xmpl3d85, 85th 'example' data file for CPO3D

7 charged toner particles

Here two new options are used, the importing charge option to set up a charged particle of finite size and the force option to calculate the net electrostatic force on the particle (or any defined set of segments).

An isolated toner particle and a group of four sit on a base plate. Two further particles form a second layer.

All 7 particles are spherical and uniformly charged (which are idealised conditions, unlikely to exist in practice).

The surrounding box has an arbitrary geometry and provides an arbitrary field. The middle part of top plate is at V4 = V3/2, arbitrarily, to send particles to the sides.

The procedure described in test3d31 has been followed for setting up the first toner particle at x = 0. The sphere has 104 segments and the charges are initially in tempout.dat, which is copied to xmpl85.dat. There are 840 'ordinary' segments. For simplicity, no reflection symmetries are used.

Then 6 further spheres are added and the contents of tempout.dat are added 6 times to the end of xmpl85.dat, so that the number of imported charges is then 728. In this way each sphere has the same uniform charge.

The 7th particle is the isolated one. Its segments are numbered 1465 to 1568. These numbers are entered in the option to find the net force on this particle. To detach it from the base plate we need V3 = 244.4, V4 = 488.8, so V4/s = 29V/micron.

Particle 5 is in the second layer, and is repelled from base plate!

The first particle is at end of the set of 4, segments 841 to 944. To detach it, V3 = -369, V4 = -738, so V4/s = 43V/micron.

When V3 = -375, V4 = -750 (an increase of 1.6%) the force becomes

1.6182E-07 1.7576E-10 5.0935E-09

This force is predominantly in the horizontal (x) direction, away from the other particles in the first layer, as expected. However by carrying out a crude trajectory integration (see below) we find that the trajectory quickly turns towards the z direction.

A crude trajectory integration (ray tracing) can be carried out manually, in steps. At each step the force on the particle is found and this is used, together with the particle's known velocity components, to calculate a new position and velocity. Then the transform option is used to move the particle to that position and the process is repeated. (Higher accuracy can be obtained by using the force at the middle of the step.) When the particle has moved sufficiently far from the other particles, so that the force is due primarily to the applied field, then the particle can be treated as a point particle and CPO3D can be used in the usual way to find the remaining trajectory.