Table 1. Linear equations of the kinetic and isothermal models used in the biosorption of AR14 by yeast biomass
Isotherm Model
|
|
Linear Equation
|
Representation Plot
|
Freundlich
|
Log 𝑞𝑒 = Log 𝐾𝐹+ 1/𝑛 Log 𝐶𝑒
|
Log 𝑞𝑒𝑣𝑠 Log 𝐶𝑒
|
Langmuir
|
𝐶𝑒/𝑞𝑒 = 𝐶𝑒/𝑞𝑚 + 1/𝐾𝐿𝑞𝑚
|
𝐶𝑒⁄ 𝑞𝑒𝑣𝑠𝐶𝑒
|
Kinetic Model
|
Pseudo first order
|
Log(𝑞𝑒-𝑞𝑡)=Log(𝑞𝑒) - (𝑘1/2.303)𝑡
|
Log (𝑞𝑒 - 𝑞𝑡) vs 𝑡
|
Pseudo second order
|
(𝑡/𝑞𝑡) = (𝑘2/𝑘2𝑞𝑒2 ) + (𝑡 /𝑞𝑒)
|
(𝑡/𝑞𝑡) vs 𝑡
|
Intra particle diffusion
|
𝑞𝑡= 𝐾𝑖𝑑𝑡0.5 + 𝐶
|
𝑞𝑡 vs 𝑡0.5
|
Where, qt is the sorption capacity (mg g-1);, qe is the sorption capacity at equilibrium (mg g-1); qm is the maximum sorption capacity (mg g-1); Ce (mg L-1) is the equilibrium concentration of the biosorbent; KL is the Langmuir constant (L mg-1); KF is the Freundlich constant of the adsorption capacity and exponent n is the adsorption intensity which varies with the heterogeneity of the material.
Table 2. Kinetic parameters of AR14 biosorption on yeast biomass
Models
|
kinetics parameters
|
Initial dye concentrations (mg L-1)
|
50
|
100
|
150
|
200
|
Pseudo first order
|
K1 (min-1)
|
0.205
|
0.194
|
0.215
|
0.195
|
R2
|
0.857
|
0.477
|
0.609
|
0.524
|
Pseudo second order
|
K2 (g mg-1 min-1)
|
0.126
|
0.051
|
0.022
|
0.014
|
R2
|
0.999
|
0.999
|
0.999
|
0.998
|
Qe (cal)
|
23.980
|
46.510
|
69.930
|
95.230
|
Qe (exp)
|
24.038
|
50.000
|
67.129
|
92.082
|
Intra-particle diffusion
|
Ki1
|
7.847
|
14.66
|
21.65
|
29.190
|
C1
|
0.549
|
1.277
|
0.955
|
0.179
|
R12
|
0.983
|
0.974
|
0.993
|
0.999
|
Ki2
|
0.030
|
0.083
|
0.022
|
0.028
|
C2
|
23.59
|
45.657
|
68.835
|
93.527
|
R22
|
0.920
|
0.254
|
0.148
|
0.035
|
Table 3. Biosorption isotherm models and their corresponding parameters for the biosorption AR14 by W. anomalus biomass
Langmuir
|
Freundlich
|
Qmax ( mg g-1)
|
KL (L mg-1)
|
R2
|
1/n
|
Kf
|
R2
|
126.58
|
0.107
|
0.954
|
0.5
|
15.87
|
0.849
|
Table 4. Contact angle values using water (θw), formamide (θF) and diiodomethane (θD), Lifshitz-vander Waals (γ LW), electron-donor (γ–) and electron-acceptor (γ+) parameters, surface energies (ΔGiwi) of W. anomalus cells before and after AR14 biosorption
|
Contact angles (°)
|
Surface tension: components and parameters (mJ m-2)
|
Surface energies
|
θw
|
θF
|
θD
|
γLW
|
γ+
|
γ–
|
ΔGiwi (mJ m-2)
|
Raw Biomass
|
34.9±0.4
|
42.2±0.6
|
49.5±1.6
|
34.45±0.9
|
0.24±0.07
|
52.57±0.6
|
37.23±1.13
|
AR14-Biomass
|
31.6±0.9*
|
44.1±0.5ns
|
36.3±0.6***
|
41.33±0.3***
|
0.08±0.02*
|
59.79±0.5***
|
44.9±1.2**
|
*statistical significance p value < 0.05
Table 5. ANOVA for process variables of the PBD
Source
|
DF
|
Adj SS
|
Adj MS
|
F-Value
|
P-Value
|
Model
|
6
|
10216.7
|
1702.79
|
8.88***
|
0.000
|
Linear
|
6
|
10216.7
|
1702.79
|
8.88***
|
0.000
|
Temperature (ºC) (A)
|
1
|
751.4
|
751.39
|
3.92NS
|
0.064
|
pH (B)
|
1
|
1272.1
|
1272.06
|
6.64**
|
0.02
|
Biomass dosage (g.L-1)) (C)
|
1
|
2241.6
|
2241.58
|
11.69**
|
0.003
|
Agitation (rpm) (D)
|
1
|
0.8
|
0.82
|
0.00 NS
|
0.949
|
Dye (mg L-1) (E)
|
1
|
5821.6
|
5821.58
|
30.37***
|
0.000
|
Contact time (min) (F)
|
1
|
129.3
|
129.30
|
0.67 NS
|
0.423
|
Error
|
17
|
3258.8
|
191.69
|
|
|
Lack-of-Fit
|
5
|
1860.8
|
372.16
|
3.19*
|
0.046
|
Pure Error
|
12
|
1398.0
|
116.50
|
|
|
Total
|
23
|
13475.5
|
|
|
|
R2 75.82; Adjusted R2 67.28; Predicted R2 51.80%.
DF: degrees of freedom; SS: sum of squares; MS: mean sum of squares,
*Significance (α = 0.05)
Table 6. Analysis of variance for response surface quadratic model.
Source
|
DF
|
Adj SS
|
Adj MS
|
F-Value
|
P-Value
|
Model
|
9
|
3821.96
|
424.66
|
21.48***
|
0.000
|
Linear
|
3
|
2762.70
|
920.90
|
46.58***
|
0.000
|
Dye (mg L-1)(A)
|
1
|
344.76
|
344.76
|
17.44***
|
0.000
|
Biomass (g L-1) (B)
|
1
|
843.87
|
843.87
|
42.69***
|
0.000
|
pH (C)
|
1
|
1574.06
|
1574.06
|
79.62***
|
0.000
|
Square
|
3
|
620.61
|
206.87
|
10.46***
|
0.000
|
A * A
|
1
|
3.03
|
3.03
|
0.15NS
|
0.700
|
B * B
|
1
|
257.68
|
257.68
|
13.03**
|
0.002
|
C * C
|
1
|
312.17
|
312.17
|
15.79***
|
0.001
|
2-Way Interaction
|
3
|
438.65
|
146.22
|
7.40**
|
0.002
|
A * B
|
1
|
0.00
|
0.00
|
0.00 NS
|
0.997
|
A * C
|
1
|
315.76
|
315.76
|
15.97***
|
0.001
|
B * C
|
1
|
122.89
|
122.89
|
6.22**
|
0.022
|
Error
|
20
|
395.38
|
19.77
|
|
|
Lack-of-Fit
|
3
|
361.66
|
120.55
|
60.77***
|
0.000
|
Pure Error
|
17
|
33.72
|
1.98
|
|
|
Total
|
29
|
4217.34
|
|
|
|
R2 90.62; Adjusted R2 86.41; Predicted R2 76.27%.