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Manuscript Title: Symbolic computation of the phoretic acceleration of convex particles suspended in a non-uniform gas
Authors: Martin Kröger, Markus Hütter
Program title: PHORETIC
Catalogue identifier: ADYI_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 175(2006)650
Programming language: Mathematica®, version 5.2 or later. PHORETIC makes use of the DiscreteMath'Combinatorica' Mathematica® package.
Computer: All platforms with a monitor.
Operating system: Linux, Windows XP, Unix, Mac-OS.
RAM: 10 MByte
Keywords: Phoretic acceleration, Forces, Torques, Thermophoresis, Rheophoresis, Barophoresis, Friction, Aerosol, Nanoparticle, Gas, Velocity distribution function, Convex particle, Cylinder, Ellipsoid, Nonequilibrium gas, Momentum expansion, Half-sphere integrals.
PACS: 51.10.+y, 05.06.-k, 02.70.Wz.
Classification: 5, 12, 23.

Nature of problem:
Starting from a non-uniform velocity distribution function of a gas in terms of its moments, i.e., field variables, and field gradients such as temperature, pressure, or velocity field, the problem is to analytically calculate forces and torques acting onto arbitrarly shaped convex tracer (aerosol) particles small in size compared to the mean free path of the gas. The collision process is modeled as a superposition of elastic and diffusive scattering processes (parameterized by 0 ≤ α ≤ 1).

Solution method:
We implemented the solution to this problem in the symbolic programming language Mathematica®. The program allows an arbitrary shape of the tracer particle and an arbitrary distribution function of the gas to be specified and returns symbolic or numerical expressions for forces and torques. The solution requires the calculation of half-sphere and base surface integrals and subsequent symbolic algebraic and tensorial manipulations.

Restrictions:
Not known. In case the software cannot calculate surface integrals analytically it offers the possibility to proceed with a numerical evaluation of the corresponding terms.

Running time:
Typical running times mostly depend on the shape of the tracer particle. For all examples included in the software distribution run times are below 5 minutes on a modern single-processor platform.