Chapter 19
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Effect of Interdroplet Forces on Centrifugal Stability of Protein-Stabilized Concentrated Oil-in-Water Emulsions 1
Amardeep S. Rehill and Ganesan Narsimhan
Department of Agricultural Engineering, Biochemical and Food Process Engineering, Purdue University, West Lafayette, IN 47907
A model for the centrifugal stability of protein stabilized concentrated oil-in-water emulsion is proposed. Interdroplet forces due to van der Waals, electrostatic and stearic interactions were evaluated. The proposed model is employed to predict the equilibrium profiles of continuous phase liquid holdup andfilmthickness for protein stabilized concentrated oil-in-water emulsion subjected to a centrifugal forcefield.The continuous phase liquid holdup as well as the film thickness and, consequently, the stability of emulsion were found to be higher for lower centrifugal accelerations, smaller emulsion drop sizes, higher protein concentrations, more favorable protein-solvent interactions and higher protein charge. The calculated profiles reflected jump transitions infilmthickness as well as continuous phase liquid holdup as a result of centrifugal force exceeding the local maximum disjoining pressure.
Protein stabilized oil-in-water emulsions are found in various branches of food industry. These include milk, cream, ice-cream, mayonnaise, gravies and meat emulsions. These emulsions have extremely large interfacial area since oil is dispersed in the form offinedroplets. Consequendy, formation of such emulsions usually results in an increase in the tree energy. As a result, these emulsions are thermodynamically unstable. In other words, emulsions will eventually break due to coalescence of drops. As the individual droplets of the dispersed phase in an emulsion approach each other due to the relative motion brought about by Brownian and gravitational forces, they are attracted to each other by van der Waals forces. Without a stabilizer, the continuous phase between the two droplets drains, leading to their coalescence. Emulsifiers and stabilizers employed in food emulsions, however, slow down the overall rate of coalescence by providing an energy barrier to coalescence thereby increasing the shelf-life. This energy barrier is a result of repulsive forces between 1
Corresponding author
0097-6156/93/0528-0229$06.00/0 © 1993 American Chemical Society Spanier et al.; Food Flavor and Safety ACS Symposium Series; American Chemical Society: Washington, DC, 1993.
230
FOOD FLAVOR AND SAFETY
emulsion droplets due to the adsorbed layer of stabilizers at the droplet surface. Caseinate, whey protein and egg protein are commonly employed to stabilize food emulsions. They tend to adsorb at the oil -in-water interface and modify the interparticle forces so as to provide kinetic stability to the emulsion. Many of the food emulsions are concentrated oil-in-water emulsions. Moreover, oil droplets flocculate due to creaming to form a concentrated cream layer in which the droplets are deformed and separated by thin Alms of continuous phase liquid. Interaction forces between droplets influence the drainage and stability of thin films which in turn determine the rates of coalescence between the droplets. It is, therefore, necessary to understand the nature of these interaction forces in order to predict long term stability or shelf life of food emulsions. Excellent reviews of protein stabilized emulsions have been written by Hailing (7), Parker (2) and Narsimhan (3). In protein stabilized emulsions, the interaction forces between droplets depend on the surface concentration of adsorbed layer, pH, ionic strength, protein structure etc. The destabilizing influence of van der Waals attraction is overcome by repulsive interactions due to electrostatic and steric effects. Even though qualitative nature of these interactions is well known, very litde quantitative information is available on these interactions in food emulsions. The centrifugation of emulsions has been used to obtain a measure of their stability (4) by observing the separation of coalesced phase as a function oftime.Smith and Mitchell (J) proposed a method of calculating the maximum force between the droplets using centrifugation. Graham and Philips (6) investigated the effect of the structure of adsorbed protein layer on the stability of oil-in-water emulsion using centrifugation. The objective of this paper is to illustrate the efficacy of inferring the interdroplet forces in a concentrated protein stabilized oil-in-water emulsion from the knowledge of the equilibrium profile of continuous phase liquid holdup (or, dispersed phase fraction) when the emulsion is subjected to a centrifugal force field. This is accomplished by demonstrating the sensitivity of continuous phase liquid holdup profile for concentrated oil-in-water emulsions of different interdroplet forces. A brief discussion of the structure of concentrated oil-in-water emulsion is presented in the next section. A model for centrifugal stability of concentrated emulsion is presented in the subsequent section. This is followed by the simulation of continuous phase liquid holdup profiles for concentrated oil-in-water emulsions for different centrifugal accelerations, protein concentrations, droplet sizes, pH, ionic strengths and the nature of protein-solvent interactions. Structure of Concentrated Oil-in-Water Emulsion Since the volume fraction of close packed spheres is 0.74, emulsion droplets in a concentrated emulsion are deformed whenever the dispersed phase volume fraction exceeds 0.74. The structure of such emulsions is very similar to polyhedral foams and has been well characterized (7). The emulsion droplets, on the average can be considered to be regular pentagonal dodecahedrons separated by thin films. A schematic of a dodecahedral droplet is shown in Figure 1. Every droplet is separated by twelve neighboring droplets as indicated by twelve faces of the polyhedron. Two neighboring droplets are separated by a thin film of continuous phase liquid. Each face of the polyhedron is the interface of thin film. Three adjacent thin films meet in a channel called plateau border. The continuous phase liquid is interconnected through a network of plateau borders. Schematic of the cross-section of the plateau border is also
Spanier et al.; Food Flavor and Safety ACS Symposium Series; American Chemical Society: Washington, DC, 1993.
19.
REHILL & NARSIMHAN
"FILM.
Protein-Stabilized Concentrated 0/W Emulsions 231
-PLATEAU BORDER (INTERSECTION OF 1/ THREE FILMS) P
P6AS BUBBLE FILM (INTERSECTION OF FACES OF TWO ADJACENT POLYHEDRA)
FIGURE 1.
Regular dodecahedral structure of a bubble and cross-sectional view of a plateau border.
Spanier et al.; Food Flavor and Safety ACS Symposium Series; American Chemical Society: Washington, DC, 1993.
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FOOD FLAVOR AND SAFETY
shown in Figure 1. Since the film is planar, the pressure in the film is the same as that of an emulsion droplet However, the pressure in the plateau border is less than that in the emulsion droplet by the capillary pressure due to the radius of curvature of the plateau border. This difference in the pressure is referred to as the plateau border suc tion. As a result of this suction, continuous phase liquid will flow from thin films to the neighboring plateau border. This will be followed by drainage of continuous phase through the network of plateau borders due to centrifugal force when the con centrated oil-in-water emulsion is centrifuged. In protein stabilized emulsions, the interface of thin film consists of interfacial adsorbed protein layer. When the thick ness of draining film becomes of the order of a few hundred angstroms, the two phases of the film experience interaction forces due to intermolecular van der Waals, electrostatic and steric interactions. The draining film will eventually reach equili brium when the repulsive interactions exactly counterbalance the plateau border suc tion. This repulsive interaction force per unit area of the film is usually referred as the 'disjoining pressure' since this force tends to 'disjoin' or pull the two faces of the film apart Model for Centrifugal Stability of protein Stabilized Concentrated Emulsions Consider a concentrated emulsion consisting of equal size droplets. Even if the emul sion drops are not of the same size but are of narrow size distribution, there would be negligible segregation of drops according to size (due to creaming) since the emul sion is highly concentrated. Consequendy, one can expect the drop size distribution to be independent of height. Since the continuous phase liquid holdup varies along the direction of centrifugal force, the emulsion can be assumed to be uniform across any cross section (perpendicular to the centrifugal force). Let the ζ coordinates be opposite to the direction of the centrifugal force (bottom to top) with ζ = 0 referring to the interface between the emulsion layer and the bottom continuous phase layer. At equilibrium, the continuous phase in the plateau border channels, being in hydrostatic equilibrium, would satisfy the equality (5), [1] where ρ is the density of the continuous phase, a is the centrifugal acceleration and is equal to co L, where ω and L are the angular velocity of the centrifuge and the dis tance from the axis of rotation, respectively, and ρ is the pressure within the plateau border. The pressure within the plateau border can be related to the pressure in the dispersed phase Pd and the plateau border suction p through c
2
c
P=Pd+Pc
[2]
where dPd
Spanier et al.; Food Flavor and Safety ACS Symposium Series; American Chemical Society: Washington, DC, 1993.
[3]
19. REHILL & NARSIMHAN
Protein-Stabilized Concentrated OfW Emulsions 233
PJ being the density of the dispersed phase and „ _
σ
[4]
where r is the radius of curvature of the plateau border and σ is the interfacial ten sion. „
[5]
σ and π being the interfacial tension between oil and water, and the surface pressure due to the adsorption of proteins and emulsifier, respectively. Combining equations 1-4, we obtain, 0
[ 6 ]
( ρ - ρ „ Κ - σ £ φ =0 az r
The radius of curvature of plateau border can be related to the area of the plateau border a and the film thickness Xp for a regular dodecahedral arrangement from geometric considerations by (9), p
1
1/2
-1.732Χ/Γ + (1.732χ^ - 0.644(0.433x - a )\ [7] r= 0.322 As pointed out earlier, the continuous phase liquid drains from thin films to pla teau border due to plateau border suction. When the thickness of thefilmsbecomes of the order of a few hundred angstroms, the intermolecular forces due to van der Waals, double layer and steric interactions give rise to a disjoining pressure Π (defined as the excess pressure that tends to 'disjoin' or pull the two faces of the film apart) which counteracts the capillary pressure. Of course, this disjoining pressure is a strong function of film thickness. The variation of Π with xp will depend upon the characteristics of interfacial protein adsorbed layer, pH, ionic strength, and concen tration of adsorbed protein segments. The film will drain until the plateau border suc tion is exacdy counterbalanced by the disjoining présure after which the film reaches equilibrium. At equilibrium, 2
F
f
p
= n(x.)
™
As pointed out earlier, the disjoining pressure is the sum of interdroplet forces due to van der Waals, electrostatic and steric interactions. Detailed discussion of the nature of these interactions and their effect on the disjoining pressure can be found elsewhere (3,8). Only the final expressions for the contributions of different interactions to the disjoining pressure are given below. The disjoining pressure Tlyw due to van der Waals interactions is given by (5),
Spanier et al.; Food Flavor and Safety ACS Symposium Series; American Chemical Society: Washington, DC, 1993.
234
FOOD FLAVOR A N D SAFETY
ΤΙγψ = -
1
A 232 6π
- A 132 6π
(XF-2L )
3
S
A131
(* -L ) F
3
[9]
4
5
when the film thickness xp £ 2L , L being the thickness of the adsorbed protein layer. In the above equation, the subscripts 1, 2 and 3 refer to the oil, protein layer and water respectively. The effective Hamaker constant A^ for the interaction between î and k through the intervening medium j is given by, 5
5
[10]
2
Aij =
(A ^-Ajj^)(A^ -Ajj^
k
u
An being the Hamaker constant for the interaction of i through vacuum. When the film thickness xp £ 2L , the disjoining pressure Ilyw is given by S
Πγψ=
-
A121
[11]
3
6πχρ
The disjoining pressure Π*/ due to electrostatic interaction is given by (5), 2
3
Tl (h) = \6nkTtfA ! + if A (A + A ) + f(2A Α el
x
2
3
x
6
λ
3
2
+ 8A A +3A +A )] 1
2
1
[12]
2
where 1 cosh(K/t/2)'
Ai =
A
= 2
A = 3
Ai-A! 2
(Kh/ 2)tanh(KA/ 2) cosh (K/i/2)
[14]
3
3
4cosh (K/i/ 2)
[13]
3A-, 2
4cosh (K/i/ 2)
l-4(^)tanh(^)
[15] 4
2cosh (K/i/ 2)
1
2 '
Spanier et al.; Food Flavor and Safety ACS Symposium Series; American Chemical Society: Washington, DC, 1993.
19.
Protein-Stabilized Concentrated 0/W Emulsions 235
REHILL & NARSIMHAN
Y=tanh(y /4),
[ 1 6 ]
y = zey /kT
[ 1 7 ]
J
s
s
In the above equations, h is the film thickness, λ is the number concentration of ζ :z symmetrical electrolyte and ψ, is the surface potential. The surface potential ψ is the potential at the interface of stem and diffuse layers and is usually replaced by the zeta potential of the droplet determined from electrophoretic measurements. When the interface has an adsorbed layer of globular proteins, it may be reasonable to assume that the shear plane is located at the interface of protein layer. When xp > 2L the disjoining pressure TI can be evaluated by replacing ψ with ζ potential and tak ing Λ as (xp - 2L ). When the thickness of the draining film is less than twice the thickness of the adsorbed protein layer, (i.e. 2L ), the approaching faces of the film experience a steric interaction because of the overlap of the adsorbed protein layers. When L
