Electrokinetic response of standard particles and more Claire - - PowerPoint PPT Presentation

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Electrokinetic response of standard particles and more Claire - - PowerPoint PPT Presentation

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I WNET 2012, RROS Electrokinetic response of standard particles and more Claire Chassagne, Maria Ibanez, Guus Stelling Environmental Fluid Mechanics Civil Engineering and Geosciences Delft University of Technology System 1)

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SLIDE 1

Electrokinetic response of “standard particles” and more…

Claire Chassagne, Maria Ibanez, Guus Stelling

Environmental Fluid Mechanics Civil Engineering and Geosciences Delft University of Technology

I WNET 2012, RØROS

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SLIDE 2

1) “standard”particles :  constant charge = 0,04 C/m^2 (sulfate latex)  radius = 265 nm (TEM)  monodisperse  Suspending medium: demi-water + salts

System

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SLIDE 3

2) “more” = non-spherical particles :  kaolinite, gibbsite, goethite (clays, oxides)  non-ideal

System

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SLIDE 4

particle

  • f charge

Q slip plane where the zeta potential ζ is defined ζ=f(Q) |ZP| = |ζ | < 25 mV AGGREGATE |ZP| = | ζ | >> 25 mV STABLE

Zeta Potential

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SLIDE 5

Application

zeta pot. > interactions > rheology

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SLIDE 6

Application

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SLIDE 7

T = constant (no “thermo-dynamic”) E = applied electric field (but “electro-dynamic”) E (V/cm) << zeta potential (mV)/ double layer (nm)  X = Xeq + dX

Assumptions

(zeta potential) double layer (ion cloud) Shear plane = surface particle :

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SLIDE 8

Relation charge / potential at eq.

We will assume a constant surface charge : fixe charge => find the zeta potential for each ionic strength using (PB) + bisection method

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SLIDE 9

Surface potential / added salt

in case of a constant charge

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0.0001 0.001 0.01 0.1 1 10 100 1000 added salt (mM) surface potential (-)

SIG=0.04 KCl SIG=0.04 MgCl

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SLIDE 10

constant surface potential The shear plane is at d(nm) from the surface The zeta potential ζ = potential at shear plane

Constant surface potential but zeta potential decreases with ionic strength when d ≠ 0

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SLIDE 11

Standard electrokinetic equations

Poisson : Conservation of mass: Note:

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SLIDE 12

Standard electrokinetic equations

Boundary conditions

Potential : No flux: No slip:

u(∞) = - U

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SLIDE 13

Electrophoresis

standard electrokinetic equations

relation electrophoretic mobility / zeta potential: found from (PB) assuming (given) constant charge found from solving numerically the set of standard electrokinetic equations found with no adjustable parameter

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SLIDE 14

Electrophoresis

constant zeta potential

Smoluchowsky limit = 1 Debye limit = 2/3 Analytical (O’Brien / Hunter) Analytical (Henry / Ohshima)

symbols: num. simulations ZP = 6x25 mV ZP = 0.1x25 mV κa

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SLIDE 15

Electrophoresis / added salt

constant charge

= x

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SLIDE 16

Electrophoresis / added salt

constant charge

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0.000001 0.00001 0.0001 0.001 0.01 0.1 1 10 100 added mM of MgCl2 ZP (mV)

no adjustable parameter (mV)

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SLIDE 17

Electrophoresis / added salt

constant charge

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0.000001 0.0001 0.01 1 100 10000 added mM of salt ZP (mV) MgCl2 ZetaSizer theory MgCl2 theory with d = 0,25 nm theory sigma = 2,5 d-2 C/m^2 Smoluchowski

same behavior for 2800 nm spheres (Kobayashi, Colloid Polym Sci (2008) 286:935–940)

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SLIDE 18

Electrophoresis / added salt

constant charge

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0.0001 0.001 0.01 0.1 1 10 100 1000 [KCl] (mM) ZP (mV)

high > low low > high NUM OHSHIMA

Gittings and Saville, Colloids and Surfaces A (1998)

curvature!

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SLIDE 19

particle concentration: 19 mg/L

260 265 270 275 280 285 290 295 300 305 0.00001 0.0001 0.001 0.01 0.1 1 10 100 [ KCl ] (mM) radius (nm)

ZetaNano Zeta3000

TEM

Hairy layer : Particle size / added salt

DLS and TEM

Gittings and Saville, Colloids and Surfaces A (1998)

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Electrophoresis / particle concentration

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0.1 1 10 100 1000

particle concentration (mg/L) ZP (mV)

no added salt 1,5 mM KCl 0,1 mM MgCl2 1 mM MgCl2 no added salt ZetaSizer 3000

“salt-free” ZP ≈ - log (1/Φ) Ohshima, Journal

  • f Colloid and

Interface Science 247, 18–23 (2002) (mV)

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SLIDE 21

Summary for spheres

  • Standard theory describes reasonably well the

electrokinetic behavior of the latex particles, with no adjustable parameter (electrophoresis, dielec. spectro., conductivity)

  • adding a Stern layer conductance does not improve the fit

=> hairy layer (“soft particles”) could be explanation for shifting the shear plane approx. 0.25 nm from the particle surface

  • behavior as function of particle volume fraction follows

prediction for nearly no salt

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SLIDE 22

Outlook

electrokinetic response of spheroidal particles

2012 : => numerical solution (=> improve analytical solution) 2008 : => analytical solution (reproduce O’Brien + Loewenberg)

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SLIDE 23

Prolate spheroids (cigars)

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SLIDE 24

Prolate spheroids (cigars)

PH I2

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20 40 60

PH I1

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20 40 60

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20 40 60

P H I1

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5

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1 2 3 4 5

PH I2

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5

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1 2 3 4 5

electrochemical potential counterions electrochemical potential co-ions

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SLIDE 25

Oblate spheroids (mentos)

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SLIDE 26

Gibbsite (original conc. : 16 mg/L)

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10 20 30 0,001 0,01 0,1 1 10 100 1000 concentration salt(mM)

  • Zeta potential (mV)

Na2SO4 (1/80) Na2SO4 (1/60) Na2SO4 (1/40) Na2SO4 (1/20)

volume fraction

Doppler electrophoresis at low volume fraction

(original vol. frac. = 0.6%)