Rheology, 20, 29–45. Launay, B., Doublier, J. L., & Cuvelier, G. (1986). Flow properties of aqueous solutions and dispersions of polysaccharides. In J. R. Mitchell, & D. A. Ledward (Eds.), Functional properties of food macromolecules. New York: Elsevier Applied Science. McClements, D. J., & Keogh, M. K. (1995). Physical properties of cold-set gels formed from heat-denatured whey protein isolate. Journal of Science Food and Agriculture, 69, 7–14. Mellema, J., de Kruif, C. G., Blom, C., & Vrij, A. (1987). Hard sphere colloidal dispersions: mechanical relaxation pertaining to thermodynamic forces. Rheological Acta, 26, 40–44. Morr, C. V. (1989). Whey proteins: manufacture. In P. F. Fox (Ed.), Developments in dairy chemistry 4. New York: Elsevier Applied Science. Morris, E. R., Cutler, A. N., Ross-Murphy, S. B., Rees, D. A., & Price, J. (1981). Concentration and shear rate dependence of viscosity in random coil polysaccharide solutions. Carbohydrate Polymers, 1, 5–21. Ogawa, A., Yamada, H., Matsuda, S., Okajima, K., & Doi, M. (1997). Viscosity equation for concentrated suspensions of charged colloidal particles. Journal of Rheology, 41, 769–785.
ARTICLE IN PRESS C.R. Daubert et al. / LWT 39 (2006) 206–215 Rao, M. A. (1999). Rheology of fluid and semisolid foods. New York: Aspen Publications. Rao, M. A., & Tattiyakul, J. (1999). Granule size and rheological behavior of heated tapioca starch dispersions. Carbohydrate Polymers, 38, 123–132. Resch, J. J. (2004). Processing parameters effects on the fundamental properties of derivatized whey protein ingredients. Ph.D. dissertation, NC State, Raleigh. Russell, W. B. (1978). The rheology of suspensions of charged rigid spheres. Journal of Fluid Mechanics, 85, 209–232. Russell, W. B., Saville, D. A., & Schowalter, W. R. (1989). Colloidal dispersions (pp. 211–257). New York.: Cambridge University Press.
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Steeneken, P. A. (1989). Rheological properties of aqueous suspensions of swollen starch granules. Carbohydrate Polymers, 11, 23–42. Vardhanabhuti, B., & Foegeding, E. A. (1999). Rheological properties and characterization of polymerized whey protein isolates. Journal of Agriculture and Food Chemistry, 47, 3649–3655. Walbridge, D. J. (1987). Preparation of solid/liquid dispersions. In T. F. Tadros (Ed.), Solid/liquid dispersions. New York: Academic Press. Yoo, B., & Rao, M. A. (1994). Effect of unimodal particle size and pulp content on rheological properties of tomato puree. Journal Textural Studies, 25, 421–436.
LWT 39 (2006) 206–215 www.elsevier.com/locate/lwt
Rheological characterization and electrokinetic phenomena of charged whey protein dispersions of defined sizes Christopher R. Daubert, Heather M. Hudson1, E. Allen Foegeding, P. Prabhasankar Department of Food Science, North Carolina State University, 130 Withers Hall, Campus Box 7624, Raleigh, NC 27695-7624, USA Received 25 October 2004; received in revised form 22 December 2004; accepted 23 December 2004
Abstract A multi-step processing technique produced large colloidal particles from whey proteins, prompting instantaneous thickening upon hydration. Analysis of the rheological characteristics and zeta potential of the modified whey suspensions of defined particle sizes allowed investigation into the role of size on ingredient functionality. Preliminarily, the modified protein powders were sieved to achieve three size ranges, and analyzes were conducted on each of the three distributions and the non-sieved fractions. Following hydration, steady and oscillatory shear analyzes were performed using a controlled stress rheometer to determine rheological characteristics. Intrinsic viscosity was determined with a capillary viscometer and application of the Huggins equation. Zeta potential was calculated from colloidal electrophoretic mobility, measured with a ZetaPALS analyser. After thorough hydration, particle-size analysis revealed a size increase of 41.3 times for each fraction. When analysed on a protein basis, increasing particle size yielded an increase to intrinsic viscosity, flow behavior index, zero shear viscosity, and a decreased zeta potential and consistency coefficient. Knowledge of the interrelationship between zeta potential, rheological properties, and particle size of the modified whey ingredient will further advance an understanding of the functionality of this protein ingredient. r 2005 Swiss Society of Food Science and Technology. Published by Elsevier Ltd. All rights reserved. Keywords: Whey protein; Rheology; Dispersion; Zeta potential; Particle size
1. Introduction Whey proteins are important to many food products, providing essential amino acids and impacting a broad range of functional characteristics including gel formation, foaming, and emulsification. These ingredients have been developed over the past few decades, often with specific application. The demand for dairy-based ingredients to mimic the functionality of hydrocolloids, starches, or gelatin in dairy systems has provoked much research into instantaneous whey protein thickeners and cold-set gelation (Barbut & Foegeding, 1993; Corresponding author. Tel.: +1 919 513 2092; fax: +1 919 515 7124. E-mail address: [email protected] (C.R. Daubert). 1 Present address: Kraft Foods, 801 Waukegan Road, Glenview, IL 60025, USA.
McClements & Keogh, 1995; Elofsson, Dejmek, Paulsson, & Burling, 1997; Hongsprabhas & Barbut, 1998; Vardhanabhuti & Foegeding, 1999; Bryant & McClements, 2000). Earlier research developed a process to modify whey protein isolate (mWPI) into an instantaneous, temperature, and pH stable thickening agent composed of charged colloidal particles with a porous structure and large size distribution (Hudson, Daubert, & Foegeding, 2000; Resch, 2004). The protein colloids are not soluble, and therefore create dispersions when reconstituted in water. A colloidal dispersion has particles much larger than molecules of the dispersed medium, but are small enough for Brownian motion not to be overwhelmed by the force of gravity (Dickinson & Stainsby, 1982). The size and size distribution of colloidal particles are important characteristics governing suspension
0023-6438/$30.00 r 2005 Swiss Society of Food Science and Technology. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.lwt.2004.12.013
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ac g_ K n z fE r Dh Dd
Nomenclature Zrel Zs Z0 Z; Za [Z] Zsp Zsp Zr
relative viscosity, Pa s pure solvent viscosity, Pa s zero shear viscosity, Pa s apparent viscosity, Pa s intrinsic viscosity, Pa s specific viscosity, Pa s specific viscosity, Pa s reduced viscosity, Pa s
behavior, as flow properties, rate of settling, aggregation, and stability are all influenced (Hunter, 1993). When shear or electric fields are applied to systems of charged particles, electrokinetic phenomena arise from a disturbance of the equilibrium double layer. Electrostatic and Brownian forces attempt to restore equilibrium by moving ions relative to the fluid, thereby dissipating energy (Russell, 1978). Electroviscous effects are electrokinetic phenomena associated with the additional stress required to deform particles with diffuse charge clouds, inducing an increased viscous response in the liquid (Russell, Saville, & Schowalter, 1989). There are three such electroviscous effects, stemming from both inter- and intra-particle phenomena, which alter many rheological properties of suspensions. Einstein found the intrinsic viscosity for rigid spheres in a Newtonian medium is precisely 5/2, independent of particle size. According to Einstein, the relative viscosity Zrel of a very dilute suspension (f51) of rigid, spherical particles in a continuous dilute liquid medium is given by Zrel ¼ 1 þ 2:5f,
(1)
where f is the volume fraction and Zrel is the ratio of the suspension viscosity (Z) to that of the pure solvent (Zs ) (Dickinson & Stainsby, 1982). Einstein’s law of viscosity has two major assumptions: the particles are solid spheres, and they are far enough apart to be treated independently (Hiemenz, 1977). The primary electroviscous effect skews viscosity values away from Einstein’s prediction, as the symmetry of the ionic atmosphere around each particle is distorted by shear flow yielding higher viscosity values than for noncharged particles of similar size (Dickinson & Stainsby, 1982). Even at high dilution, such as those used in intrinsic viscosity measurements, the interaction of the ion and its atmosphere augments energy dissipation, thereby increasing the intrinsic viscosity (Krieger, 1985). More importantly for non-dilute dispersions is the effect of electrostatic repulsive forces to increasing the effective collision diameter of charged particles in shear
207
time constant, dimensionless shear rate, s1 consistency coefficient, Pa sn flow behavior index, dimensionless dielectric constant, dimensionless zeta potential, mV effective volume fraction, dimensionless density, g/ml hydrated particle diameter, mm dry particle diameter, mm
flow, the secondary electroviscous effect. As two charged spheres approach one another due to shear flow, the trajectories are altered due to repulsive forces originating from the charged ionic cloud surrounding the particles. This secondary electroviscous effect gives an additional source of energy dissipation, and hence higher viscosity than for an equivalent suspension of uncharged particles (Krieger & Eguiluz, 1976). This effect is greatly diminished by adding electrolytes or increasing the shear forces acting on the colloidal dispersion. The tertiary electroviscous effect describes changes in dimensions of the charged layers on colloids due to changes in the valency, pH, or dielectric constant. At low ionic strength, the repulsion between like charges on the same molecule leads to expansion of the polyelectrolyte chain, which may affect the bulk rheology and the effective interactions between particles. In food dispersions containing protein or charged polysaccharides, the tertiary effect usually dominates. All of these factors influence the electrostatic repulsion between charged groups and will hence control the conformation and thickness of the double layer (Goodwin, 1987, Chapter 10). The objective of this research was to expand the understanding of the interdependence of particle size, zeta potential, and rheological properties in modified whey protein dispersions. Another goal of this research was to study the influence of particle size on the rheological characteristics of the modified whey protein dispersions.
2. Materials and methods 2.1. Materials A commercial whey protein isolate (WPI) powder (lot # JE057-7-420), containing approximately 91.2 g/100 protein (N 6.38, micro-Kjeldahl, AOAC, 1984) was used (Bipro, produced by Davisco International Inc., Le Sueur, MN, USA). All chemicals were purchased from Fisher Scientific Company (Norcross, GA, USA).
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2.2. Preparation of protein dispersions and gels WPI powder was hydrated (12 g/100 ml) in deionized (DI) water, pH adjusted with 6 mol/l HCl to 3.357.02, and thermally gelled at 80 1C for 3 h according to the procedure of Hudson et al. (2000). Gels were subsequently frozen, freeze-dried, and ground into a powder. Modified whey protein powders were then sieved to obtain three particle-size ranges: 75–125, 45–74 and 20–44 mm. The sieves had mesh sizes of 120, 200, 325 and 635 (W.S. Tyler, Mentor, OH) and yielded a wide distribution of sizes: 2.53% of 4125 mm fraction; 41.58% of 75–125 mm fraction; 37.25% of 74–45 mm fraction; 12.62% of 20–44 mm fraction, and 6.02% of 6.02 mm fraction. 2.3. Particle-size analysis Powders were suspended in silicone oil or deionized water for 24 h, and particle size and size distribution was determined via a Centrifugal Particle Size Analyzer SACP4 (V1.0) (Shimadzu Corporation, Tokyo, Japan). 2.4. Density determination Dry powder and solution densities were determined at 25 1C on a Micromeritics Multivolume Pycnometer 1305 (Norcross, GA). Sample weights were measured (70.001 g), and instrumentation readings provided volume. Tests were performed in triplicate. 2.5. Dielectric constants Powder dielectric constants were measured on a Hewlett Packard (HP) 8753E Network Analyzer attached to a HP 85070B Dielectric Probe utilizing HP Dielectric Probe Software (Rev. 01.05) (Palo Alto, CA, USA). Tests were performed at 25 1C in triplicate. 2.6. Rheological measurements Steady and small amplitude shear tests were performed on a Reologica StressTech controlled stress rheometer (ReoLogica Instruments AB, Lund, Sweden) at 25 1C. All samples (10 g/100 protein) were hydrated in deionized water during gentle agitation (o100 rpm) for 5 h at 25 1C; samples were then stored at 5 1C for X24 h. Prior to rheological analysis, samples were equilibrated to ambient temperature. Once the bob (37.9 mm high and 2.5 mm diameter) was immersed in the cup (27.0 mm diameter), a thin layer of mineral oil coated the sample surfaces to prevent moisture loss, followed by a preshear at 15/s for 30/s. The same lot of modified whey powders was sieved to achieve the three narrow particlesize ranges. For all rheological testing, suspension pH and ionic strengths were constant, and only average particle diameter was varied.
2.6.1. Zero shear Zero shear viscosity (Z0 ) was determined for five protein concentrations (6.0, 6.5, 7.0, 7.5 and 8.0 g/100) by subjecting the dispersions to stress ramps from 0.05 to 25.0 Pa, and recording viscosity and the corresponding shear rate. Apparent viscosity (Za ) was modeled via a modified cross model, Z0 Za ¼ , (2) 1 þ ðac g_ Þm where ac is a time constant, g_ is shear rate, and m is a dimensionless exponent. Equation constants were assessed using non-linear regression statistical techniques. 2.6.2. Steady shear rheology Shear rate ramps (1.0–100.0/s) were performed and viscosity was modeled using a power-law equation to determine sample consistency coefficient (K) and flow behavior index (n). Za ¼ K g_ n1 .
(3)
2.6.3. Oscillatory rheology To ascertain viscoelastic properties, mechanical spectra were conducted at a stress of 1.0 Pa as frequency was oscillated from 0.1 to 20.0 Hz. Analysis was conducted in the identified linear viscoelastic region. 2.6.4. Intrinsic viscosity Intrinsic viscosity [Z] was measured with a Cannon– Fenske capillary viscometer submerged in a water bath maintained at 25.070.1 1C. Five concentrations between 0.548 and 2.74 mg protein/ml were measured, and specific viscosity Zsp was calculated as Zsp ¼
ðt t0 Þ , t0
(4)
where t0 be the efflux time of DI water and t is the efflux time of the sample. The intrinsic viscosity was determined using the Huggins equation Zr ¼ Zsp =c ¼ ½Z þ k½Z2 c,
(5)
where c is protein concentration (g/mL); Zsp ¼ Zrel 1; Zrel is the relative viscosity and Zr ¼ Zsp =c is the reduced viscosity. 2.7. Electrokinetic analysis Electrophoretic mobility was measured on a ZetaPALS Analyzer (Brookhaven Instruments Corp., Holtsville, NY, USA), and zeta potential was calculated using the Smoluchowski equation mE ¼
z , Z
(6)
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where mE is electrophoretic mobility, is dielectric constant, z is zeta potential, and Z is the apparent viscosity of the suspending medium.
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less structural rigidity. Therefore a greater proportion of the smaller particle sizes may possess greater porosity yielding greater swelling capacities. 3.2. Volume fraction
3. Results and discussion
Many colloidal calculations and discussions are conducted on a volume fraction (f) basis, defined as
3.1. Particle-size analysis
f¼
A median particle size for 75–125, 45–74 and 20–44 mm sieved fractions and non-sieved mWPI was determined in oil to approximate a dry particle size and in DI water after a 24 h hydration period. Dry and fully hydrated diameter values are provided in Table 1. Comparison of the two particle-size data series clearly depicts the swelling capacity of these colloids, with the 20–44 mm sieved fraction swelling approximately 1.8 times its dry particle size after hydration, and all remaining fractions swelling at least 1.3 times. Deviations in the swelling capacities of the various sieved fractions may elucidate some structural characteristics of the powders influenced by size. For example, the smaller particles may possess enhanced swelling ability due to fewer structural networks or linkages between proteins within the colloid, thereby producing a more porous structure. This structure therefore may allow more water to imbibe into the colloid, increasing the particle volume and measured diameter. Walbridge (1987) found softer titanium dioxide crystals to yield finer particle fragments during milling. Hence, powder with fewer networks may mill into smaller pieces due to
Volume of particles . Volume of particles þ Volume of dispersant
(7)
Determination of particle volume fraction was necessary for dispersed colloidal systems as viscosity depends strongly on the amount of the dispersed phase, especially at high volume fractions (Dickinson & Stainsby, 1982). This experiment however based all analyzes on a percent hydrated (swollen) protein and not percent powder. Therefore, a hydrated particle or effective volume fraction (fE ) was determined for all protein concentrations. Due to significant particle swelling, incorporation of a swelling capacity ratio (Dh/Dd) into the calculation was required ½protein Dh 3 , (8) fE rpowder Dd where r is density, Dh is hydrated particle diameter, and Dd is dry particle diameter. Conversions from weight percent to an effective volume fraction for all concentrations are given in Table 2. A basis for the incorporation of swelling capacity into the calculation of volume fraction is well established for starch systems (Bagley &
Table 1 Physical and electrical properties of powdersa Sample
Density r (g/ml)
Dry diameter Dd (mm)
Hydrated diameter Dh (mm)
Zeta potential z (mV)
Dielectric constantb
WPI mWPI 75–125 mm 74–45 mm 20–44 mm
1.1570.01 1.3270.01 1.3170.00 1.3370.02 1.3270.02
N/A 25.372.7 100.9715.7 56.574.8 35.173.5
N/A 36.378.2 133.6724.1 87.4711.8 64.0 710.3
44.671.6 35.570.9 52.172.9 34.470.5 31.771.3
1.8970.04 2.0970.03 1.9070.01 1.9170.02 1.6970.02
a
Averages7standard error Dielectric constants measured at 1 Hz.
b
Table 2 Conversion of protein weight percent to effective volume fraction (fE ) Protein weight percents (g/100)
mWPI 75–125 mm 45–74 mm 20–44 mm
0.05
0.10
0.15
0.20
0.25
6.00
6.50
7.00
7.50
8.00
10.00
0.0012 0.0001 0.0015 0.0025
0.0024 0.0019 0.0030 0.0050
0.0036 0.0029 0.0045 0.0074
0.0048 0.0038 0.0060 0.0099
0.0060 0.0048 0.0075 0.0124
0.1533 0.1222 0.1926 0.3171
0.1670 0.1331 0.2097 0.3452
0.1808 0.1441 0.2271 0.3737
0.1948 0.1553 0.2447 0.4027
0.2088 0.1665 0.2623 0.4317
0.2610 0.2081 0.3278 0.5396
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Christianson, 1982; Christianson & Bagley, 1983; Steeneken, 1989). Modified powders have similar behaviors to starch in solution (significant water holding and swelling capacities), and therefore it was not surprising that for accurate volume fraction determination, both necessitate the integration of similar parameters. 3.3. Zeta potential Dispersion electrophoretic mobility depends upon the shape and size of the particle, the properties of the electrolyte solution in which it is dispersed, and the potential at the shear plane (Dickinson & Stainsby, 1982). The modified protein (0.1 g/100) colloidal suspensions tested were acidic (pHE3.7) and well below the isoelectric points of the major whey proteins, commonly given as 5.4 for b-lactoglobulin and 4.3 for a-lactalbumin (Morr, 1989, Chapter 7). Therefore, the modified whey colloids were positively charged whereas the native whey proteins (pH 6.8) had negative charges, as do many proteins in biological systems at native pH (de Wit, 1989). A direct relationship between zeta potential and colloidal diameter was observed, with the 74–125 mm fraction exhibiting a 1.6 times larger potential than the 20–44 mm fraction. The impact of zeta potential on the rheological behaviors and physical properties of the dispersions will be addressed throughout the remaining sections. 3.4. Rheological analysis Much research on colloidal dispersions has been conducted on monodisperse, hard sphere systems (Mellema, de Kruif, Blom, & Vrij, 1987; Buscall, 1991; Foss & Brady, 2000), providing a framework from which to draw upon when studying the complex dispersed colloidal systems typically seen in food. This research attempted to assimilate colloidal theory into the explanation of the rheological and functionality characteristics exhibited by the mWPI dispersions. 3.4.1. Zero shear Almost all colloidal dispersions are shear thinning; therefore, apparent viscosity will decay with increasing shear rate, and Newtonian behavior may only exist at very low rates. This situation corresponds to the horizontal Newtonian plateau (zero shear viscosity) in the viscosity shear rate plots shown in Figs. 1a–d. Increasing weight percent induced lower zero shear plateaus for each fraction (Figs. 1a–d). As the degree of colloidal interaction increased, the freedom of movement of the individual colloids was progressively restricted. Consequently, the time required to form new interactions to replace those disrupted by deformation increased. Thus, the shear rate at which Newtonian
behavior was lost moved to ever-decreasing values as concentration increased (Morris, Cutler, Ross-Murphy, Rees, & Price, 1981). Therefore, the shear rate duration at which Newtonian plateaus were present decreased with increasing weight percent for all particle sizes. This characteristic was due to the polymer dispersions becoming increasingly non-Newtonian as concentration increased (Krieger, 1985). Additionally, the magnitude of the Newtonian viscosity plateau (Z0 ) at each weight percent increased with decreasing particle size (Figs. 1a–d). The rheological dependence upon particle size was qualified by the recognition that as particle size decreases the number of particles in a given volume increases, resulting in a decrease in the average distance between particles (Russell, 1978). Therefore, the smallest fraction (20–44 mm) had the highest number of particles in solution at a given weight percent. As a result, the larger viscosity for the smallest diameter was most likely due to a concentration effect and not electroviscous in nature. This hypothesis was reinforced by the electrokinetic analysis that yielded smaller zeta potentials for smaller particles, and this fraction would be less apt to exhibit secondary electroviscous effects during zero shear analysis. Zero shear viscosities were plotted on a volume fraction basis and presented in Fig. 1e. Clearly, lower effective volume fractions achieved higher plateaus for the larger diameter colloids. Additionally, the log Z0 verses fE relationship for each fraction followed the same trend. For a dispersion of 20–44 mm particles to produce an analogous zero shear viscosity to a dispersion of 75–125 mm dispersions, effective volume fraction would need to be increased approximately 2.6 times that of the larger particles. This response was expected, as increasing particle diameter resulted in larger zeta potentials, and these particles may therefore exhibit higher secondary electroviscous behaviors (Russell, 1978). 3.4.2. Steady shear rheology The shear-thinning behavior observed in mWPI suspensions was not surprising, as many suspensions display pseudoplasticity. The proposed mechanism responsible for this behavior is layering of the colloids during increasing shear, allowing the particles to slip easily over one another resulting in a diminished viscosity (Ackerson, 1990). A clear influence of particle size on the rheology of samples during steady shear analysis was observed, with the suspensions composed of the smaller diameter particles possessing the highest viscosity (Fig. 2). When analysing the curves via the power-law model, a clear relationship between consistency coefficient (K) and particle size was evident, with K decreasing with increasing particle diameter (Fig. 3). The inverse relationship between suspension viscosity
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211
10.00
Viscosity (Pa s)
Viscosity (Pa s)
10.00
1.00
1.00
0.10
0.10
0.01 1.00
(a)
10.00 Shear rate (s-1)
0.01 1.00
100.00
10.00
(b)
100.00
Shear rate (s-1)
10.00
1.00
0.10
0.01 1.00
(c)
Viscosity (Pa s)
Viscosity (Pa s)
10.00
0.10
0.01 1.000
100.00
10.00 Shear rate (s-1)
1.00
10.000
(d)
100.000
Shear rate (s-1)
10
η (Pa s)
1
0.1
0.01 0
0.1
0.2
(e)
0.3 φE
0.4
0.5
0.6
Fig. 1. (a). Zero shear viscosity ramp of mWPI at five concentrations (6.0% (J), 6.5% (E), 7.0% (n), 7.5% (K) and 8.0% (&) protein w/w). (b). Zero shear viscosity ramp of sieved fraction 75–125 mm at five concentrations (6.0% (J), 6.5% (E), 7.0%(n), 7.5% (K) and 8.0% (&) protein w/w). (c) Zero shear viscosity ramp of sieved fraction 45–74 mm at five concentrations (6.0% (J), 6.5% (E), 7.0% (D), 7.5% (K) and 8.0% (&) protein w/ w). (d). Zero shear viscosity ramp of sieved fraction 20–44 mm at five concentrations (6.0% (J), 6.5% (E), 7.0% (n), 7.5% (K) and 8.0% (&) protein w/w). (e) Plot of Newtonian viscosity verses effective volume fraction for mWPI (n), and 75–125 mm (m), 45–74 mm (K), 20-44 mm (J) sieved fractions.
and particle size was contrary to the findings of Rao and Tattiyakul (1999), who found K to increase with increasing tapioca starch diameter. However, Yoo and Rao (1994) found smaller diameter tomato products to have larger viscosities than tomato products of larger diameters. The increasing viscosity with decreasing colloid diameter observed in the Yoo and Rao (1994) study and in this research may be a phenomenon
resulting from colloidal charge, not evident in the Rao and Tattiyakul (1999) study at any pH because starch is not charged. Previous research established that decreasing particle size increased dispersion viscosity, caused by an increase in the overlapping area of the electric double layer around each particle (Ogawa, Yamada, Matsuda, Okajima, & Doi, 1997). Thus, at a constant weight percent, there were more smaller particles present,
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212
Viscosity (Pa s)
100
10
1
0 0
20
40
60
80
100
120
140
Shear rate (s-1)
Fig. 2. Shear rate ramp (1–100/s) for mWPI (n), and 75–125 mm (&), 45–74 mm (K), 20–44 mm (~) sieved fractions.
Consistency Coefficient (K) (Pa sn)
110 100
20-44 µm
90 45-74 µm
80 70 60 mWPI
75-125 µm
50 40
0
50
100
150
200
Hydrated Diameter (µm)
Fig. 3. Consistency coefficient (K) verses hydrated particle diameter for sieved and non-sieved mWPI fractions.
allowing the electric double layer around each particle to overlap more strongly than for larger colloids. The interpartical potential (the potential acting between the particles) increased with decreasing particle diameter, and therefore so may the secondary electroviscous effects. Hence, with a decrease in charged particle diameter, the repulsive interaction between dispersed particles increased with viscosity, as observed in this study. It should be noted that consistency coefficient was additionally analysed on an effective volume fraction instead of a weight percent basis, and increasing K with decreasing diameters was still observed. A decrease in the flow behavior index (n) was observed with decreasing whey dispersion particle diameter (Table 3). Ogawa and colleagues (1997) however observed decreased pseudoplasticity with decreased particle size in a synthetic system of charged colloids (Ogawa et al., 1997). This discrepancy in behaviors was attributed to the fact that measurements in this research were conducted on a 10 g/100 weight basis in lieu of volume fraction whereas the results of
Ogawa et al. (1997) were conducted at a set volume fraction of 0.30. Therefore for comparative purposes the flow behavior indices derived in this study were analysed with respect to calculated effective volume fraction (fE ). The increasing n with decreasing particle diameter trend was observed when power-law properties were evaluated in this manner. The reduction in the magnitude of the secondary electroviscous effect at the higher shear rates tested may also be responsible for a portion of the decreased flow behavior indices seen in the colloidal dispersions. It is well established that viscous forces tend to decrease with shear rate, while electrostatic forces remain constant. Thus, the particle displacement due to charge and viscosity decreases with increasing shear rate (Russell, 1978). This decreased displacement caused a drop in the measured viscosity of dispersions. 3.4.3. Oscillatory rheology A deviation in the trend of smaller-sized particles showing superior rheological properties (on a weight percent basis) was evident in the small strain analysis. The mechanical spectra revealed a larger complex modulus (G*), and therefore stronger viscoelastic properties for the 75–125 mm sample; while all other sample fractions, regardless of size, exhibited analogous viscoelastic fluid properties (Fig. 4). For comparative purposes, the effective volume fractions (fE ) for dispersions of protein (10 g/100) are presented in Table 2. Clearly, the 75–125 mm sample achieved higher moduli values on a weight percent and fE basis. Quite possibly, higher zeta potentials and the minute shearing placed upon samples during oscillation may culminate in large electroviscous effects, thereby increasing viscosity. 3.4.4. Intrinsic viscosity At high dilution the behavior of a colloidal dispersion is described by a quantity known as intrinsic viscosity, [Z]. Because [Z] represents the hydrodynamic or sweep volume of a colloid and is related to the molecular weight and the radius of gyration, it reflects important molecular characteristics (Rao, 1999, Chapter 1). Intrinsic viscosities of mWPI and the sieved fractions are given in Fig. 5, and increased [Z] was noted with increasing particle diameter. Macromolecules that possess a large number of ionisable groups are called polyelectrolytes. When these groups dissociate in aqueous media, the result is counterions and a macroion, where the charge groups have no independent mobility because they are attached to the chain (Launay, Doublier, & Cuvelier, 1986, Chapter 1). Intrinsic viscosities for many polyelectrolytes demonstrate a peculiar behavior, increasing reduced viscosity with decreasing polyelectrolyte concentration (Frollini, Reed, Milas, & Rinaudo,
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Table 3 Steady shear flow behavior indicesa, consistency coefficients, and apparent viscosities of 10 g/100 protein solutions Sample
K (Pa sn)
n
R2
b
75–125 mm 74–45 mm 20–44 mm mWPI
50.4971.78 80.9672.16 97.9772.43 53.8071.09
0.2870.01 0.1870.01 0.1870.01 0.2070.01
0.93 0.97 0.91 0.93
Za,25 c (Pa s)
Za,75
4.53 6.82 8.72 4.15
2.40 2.39 2.84 1.85
d
(Pa s)
a
Averages7standard error. Regression coefficient for power-law model fit. c Apparent viscosity at a shear rate of 25 s1 and 25 1C. d Apparent viscosity at a shear rate of 75 s1 and 25 1C. b
10000
1.180 1.160 1.140
η/η0
G* (Pa)
1.120 1000
slope = 14.1 slope = 24.3 slope = 7.3
1.100 1.080 1.060 1.040 1.020
100 0.01
0.10
1.00
10.00
100.00
1.000 0.000 0.002 0.004 0.006 0.008 0.010 0.012 0.014 0.016 0.018 φE
Frequency (Hz)
Fig. 4. Frequency sweep of mWPI (n), and the three sieved fractions: 75–125 mm ( ), 45–74 mm (K), and 20–44 mm (~).
[η] 90
♦
∆ 71.39
76.75
0.0015
0.0020
O 80.32
84.57
80 70 ηred (mL /g)
60 50 40 30 20 10 0 0.0000
0.0005
0.0010
0.0025
0.0030
Protein Concentration (g/mL)
Fig. 5. Reduced viscosity plot of mWPI (D), and the three sieved fractions: 75–125 mm (&), 45–74 mm (J), and 20–44 mm (~).
1995), in contrast to the linear plots obtained for standard polymers. Polymerized whey protein preparations have also been shown to exhibit this behavior, attributed to a decrease in the ionic strength at high dilution, permitting polymer unfolding and yielding
Fig. 6. Verification of Einstein’s viscosity equation for a suspension of spheres using suspensions of the three sieved fractions: 75–125 mm (m), 45–74 mm (&), and 20–44 mm (~).
(increased Zr ) at lower concentrations (Vardhanabhuti & Foegeding, 1999). As represented in Fig. 5, polyelectrolytic behavior was noted for the modified whey colloids of all size fractions and was credited to the expansion of the colloidal particle due to reduced electrolytic concentrations upon dilution. The close proximity of groups carrying like charges caused the polymer expansion by electrostatic repulsion, the tertiary electroviscous effect. This effect is due to changes in the chemical environment such as valency, pH, and electrolytic concentration (Launay et al., 1986, Chapter 1) as in this case. The thickness of the double layer is inversely proportional to the square root of the electrolytic concentration in the continuous medium (Hill, 1998), and the diminished mineral content allowed heightened electroviscous effects due to ionic cloud expansion in the dispersions. The intrinsic viscosity of suspensions differs from the Einstein value of 5/2. Some of the factors shown to influence [Z] are the surface properties of the particles (due to the effects of concentration, pH, ionic strength, and adsorbed layer thickness), aggregation, non-Newtonian behavior of the continuous phase, and particle size (when in the Brownian motion size regime) (Bagley, 1992, Chapter 13). A plot of Zrel verses effective volume
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fraction was created to test Einstein’s law of viscosity for derivitized whey colloids (Fig. 6). The slope of the regression lines should yield the predicted 5/2-viscosity value, however significant deviations were observed for each of the fractions.
4. Conclusion Obtaining mWPI dispersions of defined sizes permits enhanced control of powder functionality, as rheological and electrokinetic behaviors were significantly impacted by particle size. The increase of dispersed particle diameter resulted in increased zeta potential, flow behavior index, intrinsic viscosity, and deviation from Einstein’s viscosity law. Whereas decreased consistency coefficients, zero shear plateaus and swelling capacities were witnessed with increasing particle size. Therefore, many rheological properties can essentially be controlled and conclusively manipulated through selection of mWPI dispersions of specific sizes and distribution.
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