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...Chapter dynamics ofparticles in a fluid notes on mathematical problems the of dispersed particles interacting through p e jabin and b perthame ecole normale sup erieure dmi rue d ulm paris cedex france inria rocquencourt projet mn bp le chesnay introduction this we present some related to dy namics uid are interested dilute cases mean where transport partial dierential equations phase space can be expected for density order derive these explicitely assumptions dynam ics necessary they limit validity model but still represents many possible applications namely assume that reduced two simple situations rst situation is case potential ow perfect incompressible irrotational relevant describe instance motion bubbles water see g k batchelor focuses mainly added mass eect which means acce larate requires accelerate part too second more standard stokes domains application suspensions or sedimendation around leads diculty establishing equation particle formalism was developed by russo smereka w...