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Table 2 Comparison of mass transport coefficients

From: Changes in the nanoparticle aggregation rate due to the additional effect of electrostatic and magnetic forces on mass transport coefficients

i [1]

j [1]

β(m3s−1)

βmg(m3s−1)

β mg el ( m 3 s − 1 )

L D mg el R 0 [1]

1

1

1.1×10−17

3.1×10−15

2.9×10−15

78.9

1

10

1.3×10−17

2.9×10−15

2.8×10−15

50.6

1

100

1.9×10−17

2.8×10−15

2.7×10−15

28.4

1

1,000

3.4×10−17

2.7×10−15

2.7×10−15

14.6

1

10,000

7.3×10−17

2.8×10−15

2.8×10−15

7.1

1

100,000

2.2×10−16

3.1×10−15

3.0×10−15

3.4

1

1,000,000

1.4×10−15

4.2×10−15

4.2×10−15

1.6

10

10

1.1×10−17

1.4×10−14

1.3×10−14

65.6

10

100

1.3×10−17

1.3×10−14

1.3×10−14

42.0

10

1,000

2.0×10−17

1.3×10−14

1.3×10−14

23.5

10

10,000

4.2×10−17

1.3×10−14

1.3×10−14

12.1

10

100,000

1.6×10−16

6.9×10−14

6.8×10−14

10.2

10

1,000,000

1.3×10−15

2.5×10−14

2.5×10−14

3.2

100

100

1.2×10−17

7.1×10−14

6.9×10−14

54.4

100

1,000

1.5×10−17

7.1×10−14

7.0×10−14

34.7

100

10,000

3.0×10−17

7.2×10−14

7.1×10−14

19.4

100

100,000

1.4×10−16

7.0×10−13

7.0×10−13

21.1

100

1,000,000

1.3×10−15

1.9×10−13

1.9×10−13

6.4

1,000

1,000

1.5×10−17

4.0×10−13

3.9×10−13

45.1

1,000

10,000

3.2×10−17

4.0×10−13

4.0×10−13

28.7

1,000

100,000

1.5×10−16

4.1×10−13

4.1×10−13

16.1

1,000

1,000,000

1.4×10−15

1.3×10−12

1.3×10−12

11.8

10,000

10,000

5.4×10−17

2.2×10−12

2.2×10−12

37.3

10,000

100,000

2.2×10−16

2.3×10−12

2.3×10−12

23.7

10,000

1,000,000

1.8×10−15

2.4×10−12

2.4×10−12

13.3

100,000

100,000

4.4×10−16

1.3×10−11

1.3×10−11

30.8

100,000

1,000,000

2.7×10−15

1.3×10−11

1.3×10−11

19.6

  1. A comparison of mass transport coefficients computed by the primary model β, mass transport coefficients computed in distance LD including magnetic forces βmg, and mass transport coefficients computed in distance LD including both magnetic forces and electrostatic forces β mg el . The β represents the sum of the mass transport coefficients for Brownian motion, velocity gradient and sedimentation. Computation of LD was performed by averaging of the magnetic forces (11) for particles with ratio LD/R0 higher than 15; otherwise, the computation of magnetic forces was performed accurately by summation (10) (for more information, see [20]). Results were computed using the following values: M=570 kA/m; σ=2.5×10−5 C/m2;and G=50.
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