Sedimentation Equilibrium of Mixtures of Charged Colloids

More documents

Recommendations

Info

The next constant that can be solved is b n−1 . From the relation between b n−1and b n , using equation (4.22),where ξ n−1 can be found by the normalisation1H∫ xnx n −ξ n−1dxb n−1 = b n + t n + c n−1 ξ n−1 (4.25)()b n + t n − c n−1 (x − x n ) = ¯η (4.26)we find an expression for b n−1 and thus, for all b i . By repeating the stepsfrom equation (4.24) we find expressions for all constants b n and layer widthsξ i√2Hρ s¯ηπση(x i ) = b n =3+ (b3ZnL 2 n+1 + t n+1 ) 2 (4.27)nξ i = 3Z2 i L iρ s πσ 3 (b i − b i+1 − t i+1 ) (4.28)Figure 4.17 shows a comparison with the full numerical solutions. The dottedlines represent the approximation. The left figure shows an approximationof figure 4.1. The right figure shows the packing fractions of a systemwith colloidal charge number Z = (200, 250, 300), and gravitational lengthL = (0.4, 0.7, 1)mm, and the usual system parameters (see tab. 4.1). Althoughthe slope model calculates the equilibrium properties in an instant,and can even be done by hand, the Poisson-Boltzmann calculations are consideredmore reliable, and do not need the condition of pure layers. Especiallythis last condition is not often met for the systems considered in this thesis.An additional problem with the slope model is the jump constant. Multiplecomparisons with PB-calculations show that it is indeed proportional tot n ∝ ((Z N L n ) −2 − (Z n−1 L n−1 ) −2 ), but the proportionality constant provednot always equal to σ 3 /48λ B .36
0.03(a)0.02η i0.0100 5 10 15 20x (cm)(b)0.02η i00 5 10 15 20Figure 4.17: A comparison between the slope model and the numerical solutionsbased on the Poisson-Boltzmann model. The dotted lines representthe results of the slope model. Figure (a) shows an approximation of figure4.1. Figure (b) shows the packing fractions of a system with colloidal chargenumber Z = (200, 250, 300), and gravitational length L = (0.4, 0.7, 1)mm,and the usual system parameters (see tab. 4.1).37
Page 1: Sedimentation Equilibrium of Mixtur
Page 4 and 5: 5 Charge Regulation in the Low Dens
Page 6 and 7: programming?Do I like programming?T
Page 8 and 9: Additional information, often writt
Page 10 and 11: 1.2 Sedimentation equilibrium of mi
Page 12 and 13: make them spark. . . Wait, wait! I
Page 14: dG = −SdT − V dP + ∑ αµ α
Page 17: with ν λ = ν 0 +λw, the free en
Page 20 and 21: eservoir is:µ res± = k B T ln(ρ
Page 22 and 23: x-axis, only τ xx = −(ɛ/8π)E 2
Page 24 and 25: is denoted by ρ i . The salt ions
Page 26 and 27: numbers for the parameters Z i , L
Page 28 and 29: 2Case (a)4.5Case (a)ρ +E (mV/cm)1.
Page 30 and 31: is plotted as a function of Z 2 /Z
Page 32 and 33: 0.1i=320a0.080.06η i0 5 10 15 20ρ
Page 34 and 35: Z 16=2993a0.6210 3 η iZ 11=2500.40
Page 36 and 37: 0.02210.83E x(mV/cm)0.60.40.0140.25
Page 38 and 39: 4.6.1 The influence of the diameter
Page 40 and 41: 0.01ρ s=10 −3 Mρ s=10 −5 Mρ
Page 42 and 43: 0.03108642η i 0.01500 5 10 150.031
Page 46 and 47: 4.6.5 Donnan-method for polydispers
Page 48 and 49: and try to fill the holes, or try t
Page 51 and 52: Chapter 5Charge Regulation in the L
Page 53 and 54: 5.1.2 Numerical resultsThe example
Page 55: Discussion The mean height of the s
Page 58 and 59: Z i (x) that converges, at least in
Page 60 and 61: Other extensions are planned to inc
Page 62 and 63: their buoyant mass. The force that
Page 64 and 65: (π/6)ρ i (x)σi3 the local packin
Page 66 and 67: 0.010.008ρ +0.006 i=10.5hη i/σi
Page 68 and 69: species, and (B) L i = 2 × (250/Z
Page 70 and 71: A.7 AcknowledgementsIt is a pleasur
Page 72 and 73: length by Peter Debye. In dense col
Page 74 and 75: One quick check shows ∫ ∞dx Q(x
Page 77 and 78: Appendix CThe block modelThe model
Page 79: Index of frequently usedsymbols and
Page 83 and 84: Bibliography[1] J. Perrin, (1913),

Sedimentation Equilibrium of Mixtures of Charged Colloids

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?