Fractal Dimension Analysis of Texture Formation of Whey Protein-Based Foods

Table 3

Fractal dimension () values of different types of gels, measured by using rheological method.

Reference	Gel type
Hagiwara et al. (1997a)	Heat induced: BSA; I = pH 7.0; II = 50 mM buffer pH 7.0, 30 mM CaCl2; III = 50 mM buffer pH 7.0, 5 mM CaCl2; β-Lg; IV = pH 7.0; V = pH 7.0 + 30 mM CaCl2	I = strong-link, 2.00–2.07; II = weak-link, 2.82; III = weak-link, 2.61; IV = strong-link, 2.14–2.20; V = weak-link, 2.69
Hagiwara et al. (1997b)	Heat induced β-Lg; pH = 7.0; NaCl = 1.0 M	Weak-link, 2.62
Hagiwara et al. (1998)	Heat-induced BSA; I = 50 mM buffer pH 5.1, 0.1 M NaCl; II = 50 mM buffer pH 7.0, 30 mM CaCl2; III = 50 mM buffer pH 7.0, 5 mM CaCl2	I = weak-link, 2.82; II = weak-link, 2.82; III = weak-link, 2.61
Vreeker et al. (1992)	Acid-induced cold gelation WPI (1 or 10% w/w) + 0.1 M NaCl or CaCl2 at pH 5.4	Shih et al. (1990) = 2.0; Bremer (1992) = 2.3; σ: Bremer (1992) = 2.4–2.5
Ikeda et al. (1999)	Heat-induced WPI pH 7.0 + 25–1000 mM NaCl	25 mM NaCl = 2.2; 100 mM NaCl = 1.5; (incorrectly predicted); 500 mM NaCl = 1.8; 50, 80, 500, and 1000 mM NaCl = DLCA
Alting et al. (2003)	Acid-induced cold gelation WPI 9%	2.3, acid-induced; cold gelation probably starts off as a fractal process but is rapidly taken over by another mechanism at larger length scales (>100 nm)
de Kruif et al. (1995)	Salt-induced cold gelationβ-Lg; NaCl = 0.1 or 0.5 M	After passing the gelation threshold, gel with more or less fractal-like structure was formed and it coarsens with increasing salt concentration. Nevertheless, gels properties could not completely be described using the scaling laws as explained by many authors
Marangoni et al. (2000)	Heat-induced WPI (5% w/v); Salt-induced cold gelation	CaCl2 = weak-link, 2.63; NaCl = weak-link, 2.45
Stading et al. (1993)	Heat-induced β-Lg at pH 5.3 with different heating rate	Microstructure of gels showed straight-strand type; pH 5.3 = 2.46–2.47; pH 5.7 = 2.91–2.94
Kuhn et al. (2010)	Heat-induced WPI + 150 mM NaCl or CaCl2	CaCl2 = weak-link, 2.66; NaCl = weak-link, 2.62
Andoyo et al. (2015)	Acid-induced cold gelation WPA & WPA + NMC, pH 4.5	WPA gels: strong-link; = 1.6–1.7; γ0 = 1.15; WPA + NMC gels: weak-link; = 2.6; γ0 = 2.29
Hagiwara et al. (1996)	BSA dissolved in HEPES buffer of pH 7.0 and acetate buffer of pH 5.1 to 0.1% and 0.001% solutions, heated at 95°C, varying the heating time	BSA at pH 7.0 were about 2.1 and 1.5; of heat-induced aggregates at pH 5.1 was about 1.8
Foegeding et al. (1995)	A fine-stranded matrix formed in protein suspensions contained monovalent cation (Li^+, K^+, Rb^+, and Cs^+) chlorides, sodium sulfate, or sodium phosphate at ionic strengths ≤ 0.1 mol/dm^3. This matrix varies in stress and strain at fracture at different salt concentrations	Protein-specific factors can affect the dispersibility of proteins and thereby determine the microstructure and fracture properties of globular protein gels
Verheul & Roefs (1998)	Gels were made at near-neutral pH. Protein concentration (35–89 g/l) and NaCl concentration (0.1–3 mol/dm^3) were systematically varied	Gel structure did not change much after gel formation, while gel rigidity continued to increase, and at the gel point only part of the protein in the dispersion contributes to the gel network. The fractal concept cannot simply be applied to WPI gels
Eissa, Khan (2005)	Whey protein solution: 3% and 7.5% (heat with/without transglutaminase, TG), low pH cold-set whey protein gel, final pH 4.0	CSLM: 1.96–1.98; Rheology: 2.05–2.09