Effect of Ca and P Content, Residual Lactose, and Salt-to-Moisture Ratio on the Model Parameters of Process Cheese Linear Viscoelastic Properties

Figures & data

Figure 1 Experimental design of Cheddar cheese preparation for process cheese manufacturing.

Table 1 Average formulations with different ingredients for eight different process cheeses

Ingredient %	HHH	HHL	HLH	HLL	LHH	LHL	LLH	LLL
Cheddar cheese (2 months old)	69.34	71.62	70.23	72.29	72.06	72.63	72.31	74.91
NFDM	6.77	6.58	7.17	7.21	6.67	6.77	7.33	7.30
Butter oil	0.08	0.13	0.01	0.01	0.21	0.54	0.18	0.04
Salt	0.28	0.62	0.28	0.55	0.14	0.56	0.15	0.48
TSC	2.50	2.50	2.50	2.50	2.50	2.50	2.50	2.50
Water	21.04	18.55	19.81	17.45	18.43	17.00	17.53	14.77
Total	100	100	100	100	100	100	100	100

Figure 2 Six-element linear viscoelastic (Shear stress = 750 Pa) mechanical model used for describing creep behavior of process cheeses. E₀ = Instantaneous elastic modulus of free spring; E₁ and E₂ = Retarded modulus of the first and second Kelvin-Voigt element respectively; η₁ and η₂ = Retarded viscosity of the first and second Kelvin-Voigt element respectively; η_v = Newtonian viscosity of the free dashpot.

Table 2 Composition of process cheese

Parameters	HHH	HHL	HLH	HLL	LHH	LHL	LLH	LLL
pH	6.10 ^a	5.76 ^c	6.16 ^a	5.9 ^b	5.96 ^b	5.65 ^d	5.99 ^b	5.77 ^c
Moisture (%)	42.9 ^a	43.1 ^a	42.9 ^a	43.6 ^a	42.9 ^a	43.2 ^a	42.9 ^a	43.0 ^a
Fat (%)	25.6 ^a	25.5 ^a	25.5 ^ab	25.4 ^ab	24.9 ^b	25.4 ^ab	25.7 ^a	25.2 ^ab
Salt (%)	2.05 ^ab	2.02 ^ab	2.14 ^a	1.99 ^ab	2.02 ^ab	1.87 ^b	2.14 ^b	2.07 ^ab
S/M (%)	4.77 ^ab	4.70 ^ab	4.99 ^a	4.57 ^ab	4.71 ^ab	4.34 ^b	4.98 ^a	4.81 ^ab
Total Ca (%)	0.56 ^a	0.53 ^a	0.56 ^a	0.56 ^a	0.48 ^b	0.48 ^b	0.46 ^b	0.46 ^b
Total P (%)	0.39 ^a	0.38 ^a	0.39 ^a	0.39 ^a	0.35 ^b	0.35 ^b	0.34 ^bc	0.33 ^c
Lactose (%)	1.38 ^b	1.15 ^c	0.25 ^e	0.07 ^f	1.71 ^a	1.29 ^bc	0.50 ^d	0.11 ^ef
^a,b,c,d,e,fMeans within row not sharing common superscript differ significantly (P < 0.05).

Figure 3 Region of linear viscoelasticity (a) G' and (b) G” for process cheeses at 20°C.

Figure 4 Frequency dispersion of (a) elastic and (b) viscous modulus at 20°C for process cheese.

Table 3 Power-law model parameters for process cheeses

	Storage or elastic modulus (G′)			Loss or viscous modulus (G″)
Treatments	a (kPa)	b	R^2	c (kPa)	d	R^2
HHH	50.7 ^b	0.198 ^b	0.99	16.8 ^ab	0.173 ^ab	0.99
HHL	41.3 ^c	0.194 ^b	0.99	13.7 ^c	0.177 ^ab	0.99
HLH	62.0 ^a	0.181 ^c	0.99	19.5 ^a	0.169 ^b	0.99
HLL	41.4 ^bc	0.205 ^ab	0.99	14.3 ^bc	0.177 ^ab	0.99
LHH	38.2 ^c	0.197 ^b	0.99	12.7 ^c	0.169 ^b	0.99
LHL	37.7 ^c	0.204 ^ab	0.99	12.9 ^c	0.178 ^ab	0.99
LLH	39.9 ^c	0.203 ^ab	0.99	13.8 ^c	0.170 ^b	0.99
LLL	42.7 ^bc	0.211 ^a	0.99	14.9 ^bc	0.184 ^a	0.99
^a,b,cMeans within column not sharing common superscript differ significantly (P < 0.05).

Figure 5 Creep and recovery compliance for process cheeses at 20°C (Shear stress = 750 Pa).

Figure 6 Typical creep response showing correspondence to six-element mechanical model and Equation (4.4) J₀ = Instantaneous rigidity compliance, J₁ and J₂ = retarded compliance, η_V = Newtonian viscosity, t = time.

Table 4 Viscoelastic parameters for six-element mechanical model in creep test for process cheeses at 20°C

Six-elements Kelvin model Parameters	HHH	HHL	HLH	HLL	LHH	LHL	LLH	LLL
J0 (1/Pa) (× 10^−5)	2.30 ^c	2.78 ^ab	2.51 ^bc	2.97 ^a	2.67 ^abc	2.97 ^a	3.00 ^a	2.85 ^ab
J1 (1/Pa) (× 10^−5)	1.88 ^b	2.05 ^b	2.07 ^b	3.20 ^a	1.96 ^b	3.33 ^a	2.70 ^ab	2.19 ^b
J2 (1/Pa) (× 10^−5)	3.36 ^bcd	4.19 ^abcd	3.03 ^cd	4.41 ^abc	4.11 ^abcd	2.90 ^d	4.89 ^a	4.61 ^ab
τ1 (s)	3.49 ^bc	3.47 ^bc	3.40 ^c	3.69 ^a	3.52 ^bc	3.60 ^ab	3.50 ^bc	3.57 ^ab
τ2 (s)	36.1 ^b	35.5 ^b	35.4 ^b	39.2 ^a	35.9 ^b	36.5 ^b	36.4 ^b	36.3 ^b
η1 (Pa.s) (× 10^5)	1.90 ^a	1.70 ^ab	1.74 ^ab	1.25 ^cd	1.80 ^a	1.18 ^d	1.35 ^bcd	1.68 ^abc
η2 (Pa.s) (× 10^5)	11.2 ^abc	8.50 ^bc	13.5 ^ab	9.76 ^abc	8.76 ^bc	14.5 ^a	7.67 ^c	8.24 ^c
ηv (Pa.s) (× 10^6)	3.64 ^ab	3.15 ^abc	3.88 ^a	2.27 ^c	3.04 ^abc	2.93 ^abc	2.62 ^bc	3.41 ^ab
R^2	0.99	0.99	0.99	0.99	0.99	0.99	0.99	0.99
^a,b,c,dMeans within column not sharing common superscript differ significantly (P < 0.05).