FIG. 5.

Demonstration of the importance of ROT-ICEO in producing rotating particle samples in the direction of applied rotating field on the surface of a metal square by solving $d(\rho \hspace{0.17em}\text{cos}\hspace{0.17em}\theta ,\rho \hspace{0.17em}\text{sin}\hspace{0.17em}\theta )/\mathit{d}\mathit{t}={\mathit{u}}_{\mathit{\theta }}$ numerically with arrows, line, the left and right bar indicating ${\mathit{u}}_{\mathit{\theta }}$, transient FSL, particle velocity, and $\left|{\mathit{u}}_{\mathit{\theta }}\right|$, respectively, for fixed E₀ = 10 V/mm (supporting movie 2): (a) for $f<f_{\mathit{p}\mathit{e}\mathit{a}\mathit{k}}$, particle moves to the position ${\theta }_0=\frac{1}{2}\arcsin \left(\frac{2\omega \eta \left(1+\delta \right)}{\epsilon E_0^2}\right)$ to first meet and then follow the rotating FSL, with a synchronous rotating rate ${\mathrm{\Omega }}_p\mathrm{=-2\pi f}$; (b) at $f=f_{\mathit{p}\mathit{e}\mathit{a}\mathit{k}}=\frac{\epsilon {E_0}^2}{4\pi \eta \left(1+\delta \right)}$, particle always stays where the transient hydrodynamic torque is largest, thus the synchronous rotating mode becomes maximized with ${\Omega }_{\max }=-\frac{\epsilon {E_0}^2}{2\eta \left(1+\delta \right)}$; (c) at $f>f_{\mathit{p}\mathit{e}\mathit{a}\mathit{k}}$, particle locus oscillates constantly, but still performs a net co-field rotating motion, with the time-averaged rotating rate $⟨\Omega ⟩=-\left(\omega -\sqrt{{\omega }^2-{\left(\frac{\epsilon E_0^2}{2\eta \left(1+\delta \right)}\right)}^2}\right)$.