Table 2 Kinetics models for K release from classical fertilizers (control) and NEF in water and soil

First order

Ln(q₀–q_t) = a − (K_d * T)

q₀ = amount of K released at equilibrium mg·g⁻¹, q or q_t = amount of K released at time t (h) mg·g⁻¹, K_d = Solubility rate (h⁻¹) a = constant (mg.g⁻¹)

K_d

a

R²

SE

0.017

6.805

0.933

0.289

0.016

6.490

0.872

0.386

0.019

7.352

0.908

0.399

0.007

4.031

0.939

0.205

0.006

3.111

0.903

0.220

0.005

5.582

0.942

0.151

Elovich

q_t = (1/β)ln(αβ) + (1/β)lnt

α = initial desorption rate of K (mg/g·h)

β = constant related to K release (mg.g⁻¹)

α

β

R²

SE

103.6

0.007

0.818

122.5

65.39

0.011

0.740

102.4

194.1

0.004

0.865

175.4

0.380

0.063

0.940

3.069

1E-01

0.153

0.887

1.770

2E-01

0.012

0.893

22.01

Parabolic diffusion

q = a + k_dt ^1/2

a = constant (mg.g⁻¹)

K_d = apparent diffusion rate coefficient (mg/g.h^1/2.)

K_d

a

R²

SE

58.82

17.68

0.974

46.76

40.31

26.17

0.934

51.48

98.65

6.99

0.990

46.83

2.652

14.16

0.991

1.206

1.098

7.185

0.962

1.016

13.70

79.07

0.963

12.81

Power function^a

logq = logk_dC_ο + 1/m logt

K_d = apparent desorption rate coefficient (h⁻¹)

1/m = constant

Co = initial K concentration

K_d

1/m

R²

SE

67.80

0.457

0.973

0.063

46.15

0.444

0.930

0.101

124.2

0.449

0.985

0.046

0.180

0.902

1.000

0.006

0.288

1.054

0.998

0.016

0.900

0.902

0.993

0.024

Second order

qt = k_dq_e²t /1 + k_dq_et

k_d = apparent desorption rate

coefficient (h⁻¹)

K_d

q_e

R²

SE

0.561

1000

0.849

0.084

0.361

714.3

0.717

0.168

0.875

1666

0.913

0.075

0.028

2000

0.955

0.014

0.011

1000

0.787

0.066

31.62

11,111

0.472

0.032