If you have an ion density gradient you will generate electrical fields in accordance with Poisson's equation. Since the dust particles in a plasma are usually charged on the surface, they will, of course, experience a electric force acting on them.

The ion density or velocity gradient works in two different ways on dust particles. Firstly, the density gradient generates a electric field (as discussed by Gruenwald) , in this E-field ions get energy and exert a force , called ion drag force. Also, the dust particles are negatively charged particles, therefore the electrostatic force will also act on the particles. The dynamics of dust grains will be determined by the resultant force (both forces have opposite direction) acting on them.

Secondly, the ion density gradient can also creates a gradient in ion drag force, which can exert a torque on the dust particles if there exist an E-field or non-harmonic force, making some angle with the ion drag force gradient. Due to this tuque, dust grains start to rotate and can form a vortex structure if dust grains are strongly coupled.

There are many research articles on these topics. I suggest you to read the articles related to void formation in dusty plasma for first concept and dust vortex motion in dusty plasma for second concept. Good luck

Thank you Johannes Gruenwald and Mangilal Choudhary for your answers.

Any type of density gradient in plasma will create an electric field , which will affect the dynamics of other charged particles. It may be dusty particle in the plasma which is normally negatively charged.