Thermophoretic forces (TF) play important roles in many areas including microparticle transport phenomena under microgravity conditions. However, to our knowledge no
experimental study has been done on the dependence of thermophoretic force on particle shape. We
have measured the thermophoretic force on two- and three-sphere aggregates, as well as single
spheres of polystyrene latex (PSL) particles in nitrogen gas in the transition regime (Knudsen number 0.1 to 10). Our data indicate that particle aggregation may be accelerated by
thermophoresis.
Wang and Davis [1][2] have successfully used an electrodynamic balance (EDB) to measure the thermophoretic force on single microsphere particles. In an EDB a vertical dc
field cancels the gravitational force on a particle and the thermophoretic force is measured in
terms of this dc voltage. Another superimposed ac field keeps the levitated particle stable.
However, there are two challenges in using an EDB to measure thermophoretic forces. One is to keep
trapped particles stable at the very low ac voltage that is necessary to avoid gas glow
discharge at reduced pressure. The other is to determine the size and mass of the single
particles, especially non-spherical ones, accurately in order to interpret the data.
Particle stability was improved by adding two independent dc fields in the
radial direction with a new octuple double-ring design for the EDB electrodes, as shown in Fig. 1. A
conventional double-ring EDB was modified by splitting each ring into four equal electrically
independent sections. Three dc sources were combined such that eight potentials were applied
to the eight sections of the electrodes. An additional ac voltage was superimposed on each
ring section as in the conventional double-ring EDB. The resulting electric field has dc components
in the x, y and z-directions, which can be controlled independently by the three dc supplies.
The z component is equivalent to the dc field in the conventional EDB and can be used to balance
and measure any vertical force such as gravity. The x and y fields can be used to suppress
radial oscillations of the trapped particles that arise due to gas convection or distortion of the electric
field by the view ports in the chamber walls.
The aerodynamic size of the trapped particles can be determined by a stable
oscillation technique that we have developed previously [3]. This technique involves partially
balancing the particle against gravity and allowing the particle to oscillate in the ac field. The
oscillation trajectories are recorded with a fast linescan camera and are fit to the solutions of the
particle equation of motion. With the aid of a video microscopy system the shape and orientation of
the particle with respect to the electric field is determined. The geometric dimensions and mass
of the particles can be calculated from the aerodynamic size, the shape and the orientation with
the knowledge of particle density. Using this method we were able to determine the size and mass
of PSL particles of two- and three-sphere aggregates.
We have measured the thermophoretic force on these PSL aggregates in nitrogen
gas in the Knudsen regime. The thermophoretic force data, as well as particle shapes and
equivalent volume diameters, are shown in Fig. 2. At a Knudsen number of one, the
normalized thermophoretic force on the two- and three-sphere aggregate is, respectively,
23% and 10% greater than that on a single sphere. This implies that two- and three-sphere
aggregates drift faster due to thermophoresis than single spheres. Once aggregate particles form
there may be a positive feedback mechanism for more aggregation due to the higher mobility of
the aggregate spheres.
Davis, E.J., Zhang, Thermophoretic Force Measurements on Single Spherical and Nonspherical Particles, Fifth Microgravity Fluids and Transport Phenomena Conference, NASA Glenn Research Center, Cleveland, OH, CP-2000-210470, pp. 1283-1285, August 9, 2000.