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Copyright Brian J. Kirby. With questions, contact Prof. Kirby here. This material may not be distributed without the author's consent. When linking to these pages, please use the URL http://www.kirbyresearch.com/textbook.

This web posting is a draft, abridged version of the Cambridge University Press text. Follow the links to buy at Cambridge or Amazon or Powell's or Barnes and Noble. Contact Prof. Kirby here. Click here for the most recent version of the errata for the print version.

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Jump To: [Kinematics] [Couette/Poiseuille Flow] [Fluid Circuits] [Mixing] [Electrodynamics] [Electroosmosis] [Potential Flow] [Stokes Flow] [Debye Layer] [Zeta Potential] [Species Transport] [Separations] [Particle Electrophoresis] [DNA] [Nanofluidics] [Induced-Charge Effects] [DEP] [Solution Chemistry]

B.4 Effects of solutes [water properties top]

In the dilute solution limit, the effects of added solvents or dissolved solutes are assumed to be negligible. However, as the concentrations of these other solvents or solutes increase, the effects of these solutes on the liquid properties cannot be ignored. As a first approximation, these effects can be linearized and treated in terms of differential properties. Here we focus on the differential effects of solutes on the viscosity and permittivity of aqueous solutions.

B.4.1 Dielectric increments

Solutions of electrolytes have electrical permittivities that are different from that of pure water. This is typically reported in terms of adielectric increment microfluidics textbook nanofluidics textbook Brian Kirby Cornell, which stems from a first-order Taylor series approximation of the electrical permittivity as a function of concentration:
microfluidics textbook nanofluidics textbook Brian Kirby Cornell
(B.18)

Table B.3 lists dielectric increments for several solutes. Small ions tend to reduce the dielectric constant of water when in solution. Zwitterionic saltstend to increase the dielectric constant of water because these molecules have a permanent dipole larger than water when they are ionized. The pH ranges listed for some solutes refer to the pH range in which their positive and negative sites can be assumed fully ionized—outside this range, the dielectric increment is reduced by the fact that the charges are no longer fully ionized. Homologous sets, i.e., groups of molecules that have similar structure, show how greater separation of charge leads to a largerdipole moment—so Gly-Gly-Gly has a larger dipole moment than Gly because three dipoles are lined up in order, and triethylammoniobutane sulfonate has a higher dipole moment than triethylammonioethane sulfonate because its charges (i.e., the quaternary ammonium and the sulfonate) are separated by a C4 linker rather than a C2 linker. Larger dipole moments lead to larger permittivities and therefore larger positive dielectric increments. These relationships work for relatively small chains, e.g., 2-6 carbon links. Above that, the molecule has enough flexibility that the positive and negative charges can loop around and attract each other, reducing the dipole moment and thus the dielectric increment.




Solute Dielectric increment, microfluidics textbook nanofluidics textbook Brian Kirby Cornell, [M-1]


Na+ -8 [260]
K+ -8 [260]
H+ -17 [260]
Mg+2 -24 [260]
Cl- -3 [260]
OH- -13 [260]
SO4-2 -7 [260]
Glycine 24 [39]
Lactose -8.2 [261]
Sucrose -8.2 [261]
Trehalose -7.6 [261]
Maltose -8.9 [261]
Sorbitol -2.9 [261]
Mannitol -2.5 [261]
Inositol -1.9 [261]
Ethanol -4.6  [262]
Methanol -2.1 [262]
Glycerol -1.9 [261]
Gly-Gly 72 [39]
Gly-Gly-Gly 126 [39]
cyclohexylaminoethane sulfonate, 4.0 < pH < 6.3 23 [47]
cyclohexylaminopropane sulfonate, 4 < pH < 7.4 38 [47]
cyclohexylaminobutane sulfonate, 4 < pH < 7.7 68 [47]
trimethylammoniopropane sulfonate, 4 < pH < 10 42–52 [4647]
triethylammonioethane sulfonate, 4 < pH < 10 42 [263]
triethylammoniopropane sulfonate, 4 < pH < 10 59 [263]
triethylammoniobutane sulfonate, 4 < pH < 10 73 [263]



Table B.3: Dielectric increments of a variety of solutes. Numbers in brackets refer to the references. The linear model for the dielectric increment in general is applicable only for finite concentrations, typically up to about 3 M.


microfluidics textbook nanofluidics textbook Brian Kirby Cornell


[Return to Table of Contents]



Jump To: [Kinematics] [Couette/Poiseuille Flow] [Fluid Circuits] [Mixing] [Electrodynamics] [Electroosmosis] [Potential Flow] [Stokes Flow] [Debye Layer] [Zeta Potential] [Species Transport] [Separations] [Particle Electrophoresis] [DNA] [Nanofluidics] [Induced-Charge Effects] [DEP] [Solution Chemistry]

Copyright Brian J. Kirby. Please contact Prof. Kirby here with questions or corrections. This material may not be distributed without the author's consent. When linking to these pages, please use the URL http://www.kirbyresearch.com/textbook.

This web posting is a draft, abridged version of the Cambridge University Press text. Follow the links to buy at Cambridge or Amazon or Powell's or Barnes and Noble. Contact Prof. Kirby here. Click here for the most recent version of the errata for the print version.


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