Particle focusing in a small-amplitude wavy channel

Both inertial lift forces and oscillatory straining effects have been suggested as mechanisms for particle focusing in wavy channels. To determine the dominant mechanism, we predict the focusing locations of rigid neutrally buoyant particles in a small-amplitude wavy channel. We decompose the undisturbed channel flow into a main-order Poiseuille flow and secondary eddies induced by the waviness. We calculate the perturbation of the particle on the undisturbed flow and the resulting lateral lift force exerted on the particle with the method of matched asymptotic expansions. We obtain a main-order lift force determined from the Poiseuille flow and a first-order lift force due to the waviness of the channel. Unlike the main-order lift force which is only a function of the lateral position of the particle, the first-order lift force also varies sinusoidally along the channel. By employing the Maxey-Riley equation, we identify the lift force as the predominant mechanism for particle focusing. The balance between the main- and first-order lift forces determines the focusing locations, which do not significantly deviate from those in a straight channel. We validate the predictions experimentally at Reynolds numbers ranging from 10 to 250.