W-waveform Standing Surface Acoustic Waves with Two Equilibrium Positions under Linear Phase Modulation for Patterning Microparticles into Alternate Grid Patterns

This paper presents W-waveform Standing Surface Acoustic Waves (W-SSAW), and as its application, patterning of two groups of microparticles with different sizes alternately without fixing firstly patterned particles. W-SSAW is constructed by two standing surface acoustic waves of frequencies $f$ and $2f$. Combined with linear phase modulation to translate Gor'kov potential at a constant speed, W-SSAW can selectively trap particles. The trapped particles follow the moving Gor'kov potential maintaining force equilibrium between Stokes' drag and the radiation force by W-SSAW. There exist two asymmetric equilibrium positions every period, and by the asymmetry, each group of particles is trapped at different equilibrium positions to form an alternate pattern. This technique is extended to two-dimensional alternate patterning by maintaining phase difference $90^\circ$ between X- and Y-directional W-SSAWs. The patterning method utilizing W-SSAW is advantageous over SSAW-based patterning in that it does not require temporal separation to fix firstly patterned particles.