Table 3 Kinetics models for Mg release from classical fertilizers (control) and NEF in water and soil

First order

Ln(q₀–q_t) = a − (K_d * T)

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

a = constant (mg.g⁻¹)

K_d

a

R²

SE

0.012

5.657

0.979

0.112

0.011

5.302

0.929

0.210

0.012

5.967

0.975

0.129

0.006

3.215

0.911

0.221

0.006

2.753

0.913

0.261

0.006

3.178

0.911

0.207

Elovich

q_t = (1/β)ln(αβ) + (1/β)lnt

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

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

α

β

R²

SE

63.92

0.021

0.875

38.29

3E + 01

0.032

0.837

29.78

5E + 01

0.015

0.882

50.58

0.1506

0.140

0.898

1.820

8E-02

0.221

0.916

1.035

2E-01

0.142

0.882

1.945

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

20.41

22.87

0.986

11.55

13.43

4.807

0.964

12.47

27.95

6.495

0.993

11.47

1.199

7.378

0.971

0.982

0.753

5.514

0.974

0.579

1.183

6.576

0.961

1.127

Power function^a

logq = logk_dC_ο + 1/m logt

K_d = apparent desorption rate coefficient (h⁻¹)

1/m = constant

Co = initial Mg concentration

K_d

1/m

R²

SE

44.96

0.349

0.977

0.047

23.65

0.379

0.962

0.067

29.70

0.478

0.992

0.035

0.050

0.959

0.994

0.024

0.002

1.416

0.988

0.050

0.110

0.832

0.985

0.034

Second order

q_t = k_dq_e²t /1 + k_dq_et

k_d = apparent desorption rate coefficient (h⁻¹)

K_d

q_e

R²

SE

0.518

333.3

0.917

0.059

0.317

222.2

0.849

0.121

0.438

434.8

0.899

0.051

0.013

1250

0.070

0.364

0.014

81.30

0.598

1.282

0.027

500

0.334

0.365