Experimental design and response surface methodology applied to the dielectric properties of hydroalcoholic solutions containing sodium chloride

Morais, Anderson dos Santos; Damasceno, João Jorge Ribeiro; Ataíde, Carlos Henrique

doi:10.1590/1981-6723.08517

Anderson dos Santos Morais

Universidade Federal de Uberlândia (UFU), Faculdade de Engenharia Química, Uberlândia/MG - Brasil

João Jorge Ribeiro Damasceno

Universidade Federal de Uberlândia (UFU), Faculdade de Engenharia Química, Uberlândia/MG - Brasil

Carlos Henrique Ataíde

Universidade Federal de Uberlândia (UFU), Faculdade de Engenharia Química, Uberlândia/MG - Brasil

Anderson dos Santos Morais, Universidade Federal de Uberlândia (UFU), Faculdade de Engenharia Química, Bloco 1K, Santa Mônica, CEP: 38408-144, Uberlândia/MG - Brasil, e-mail: ander_morais@yahoo.com.br

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Figure 1
Schematic diagram of the system for determining the dielectric properties. Adapted from Tanaka et al. (2008) TANAKA, F.; UCHINO, T.; HAMANAKA, D.; ATUNGULU, G. G.; HUNG, Y.-C. Dielectric properties of mirin in the microwave frequency range. Journal of Food Engineering , v. 89, n. 4, p. 435-440, 2008. http://dx.doi.org/10.1016/j.jfoodeng.2008.05.029.
http://dx.doi.org/10.1016/j.jfoodeng.20... .

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Figure 2
Measuring system setup.

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Figure 3
(a) Probe and (b) calibrator.

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Figure 4
Graph of residuals for y₁ (ε”).

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Figure 5
Graph of residuals for y₂ (ε’).

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Figure 6
Graph of residuals for y₃ (tgδ).

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Figure 7
Estimated vs. observed values for y₁ (ε”).

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Figure 8
Estimated vs. observed values for y₂ (ε’).

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Figure 9
Estimated vs. observed values for y₃ (tgδ).

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Figure 10
Response surface for y₁ – ε” [ – ] with fixed C_NaCl x₁ [−].

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Figure 11
Response surface for y₁ (ε”) with fixed C_EtOH x₂ [−].

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Figure 12
Response surface for y₁ – ε” [ – ] with fixed x₃ T [−].

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Figure 13
Response surface for y₂ – ε’ [ – ] with fixed C_NaCl x₁ [−].

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Figure 14
Response surface for y₂ – ε’ [ – ] with fixed C_EtOH x₂ [−].

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Figure 15
Response surface for y₂ – ε’ [ – ] with fixed T x₃ [−].

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Figure 16
Response surface for y₃ – tgδ[−] with fixed C _NaCl x₁ [−].

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Figure 17
Response surface for y₃ – tgδ[−] with fixed C _EtOH x₂ [−]

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Figure 18
Response surface for y₃ – tgδ [−] with fixed T X₃ [−].

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Table 1
The design variables and levels.

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Table 2
The design matrix, showing the operating conditions of the 17 experiments.

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Table 3
Experimental results.

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Table 4
Multiple regression analysis for y1 (ε”).

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Table 5
Multiple regression analysis for y2 (ε’).

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Table 6
Multiple regression analysis for y3 (tgδ).

(1)

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

Coded variables	(–α)	–1	0	1	(α)
$C_{N a C l}$	0.19	0.60	1.20	1.80	2.21
$C_{E t O H}$	4.64	6.00	8.00	10.00	11.36
T	53.00	60.00	70.00	80.00	87.00

Experiment	*x₁(%)*	*x₂(%)*	*x₃(°C)*
1	0.60	6.00	60
2	1.80	6.00	60
3	0.60	10.00	60
4	1.80	10.00	60
5	0.60	6.00	80
6	1.80	6.00	80
7	0.60	10.00	80
8	1.80	10.00	80
9	0.19	8.00	70
10	2.21	8.00	70
11	1.20	4.64	70
12	1.20	11.36	70
13	1.20	8.00	53
14	1.20	8.00	87
15	1.20	8.00	70
16	1.20	8.00	70
17	1.20	8.00	70

x₁	x₂	x₃	*y1 ε”*	*y2 ε’*	*y3tgδ*
-1	-1	-1	65.7843	25.7205	2.5577
1	-1	-1	62.7598	16.5267	3.7975
-1	1	-1	63.043	21.9390	2.8736
1	1	-1	61.1245	18.0666	3.3833
-1	-1	1	64.2749	27.7580	2.3155
1	-1	1	60.2523	15.0664	3.9991
-1	1	1	59.9301	22.3730	2.6787
1	1	1	58.5546	14.1140	4.1487
-1.682	0	0	63.084	27.6120	2.2847
1.682	0	0	59.8527	18.3052	3.2697
0	-1.682	0	65.0083	29.1054	2.2336
0	1.682	0	60.2302	26.0313	2.3137
0	0	-1.682	63.6284	21.4045	2.9727
0	0	1.682	59.4921	14.9332	3.9839
0	0	0	61.299	25.6367	2.3911
0	0	0	61.301	25.6363	2.3912
0	0	0	61.298	25.6359	2.3911

Coefficients		Error	t (10)	P
β₀	61.4671	0.0977	629.00	2.54E-24
β₁	-1.1551	0.0803	-14.38	5.25E-08
β₂	-1.3513	0.0803	-16.82	1.16E-08
β₃	-1.2196	0.0803	-15.18	3.11E-08
β₂₂	0.4376	0.0822	5.32	3.37E-04
β₁₂	0.4691	0.1050	4.47	1.20E-03
β₂₃	-0.2082	0.1050	-1.98	7.54E-02
Level of significance (α) 0.10

Coefficients		Error	t (13)	P
β₀	25.9524	1.1114	23.35	5.34E-12
β₁	-3.6367	0.6952	-5.23	1.62E-04
β ₁₁	-1.5450	0.7309	-2.11	5.44E-02
β ₃₃	-3.2380	0.7309	-4.43	6.79E-04
Level of significance (α) 0.10

Coefficients		Error	t (13)	P
β₀	2.4146	0.1588	15.21	1.16E-09
β₁	0.4803	0.0993	4.84	3.25E-04
β ₁₁	0.2033	0.1044	1.95	7.35E-02
β ₃₃	0.4511	0.1044	4.32	8.31E-04
Level of significance (α) 0.10

[1] Anderson dos Santos Morais, Universidade Federal de Uberlândia (UFU), Faculdade de Engenharia Química, Bloco 1K, Santa Mônica, CEP: 38408-144, Uberlândia/MG - Brasil, e-mail: ander_morais@yahoo.com.br

Brasil

Brasil

Experimental design and response surface methodology applied to the dielectric properties of hydroalcoholic solutions containing sodium chloride

Planejamento de experimentos e metodologia de superfície de resposta, aplicados às propriedades dielétricas de soluções hidroalcoólicas com cloreto de sódio

Abstract