Dear Student
Fine mud particles can be separated aa result of sedimentation, mud particles will settle as precipitate, which can later on be separated by filtration.
Mud particles are dense enough to settle down from water, if the vessel is left undisturbed for some time.
Centrifugation can be used for fast separation. It settles down the mud particles as pellet.
Centrifuge machine is used for centrifugation. Material is spun at a very high speed which results in the separation.
Regards