A new class of magnetically actuated pumps and valves for microfluidic applications

Abstract

We propose a new class of magnetically actuated pumps and valves that could be incorporated into microfluidic chips with no further external connections. The idea is to repurpose ferromagnetic low Reynolds number swimmers as devices capable of generating fluid flow, by restricting the swimmers' translational degrees of freedom. We experimentally investigate the flow structure generated by a pinned swimmer in different scenarios, such as unrestricted flow around it as well as flow generated in straight, cross-shaped, Y-shaped and circular channels. This demonstrates the feasibility of incorporating the device into a channel and its capability of acting as a pump, valve and flow splitter. Different regimes could be selected by tuning the frequency and amplitude of the external magnetic field driving the swimmer, or by changing the channel orientation with respect to the field. This versatility endows the device with varied functionality which, together with the robust remote control and reproducibility, makes it a promising candidate for several applications.

Figure 1

(a) Fabrication of a ferromagnetic swimmer with a hard cubic NdFeB particle (0.6 mm × 0.6 mm × 0.45 mm), and soft Fe cylindrical particle (0.7 mm long, diameter 0.5 mm) with an overall length 3.6 mm, thickness 0.5 mm and a particle centre to centre separation of 2.2 mm. The final device is pinned using a 0.25 mm diameter non-magnetic rigid wire. The diagrams (made to scale) of channel geometries show the pinned swimmer within (b) a straight channel of width 10 mm, (c) a cross-shaped channel of width 11 mm, (d) a Y-shaped channel of width 10 mm, and (e) two closed circuits (one with a uniform cross section of 2 mm × 1.1 mm and the other 7.2 mm wide close to the swimmer well tapering down to 0.5 mm). (f) Diagram of the experimental set up, showing a channel with a swimmer between two Helmholtz coils and a camera for observation.

Figure 2

Typical surface flow generated by a pinned swimmer actuated by an external magnetic field of strength 2.0 mT and frequency 60 Hz. The overlay of the schematic swimmer in the middle indicates its mean orientation around which it oscillates (radially and tangentially). The amplitude of the radial and tangential oscillations is on a sub-mm length scale. The swimmer is prevented from translation by a thin post protruding through the elastic circular link (not shown in the picture). The arrows indicate the direction of flow.

Figure 3

Fluid flow around a pinned swimmer under a magnetic field of strength 1.5 mT and frequency of (a) 90 Hz (θ₁ =  +25° relative to the applied magnetic field) and (b) 130 Hz (θ₂ = −30° relative to the applied magnetic field). The overlay of the schematic swimmer shows the mean orientation of the pinned swimmer, different at the two frequencies. The arrows represent the direction of flow (but not the magnitude of the velocity).

Figure 4

Free 3.6 mm swimmer in a straight channel of 11 mm width. Trajectories of the hard particle (blue dots) and the soft particle (yellow dots) are overlaid on the image of the channel. The three panels show different propagation modes of the swimmer at a constant magnetic field strength of 1.5 mT and varying frequency (40, 130 and 140 Hz) for a period of 0.8 s. The external magnetic field is aligned along the main axis of the channel. The grey arrows indicate the direction of swimming.

Figure 5

Swimming speed as a function of channel width at field strength of 1.5 mT and frequency of 40 Hz. The upper horizontal axis is the ratio between the swimmer’s size (3.6 mm) and the channel width.

Figure 6

Surface flow speed at different kinematic viscosities in a channel of width 11 mm (a) as a function of field frequency at an amplitude of 1.5 mT, (b) as a function of magnetic field strength at a frequency of 50 Hz. The values of the fluid kinematic viscosity (in m² s⁻¹) are given in the insets. The error bars represent the standard deviation from 3 measurements.

Figure 7

Flow speed as a function of channel width at field strength of 1.5 mT and frequency of 40 Hz. The upper horizontal axis is the ratio between the swimmer’s size (3.6 mm) and the channel width.

Figure 8

Mean orientation of the pinned swimmer in channels of increasing width. The magnetic field is aligned along the main axis of the channel and the numbers indicate the width of the channel in mm. Magnetic field parameters: frequency 40 Hz, amplitude 1.5 mT. Swimmer’s mean orientation was determined by analysing SI Movie 5 and the flow speeds are shown in Fig. 7. The direction of flow is downwards.

Figure 9

Frequency dependences of the flow speed at three different orientations between the channel axis and the external magnetic field (0°, 90° and 180°) for (a) channel of width 11 mm and (b) channel of width 5 mm. (c) Contour map representing mid-channel flow speed as a function of frequency and channel orientation for the 11 mm channel. The magnetic field amplitude is 1.5 mT.

Figure 10

Flow in a cross-shaped channel. The flow lines for four different orientations of the channel relative to the applied magnetic field (0°, 10°, 20°, and 30°) are shown with blue dashed lines and arrows. A schematic diagram of the swimmer is overlaid to show its mean orientation in the centre of the cross. In all orientations, the magnetic field has frequency 40 Hz and strength 1.5 mT.

Figure 11

Flow in a Y-shaped channel. The swimmer is pinned at the centre of the junction and the bottom branch of the channel is aligned in parallel to the external magnetic field. The direction of the flow is shown with white arrows. (a) Flow direction in the presence of an applied magnetic field of strength 2.40 mT at a frequency of 60 Hz. (b) Flow direction in the presence of an applied magnetic field of strength 1.38 mT at a frequency of 130 Hz.

Figure 12

Pinned swimmer in a circular channel. The swimmer is positioned in the lower part of the channel in a well and the channel is filled with water. (a) A few drops of ink are placed in the upper part of the channel; (b) ink distribution 2.3 s after the activation of the swimmer; (c) ink distribution 2.9 s after the activation of the swimmer; (d) ink distribution 4.3 s after the activation of the swimmer. The magnetic field frequency is 50 Hz and the amplitude is 1.5 mT.

Figure 13

Velocity profile at the surface of the liquid in a closed channel. The red dashed line shows a fitted parabolic function. The velocity profile was measured opposite to the position of the swimmer, where the channel had a cross-section of 0.5 mm × 0.5 mm. External magnetic field of 100 Hz and 3.0 mT. The inset shows a model of the 3D printed channel.