The MPEK software package computes the mobility and polarizability of spherical polymer-coated colloidal particles (sometimes referred to as ‘soft’ or ‘fuzzy’) from solutions of the governing electrokinetic transport equations. The polymer coatings are assumed to be rigid porous media, with a predetermined radial distribution of segments that provides hydrodynamic resistance and - for polyelectrolyte coatings - a radial distribution of fixed charge.

The document below describes how to use the MPEK package. Two programs are available that compute ‘exact’ solutions of the governing electrokinetic equations. The procedure requires solving a nonlinear equilibrium problem (the Poisson-Boltzmann equation), and then solving a linear, but numerically stiff, problem for the perturbed electrostatic potential and ion densities. The far-field decay of the scalar fields for the fluid velocity, electrostatic potential, and ion densities are used to compute ‘measurable’ quantities, such as the hydrodynamic drag coefficient, electrophoretic mobility, polarizability, and dynamic mobility.

MPEK documentation
[MPEK-0.02.pdf - PDF - 355.01 KB]
Latest documentation for the MPEK software package.

The electrokinetic model and the numerical method were described in detail by Hill, Saville and Russel (J. Colloid Interface Sci., 2003). In addition to electrophoresis and dielectric relaxation spectroscopy, the calculations provide important characteristics for interpreting the dynamic mobility from electrokinetic-sonic-amplitude, conductivity, and sedimentation experiments involving dilute colloidal dispersions. Researchers also use the calculated polarizability to interpret dielectrophoretic phenomena and guided assembly of colloidal structures.

Included with the package are 'driver' programs to perform powerful parametric studies of arbitrary complexity. These are extremely valuable for optimally interpreting laboratory experiments. Below is a typical example, where the electrophoretic mobility of 180 nm diameter latices is plotted as a function of NaCl electrolyte concentration for several constant values of the surface charge density (C per square m).

If you would like a copy of the MPEK-0.02 software for academic research purposes, please send an e-mail request to R.J. Hill with your name and contact information. A distribution is now available to run under Windows with the Cygwin platform. For students in my group, Linux and Windows/Cygwin distributions of MPEK are available from the shared network directory.

User resources

If you have published results from MPEK, you are invited to submit a driver.c file (to be posted below) that reproduces a published figure. In this manner, the research community will have a convenient repository of driver.c templates for performing a variety of parametric studies. Please submit your driver.c file to R.J. Hill with appropriate citation and figure number. Your name will be published below with your file.

Contributions

driver.c file to generate O'Brien and White's 1978 figure 4
[driver_OBWHITE1978_FIG04.txt - Plain text - 12.71 KB]
Rename this file to driver.c and compile in the MPEK directory to reproduce O'Brien and White's figure 4 of their famous 1978 paper (J. Chem. Soc. Faraday Trans. II, vol 74). Contributed 11/08/08 by Reghan J. Hill.

driver.c file to generate Hill and Saville's 2005 figure 11
[driver_HILLSAVILLE2005_FIG11.txt - Plain text - 14.87 KB]
Rename this file to driver.c and compile in the MPEK directory to reproduce Hill and Saville's figure 11 (Colloids and Surfaces A: Physicochem. Eng. Aspects, 267: 31-49). Contributed 28/08/08 by Reghan J. Hill.

FAQs

Q: What values of the coating thickness should be used when modeling bare particles?

A: Set the segment size or segment density to a small (but finite) value that guarantees a large, practically infinite Brinkman screening length. In that manner, a coating with finite thickness has no influence on the bare-particle behavior.

Q: The driver programs I downloaded from the web-site don't run under Cygwin.

A: Change "steady", "oscill" and "postproc" commands in driver.c to "steady.exe", "oscill.exe" and "postproc.exe".

Q: I type the name of an executable file at the command line (e.g., > postproc ...), but it does not execute.

A: Execute as > ./postproc ...