It s not possible simply to answer such a complex question since it depends on so many factors and parameters. For example heavy particles with macroscale diameters can travel only several meters at ordinary windspeed. On the other side aerosol particles with diameters under PM 5 with complex shape and low density can be transported intercontinentally.

There are many ways how to deal with airborne particulates modeling. Basicly it s necessary to add a term representing the gravitational sedimentation, arcimedean buyancy term and air friction term to the diffusion equations. Sedimentation happen when gravitational force exceeds air friction and archimedean buoyancy. An important parameters are shape, diameter and mass of particles.

Particles can be also washed out by atmospheric precipitation. This phenomenon can significantly modify flying range of particulates.

When describing intercontinental transport, an airpressure drop in higher altitudes should be taken under account and diffusion terms must be modifyed properly.

Check the attached paper dealing with cosmogenic radionuclide 7Be carried by aerosols

http://ac.els-cdn.com/S1352231009000260/1-s2.0-S1352231009000260-main.pdf?_tid=ee4d72ee-d91b-11e4-9f0c-00000aab0f01&acdnat=1427967651_31e40e50c19563c45902dfe7dd02e987

The gravitational settling of particles is so slow that particles with size of tenths of micrometers can travel over thousands of kilometers. An example id the Asian cloud over the USA and Arctic haze.,This haze is transported from Asia over the Arctic region to northern Alaska

My question is what plume are you thinking of?

N.B. so-called adsorptive gases, like ammonia that is even lighter than air does not travel as far as particles because they are much more rapidly deposited via Brownian motion.

One similar problem: how far the human exhaled particles/droplets will transport? I attached one our previous work for your reference. We proposed  non-dimensional parameters to scale some important factors.  Maybe the approach be helpful for your similar research.

The answer depends on the model applied in a sensitive way since the spread of transported distances is dependend on the velocity field and vertical velocity at emission location. I suggest to try out a standard lagrange transport model first using a prescribed wind field. The further details depend on your particles and more detailed questions. E.g. pollen can be transported very far due to low deposition velocities.