Optimization of spray-drying conditions for the preparation of whey protein concentrate–iron complex using response surface methodology

Figures & data

Table 1. Factors and levels tested for central composite rotatory experimental design

Parameter	TS (%)	Flow rate (ml/min)	Inlet temperature (°C)
Factor	A	B	C
Low	5	2.5	140
Center	10	5.25	160
High	15	8	180

Table 2. Experimental results and predicted values of the responses for each set of run

				Response 1		Response 2		Response 3		Response 4
Factor 1		Factor 2	Factor 3	Moisture content (%)		Solubility (%)		Yield (g/100 ml)		Oultet temperature (°C)
Run	A: TS (%)	B: Flow rate (ml/min)	C: Inlet temperature (°C)	AV	PV	AV	PV	AV	PV	AV	PV
1	15	2.5	180	4.47	3.98	87.29	88.95	8.18	8.52	60.7	62.84
2	1.59	5.25	160	6.56	6.44	88.05	89.35	1.40	2.23	49.1	51.50
3	10	5.25	160	7.42	7.42	85.03	85.76	5.39	3.63	52.5	46.10
4	5	8	180	8.48	8.56	82.07	82.65	3.72	1.31	61.2	58.26
5	5	2.5	140	5.62	5.55	86.95	89.99	4.04	4.40	51.6	46.32
6	5	8	140	7.91	8.38	81.19	84.79	3.91	2.23	46.9	46.1
7	15	8	180	7.31	7.36	81.46	85.67	5.12	4.13	60.9	59.5
8	15	2.5	140	4.56	4.46	86.85	86.53	6.19	4.90	44.6	42.8
9	15	8	140	7.47	7.34	78.09	82.23	4.43	0.29	42.2	42.5
10	10	9.87	160	9.92	9.64	74.01	79.71	3.14	0.87	42.7	46.4
11	10	5.25	160	7.54	7.42	84.52	85.76	5.05	3.63	46.6	46.1
12	10	5.25	160	7.33	7.42	84.29	85.76	4.77	3.63	45.6	46.1
13	5	2.5	180	5.12	5.23	87.69	86.82	3.87	3.27	61.4	61.4
14	10	5.25	126.36	6.97	6.86	86.14	85.28	5.59	2.49	44.9	44.2
15	18.40	5.25	160	4.12	4.53	82.57	88.98	6.88	5.02	51.9	49.6
16	10	5.25	160	7.44	7.42	85.95	85.76	4.93	3.63	46.1	46.1
17	10	5.25	160	7.11	7.42	84.76	85.76	5.45	3.63	44.1	46.1
18	10	5.25	193.63	6.47	6.61	87.95	85.52	6.84	4.77	69.1	71.2
19	10	0.63	160	4.11	4.43	86.31	86.83	5.80	6.39	47.7	49.4
20	10	5.25	160	7.73	7.42	86.74	85.76	4.98	3.63	48.1	46.1

Table 3. Estimated coefficients of linear, quadratic, and interaction terms for each response variables, i.e., moisture content (%), solubility (%), yield (g 100 ml⁻¹), and outlet temperature (ºC)

	Moisture content		Solubility		Yield		Outlet temperature
Source	Sum of squares	p-Value Prob > F	Sum of squares	p-Value Prob > F	Sum of squares	p-Value Prob > F	Sum of squares	p-Value Prob > F
Model	45.01	<0.0001	238.05	<0.0001	39.84	<0.0001	1,034.75	0.0002
A-TS	4.04	0.0001	13.20	0.0048	22.67	<0.0001	4.68	0.4746
B-Flow rate	32.82	<0.0001	159.39	<0.0001	6.71	0.0001	17.61	0.1799
C-Inlet temperature	0.0763	0.4180	5.26	0.0461	1.43	0.0178	726.38	<0.0001
AB	0.0012	0.9160	1.29	0.2864	2.58	0.0035	0.91	0.7497
AC	0.0128	0.7366	0.60	0.4600	1.16	0.0292	14.31	0.2229
BC	0.1250	0.3050	1.18	0.3067	0.2178	0.2955	6.30	0.4078
A^2	7.53	<0.0001	1.377E-007	0.9997	1.64	0.0126	42.58	0.0488
B^2	0.2454	0.1608	47.78	<0.0001	0.7035	0.0754	0.35	0.8440
C^2	0.7945	0.0214	5.42	0.0435	2.26	0.0052	232.55	0.0004
Residual	1.07		10.16		1.79
Lack of fit	0.8549	0.0778	5.71	0.3952	1.43	0.0790	42.09	0.5055
Pure error	0.2147		4.45		0.3611		42.63
Cor total	46.08		248.21		41.63		1,119.47
C.V. %	4.89		1.19		8.48		5.72
PRESS	7.06		51.30		11.68		380.73
R-squared	0.9768		0.9591		0.9571		0.9243
Adj. R-squared	0.9559		0.9223		0.9184		0.8562
Pred. R-squared	0.8468		0.7933		0.7195		0.6599
Adeq. precision	24.528		19.259		21.3593		14.065

Figure 1. Effect of (a) inlet air temperature and feed flow rate at 10% TS, (b) inlet air temperature and TS (%) at feed flow rate of 5.25 ml/min, and (c) flow rate and TS at inlet temperature of 160ºC on the moisture content

Figure 2. Effect of (a) TS and feed flow rate at inlet air temperature of 160ºC, (b) inlet air temperature and feed flow rate at 10% TS, and (c) inlet temperature and TS at feed flow rate of 5.25 ml/min on the solubility

Figure 3. Effect of (a) TS and feed flow rate at inlet air temperature of 160ºC, (b) inlet air temperature and feed flow rate at 10% TS, and (c) inlet air temperature and TS at feed flow rate of 5.25 ml/min on the yield

Figure 4. Effect of (a) TS and feed flow rate at inlet air temperature of 160ºC, (b) inlet air temperature and feed flow rate at 10% TS, and (c) inlet temperature and TS at feed flow rate of 5.25 ml/min on the outlet temperature

Table 4. Experimental verification of predicted response variables

Response	Predicted value (pre)	Actual value*^a (exp)	SE^b	Difference	% error^c
Moisture content (%)	4.11	4.19 ± 0.12	0.122	0.38	0.08463
Solubility (%)	87.63	87.53 ± 0.13	0.135	−0.10	0.00114
Yield (g 100 ml^−1)	8.29	8.21 ± 0.23	0.234	−0.08	0. 00974
Outlet temperature (°C)	60.64	60.70 ± 0.27	0.275	−0.06	0.00098

*All the experiments were repeated three times.

^aExperimental values were expressed as mean ± standard deviation.

^bMean standard error.

^c% error = (|exp − pre|/exp) × 100.