Rheological Characteristics of Arabic Gum in Combination With Guar and Xanthan Gum Using Response Surface Methodology: Effect of Temperature and Concentration

Figures & data

Table 1 Variables and levels for a rotatable central composite design used in arabic –guar gum and arabic-xanthan gum combination rheology experiments

	Coded-variable levels
Variables	Symbol	−2	−1	0	+1	+2
Temperature (°C)	X1	20	35	50	65	80
Gum concentration (%)	X2	0.25	0.50	0.75	1.0	1.25

Table 2 Central composite rotatable design arrangement and responses

Independent variables				Response variables
				AG				AX
Treatment	X1	X2	τ0	K	n	η	τ0	K	n	η
1	−1	−1	0.1210	0.1201	0.7866	0.0365	0.0337	0.0165	1.034	0.0198
2	+1	−1	0.0493	0.0373	0.8711	0.0185	0.0031	0.0097	0.997	0.0118
3	−1	+1	1.028	0.9984	0.6044	0.1084	0.1448	0.0213	1.036	0.0266
4	+1	+1	0.4734	0.4177	0.6433	0.0568	0.0085	0.0121	0.885	0.0141
5	−2	0	0.7029	0.5686	0.6650	0.0870	0.1196	0.0273	1.023	0.0315
6	+2	0	0.1433	0.1490	0.7331	0.0338	0.0098	0.0087	1.034	0.0104
7	0	−2	0.0396	0.0149	0.9565	0.0120	0.0007	0.0116	1.031	0.0138
8	0	+2	2.043	2.106	0.4553	0.1209	0.2102	0.0232	0.832	0.0246
9	0	0	0.4082	0.3875	0.6953	0.0464	0.0018	0.0138	1.028	0.0160
10	0	0	0.4321	0.3445	0.7231	0.0421	0.0437	0.0194	0.974	0.0169
11	0	0	0.3567	0.2722	0.6575	0.0463	0.0018	0.0128	0.992	0.0123
12	0	0	0.4823	0.3673	0.7012	0.0312	0.044	0.0176	1.009	0.0176
13	0	0	0.3232	0.1943	0.6045	0.0453	0.0434	0.0211	1.004	0.0124
14	0	0	0.4786	0.3956	0.7123	0.0357	0.0021	0.0183	0.967	0.0173
15	0	0	0.4876	0.2445	0.6789	0.0453	0.0031	0.0144	0.973	0.0126
16	0	0	0.4034	0.3965	0.6876	0.0356	0.0432	0.0134	0.998	0.0124

Table 3 Fitting of various flow models based on standard errors

No.	Model	Arabic gum (20%) and guar gum (1%) at 65°C	Arabic gum (20%) and xanthan gum (1%) at 65°C
1	Herschel Bulkley model	4.12	3.96
2	Power law model	5.28	4.19
3	Casson model	19.77	7.62
4	Bingham model	36.19	6.42
5	Newtonian model	83.19	6.47

Figure 1a Rheogram of 20% Arabic gum and various combinations of guargum at selected temperatures.

Figure 1b Rheogram of 20% arabic gum and selected combinations xanthan at selected temperatures.

Table 4 Comparative studies on rheological parameters of individual gum and combinations at 20°C.

	Yield stress (Pa)	Consistency coefficient (Pa.s^n)	Flow index (-)	Apparent viscosity at 250 s^−1 (Pa)
Arabic gum (20%)	0.005	0.018	0.994	0.012
Guar gum (0.75%)	0.342	2.518	0.372	0.092
Xanthan gum (0.75%)	3.73	1.005	0.454	0.083
Arabic (20%) + Guar gum (0.75%)	0.703	0.569	0.665	0.087
Arabic (20%) + Xanthan gum (0.75%)	0.120	0.027	1.023	0.032

Table 5a Regression coefficients and analysis of variance of the regression models for rheological parameters of AG

Term		Y1			Y2			Y3			Y4
	b	S.E.	P	B	S.E.	P	b	S.E.	P	b	S.E.	P
Constant	0.383	0.041	<0.0001	0.277	0.053	0.0004	0.688	0.013	<0.0001	0.041	0.002	<0.0001
X1	−0.145	0.035	0.0021	−0.125	0.046	0.0206	0.022	0.011	0.082	−0.015	0.002	<0.0001
X2	0.414	0.034	<0.0001	0.453	0.043	<0.0001	−0.118	0.011	<0.0001	0.027	0.002	<0.001
X1*X1	−0.002	0.024	0.945	0.010	0.031	0.7473	0.006	0.008	0.4728	0.005	0.001	0.001
X1*X2	−0.121	0.061	0.077	−0.124	0.079	0.1466	−0.011	0.019	0.5694	−0.008	0.003	0.017
X2*X2	0.130	0.024	0.0003	0.186	0.031	0.0001	0.007	0.008	0.3542	0.007	0.001	0.0002

Table 5b Regression coefficients and analysis of variance of the regression models for rheological parameters of AX

Term		Y1			Y2			Y3			Y4
	b	S.E.	P	b	S.E.	P	b	S.E.	P	b	S.E.	P
Constant	0.022	0.008	0.022	0.016	9.9E-4	<0.0001	0.987	0.012	<0.0001	0.015	7.3E-4	<0.0001
X1	−0.032	0.007	0.001	−0.004	8.4E-4	0.0004	−0.014	0.011	0.222	−0.005	6.3E-4	<0.0001
X2	0.045	0.007	<0.000	0.003	8.4E-4	0.0133	−0.042	0.011	0.003	0.003	6.3E-4	0.002
X1*X1	0.010	0.005	0.054	0.000	5.7E-4	0.5620	0.011	0.007	0.167	0.002	4.3E-4	0.004
X1*X2	−0.026	0.012	0.051	−0.000	1.5E-3	0.6833	−0.286	0.018	0.151	−0.001	1.1E-3	0.344
X2*X2	0.020	0.005	0.001	0.000	5.7E-4	0.7311	−0.013	0.007	0.091	0.001	4.3E-4	0.023

Table 6 Regression equations of rheological parameters for different combinations of gums

Combination	Equation	R^2	RMSE
AG	Y1 = 0.38655 −0.14546X1+0.444832X2+0.148981X2^2	0.932	0.123	(4)
	Y2 = 0.286808−0.12523X1+0.453408X2+0.183762 X2^2	0.920	0.158	(5)
	Y3 = 0.688702−0.1177X2	0.920	0.039	(6)
	Y4 = 0.041133 − 0.014665X1+0.027342X2 + 0.005094X1^2 −0.00084X1X2 + 0.006596 X2^2	0.975	0.006	(7)
AX	Y1 = 0.030719−0.0322X1+0.044632X2+0.018474 X2^2	0.901	0.023	(8)
	Y2 = 0.016284−0.00443X1+0.002537X2	0.792	0.003	(9)
	Y3 = 0.0988738−0.0423X2	0.730	0.037	(10)
	Y4 = 0.014857−0.00522X1 + 0.002569X2 + 0.001587X1^2 + 0.001144 X2^2	0.904	0.002	(11)

Figure 2a Effect of temperature and concentration of guargum on arabic gum-guar gum mixture on yield stress.

Figure 2b Effect of temperature and concentration of xanthan gum on yield stress of arabic gum-xanthan gum combination.

Figure 3a Effect of temperature and concentration on consistency coefficient of arabic gum-guar gum combination.

Figure 3b Effect of temperature and concentration on consistency coefficient of arabic gum-guar gum combination.

Figure 4a Effect of temperature and concentration on apparent viscocity of arabic gum-guar gum combination.

Figure 4b Effect of temperature and concentration on apparent viscocity of arabic and xanthan gum combination.