Microfluidic propulsion by the metachronal beating of magnetic artificial cilia: a numerical analysis

Abstract

In this work we study the effect of metachronal waves on the flow created by magnetically driven plate-like artificial cilia in microchannels using numerical simulations. The simulations are performed using a coupled magneto-mechanical solid-fluid computational model that captures the physical interactions between the fluid flow, ciliary deformation and applied magnetic field. When a rotating magnetic field is applied to super-paramagnetic artificial cilia, they mimic the asymmetric motion of natural cilia, consisting of an effective and recovery stroke. When a phase difference is prescribed between neighbouring cilia, metachronal waves develop. Due to the discrete nature of the cilia, the metachronal waves change direction when the phase difference becomes sufficiently large, resulting in antiplectic as well as symplectic metachrony. We show that the fluid flow created by the artificial cilia is significantly enhanced in the presence of metachronal waves and that the fluid flow becomes unidirectional. Antiplectic metachrony is observed to lead to a considerable enhancement in flow compared to symplectic metachrony, when the cilia spacing is small. Obstruction of flow in the direction of the effective stroke for the case of symplectic metachrony was found to be the key mechanism that governs this effect.

Cilia beating patterns are not hydrodynamically optimal

“…7 and 9): one antiplectic and one symplectic. This is consistent with previous computational results 26,37,38 . The optimal values of ∆φ are summarized in Table I.…”

Fluid–structure interaction of three-dimensional magnetic artificial cilia

“…The flow is always larger for the cilia beating with antiplectic metachrony compared with synchronously beating cilia (in accordance with Khaderi et al (2011b)). In the case of symplectic metachrony, the cilia obstruct the flow caused by their neighbours during the effective stroke (as also seen in the two-dimensional case FIGURE 7.…”

“…We apply a magnetic field of magnitude B ext = 20 mT, rotating about the y-axis with a frequency of 50 Hz. As the cilia are SPM, the cilia complete one beat cycle in t beat = 10 ms (Khaderi, den Toonder & Onck 2011b). In the simulations, the fixed edges of the cilia are placed 0.1L above the no-slip boundary, to mimic the presence of the sacrificial layer used during the manufacturing process (den Toonder et al 2008;Fahrni et al 2009).…”

“…The velocity profiles for the set of phase differences corresponding to A, B and C are shown in figure 8: (a) primary flow; (b) secondary flow. Khaderi et al (2011b)). As a result, for antiplectic metachrony the flow is larger and for symplectic metachrony the flow is smaller than synchronously beating cilia, although the magnitude of increase is larger (for antiplectic metachrony) than the decrease (for symplectic metachrony).…”

Mixing and transport by ciliary carpets: a numerical study

“…by a single cilium and Khaderi et al (2011); Khaderi & Onck (2012) for the flow field generated by a finite number of artificial cilia. These studies focus primarily on the performance of the ciliary systems in fluid transport and pumping.…”