Orientational ordering of colloidal dispersions by application of time-dependent external forces

We discuss a method of organizing incoherent motion of a colloidal suspension to produce synchronized, coherent motion, extending the discussion of our recent Letter [Moths and Witten, Phys. Rev. Lett. 110, 028301 (2013)]. The method does not require interaction between the objects. Instead, the effect is controlled by the "twist matrix" which gives the angular velocity of an asymmetric object in a fluid resulting from a weak external force. We analyze the two types of forcing considered in the Letter: a force alternating between two directions and a continuously rotating force. For the alternating force, we justify the claim of the Letter that under appropriate forcing conditions, the orientational entropy of the objects decreases indefinitely with time, on average. We provide a bound on that rate in terms of the twist matrix. For the case of rotating force, we derive conditions for phased-locked motion of the objects to the force and prove that there is only one stable phase-locked orientation under these conditions. We find numerically that the fastest alignment typically occurs for tilt angles of order unity. We discuss how the alignment effect scales with the object size for external forcing caused by gravity or an electric field. Under practical forcing conditions we estimate that the alignment should persist despite rotational diffusion for objects larger than about 10 microns. Potential misalignment owing to hydrodynamic interaction of the objects is estimated to be negligible at volume fractions smaller than about 10(-4.5) (10(-3)) when the forcing is gravitational (electrophoretic).