Impact of MG²⁺ and Tara Gum Concentrations on Flow and Textural Properties of WPI Solutions and Cold-Set Gels

Figures & data

Table 1 Box-Behnken experimental design matrix

	WPI concentration		TG concentration		Mg^2+ concentration
Runs	Coded X1	Uncoded WPI (wt%)	Coded X2	Uncoded TG (wt%)	Coded X3	Uncoded Mg^2+ (mM)
1	−1	6.0	−1	0.20	0	50
2	−1	6.0	0	0.35	−1	25
3	−1	6.0	0	0.35	1	75
4	−1	6.0	1	0.50	0	50
5	0	7.5	−1	0.20	−1	25
6	0	7.5	−1	0.20	1	75
7	0	7.5	0	0.35	0	50
8	0	7.5	0	0.35	0	50
9	0	7.5	0	0.35	0	50
10	0	7.5	1	0.50	−1	25
11	0	7.5	1	0.50	1	75
12	1	9.0	−1	0.20	0	50
13	1	9.0	0	0.35	−1	25
14	1	9.0	0	0.35	1	75
15	1	9.0	1	0.50	0	50

Table 2 Values of apparent viscosity for native (η_ap ^ND) and heat-denatured (η_ap ^HD) WPI solutions, at 25°C

CWPI (wt%)	ηap ^ND (Pa.s)	ηap ^HD (Pa.s)
6.0	0.0020 ± 0.0001	0.0029 ± 0.0002
7.5	0.0021 ± 0.0001	0.0049 ± 0.0003
9.0	0.0032 ± 0.0002	0.0068 ± 0.0003

Table 3 Cross (τ, m) and Carreau (λ, k) adjustable parameters for steady simple shearing, obtained for TG solutions, at 25°C

CTG (wt%)	η0 (Pa.s)	τ (s)	m (−)	ARD* (%)	η0 (Pa.s)	λ (s)	k (−)	ARD* (%)
0.20	0.042	0.03	0.53	1.4	0.039	0.22	0.17	4.8
0.35	0.252	0.05	0.59	1.8	0.236	0.30	0.19	4.8
0.50	0.978	0.08	0.62	2.9	0.922	0.36	0.22	3.8
*Average relative deviation,

Figure 1 Flow curves for tara gum native (ND) solutions (open symbols) and heat denatured (full symbols) dispersions, for different concentration values, at 25°C. Symbols: (□) 0.20 wt%, (△) 0.35 wt%, (○) 0.50 wt%, and (⋄) 0.65 wt%. Full line represents predictions of the Cross model and dotted lines those of the Carreau model.

Figure 2 Shear rate/concentration superposition for tara gum, native (ND) solutions (open symbols) and heat denatured (full) dispersions, at 25°C. Master curve at the reference concentration of 0.20 wt% TG. Symbols: (□) 0.20 wt%, (△) 0.35 wt%, (○) 0.50 wt% and (⋄) 0.65 wt%.

Figure 3 Horizontal (open symbols) and vertical (full symbols) shift factors as a function of the tara gum concentration, used to obtain the flow master curves of Fig. 2.

Table 4 Cross (τ, m) and Carreau (λ, k) adjustable parameters for steady simple shearing, of the native and heat-denatured mixed solutions of WPI+TG, at 25°C

CWPI (wt%)	CTG (wt%)	η0 (Pa.s)	τ (s)	m (−)	ARD (%)	η0 (Pa.s)	τ (s)	m (−)	ARD (%)
Native solutions
7.5	0.20	0.066	0.54	0.39	9.2	0.074	0.45	0.69	2.2
7.5	0.35	0.466	0.39	0.52	6.7	0.495	0.27	1.22	3.9
7.5	0.50	2.126	0.16	0.81	8.6	2.159	0.15	1.68	3.8
Heat-denatured solutions (75°C/20 min)
7.5	0.20	0.074	1.82	0.21	2.6	0.076	0.34	0.84	2.2
7.5	0.35	0.511	0.39	0.50	7.4	0.517	0.24	1.23	4.8
7.5	0.50	2.458	0.14	0.86	8.8	2.505	0.14	1.69	3.9
*Average relative deviation, .

Table 5 Mechanical properties of the cold-set WPI and WPI+TG gels

CWPI (wt%)	CTG (wt%)	CMg ^2+ (mM)	Fractura-bility (N)	Puncture resistance (N)	Rupture strain (−)	Rigidity (N m^−1)	Young's modulus (kPa)
6.0	0.20	50	0.08 ± 0.01	0.11 ± 0.02	45 ± 3	7 ± 0.5	1.84 ± 0.21
	0.35	25	0.11 ± 0.01	0.10 ± 0.01	41 ± 3	7 ± 0.4	0.71 ± 0.08
		75	0.16 ± 0.03	0.24 ± 0.02	61 ± 4	14 ± 1.2	3.09 ± 0.28
	0.50	50	0.28 ± 0.03	0.40 ± 0.03	57 ± 5	17 ± 1.5	6.86 ± 0.35
7.5	0.20	25	0.17 ± 0.02	0.24 ± 0.02	71 ± 7	11 ± 1	3.03 ± 1.29
		75	0.31 ± 0.03	0.36 ± 0.03	65 ± 5	39 ± 3	4.44 ± 1.31
	0.35	50	0.47 ± 0.04	0.64 ± 0.05	35 ± 4	60 ± 5	17.52 ± 1.51
	0.50	25	0.57 ± 0.03	0.83 ± 0.05	78 ± 8	30 ± 2	11.28 ± 1.42
		75	1.06 ± 0.06	1.31 ± 0.08	69 ± 6	97 ± 6	16.51 ± 1.48
9.0	0.20	50	0.61 ± 0.04	0.74 ± 0.05	45 ± 4	53 ± 3.4	13.07 ± 0.37
	0.35	25	0.78 ± 0.04	1.12 ± 0.06	39 ± 4	86 ± 6.8	19.60 ± 0.49
		75	1.41 ± 0.09	1.86 ± 0.09	41 ± 5	134 ± 9.3	21.40 ± 1.52
	0.50	50	2.06 ± 0.12	2.69 ± 0.12	57 ± 5	130 ± 8.2	48.58 ± 2.64

Table 6a Regression coefficients of fracturability, puncture resistance, rupture strain, rigidity and Young's modulus

	Fracturability (N)	Puncture resistance (N)	Rupture strain (−)	Rigidity (N m^−1)	Young's modulus (kPa)
b 0	7.25	8.96	45.5	111	26.8
b 1 (CWPI)	−1.58	−2.03	35.0	−35.7	−12.3
b 2 (CTG)	−12.4	−15.05	−603	−174	−180
b 3 (CMg ^2+)	−2.40 × 10^−2	−2.20 × 10^−2	−1.42	−1.63	1.20
b 11 (CWPI×CWPI)	8.30 × 10^−2	0.110	−2.06	1.72	0.545
b 22 (CTG×CTG)	4.44	4.52	917	−539	−51.5
b 33 (CMg ^2+×CMg ^2+)	−6.80 × 10^−5	−8.53 × 10^−5	2.40 × 10^−2	−6.00 × 10^−3	−1.20 × 10^−2
b 12 (CWPI×CTG)	1.39	1.84	1.74 × 10^−6	74.4	33.9
B 13 (CWPI×CMg ^2+)	4.00 × 10^−3	4.00 × 10^−3	−0.121	0.273	−4.00 × 10^−3
b 23 (CTG×CMg ^2+)	2.30 × 10^−2	2.40 × 10^−2	−0.202	2.60	0.255

Table 6b analyses of variance (p value) of fracturability, puncture resistance, rupture strain, rigidity and Young's modulus

	Fracturability (N)	Puncture resistance (N)	Rupture strain (−)	Rigidity (N m^−1)	Young's modulus (kPa)
CWPI	<0.01	<0.01	<0.01	<0.01	<0.01
CTG	<0.01	<0.01	0.02	<0.01	<0.01
CMg^2+	<0.01	0.01	0.06	<0.01	0.10
CWPI ×CTG	<0.01	<0.01	0.87	0.01	0.01
CWPI × CMg^2+	0.01	0.03	0.01	0.02	0.53
CTG × CMg^2+	0.03	0.07	0.27	0.03	0.04