Qualitative interpretation of MMS focussing data at low (panel a; cf. Fig 8A) and high (panel b; cf. Fig 8B) flow rates.

<p>The coloured maps are analogous to those shown in <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169919#pone.0169919.g003" target="_blank">Fig 3</a>. That is they represent the magnitude of the net lateral force acting on particles excluding the drag associated with the induced secondary flow. The latter is represented by arrows. The outwardly-directed magnetic field gradient is canted downwards by 25 degrees relative to the horizontal to reflect experimental conditions.</p

Schematic plan and (cross-sectional) side views of the array used to produce an octupolar magnetic field.

<p>Each 3.2 mm × 3.2 mm × 9.5 mm NdFeB magnet is magnetized parallel to its long axis. The distance between faces of opposing magnets is 17.7 mm and the diameter of the accessible bore is 16 mm. Curved arrows shown in the plan view indicate the qualitative sense of magnetic field lines. A thin annular ferromagnetic shield (green; side view only) between the array and the plane of the microfluidic spiral screens the magnetic field in the vicinity of the outlet ports and provides a field-free region for particle extraction. The distance of closest approach between the microfluidic spiral (represented by the dashed curve/line) and the plane of the shield is set by a microscope slide (not shown). See also <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169919#pone.0169919.g006" target="_blank">Fig 6</a>.</p

Inertial focussing of particles in microfluidic channels (qualitative).

<p>The coloured maps represent (a) the downstream fluid speed U and (b and c) the magnitude of the net lift force F_NL; see Appendix A. The oriented texture superimposed on the latter is generated via line integral convolution [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169919#pone.0169919.ref052" target="_blank">52</a>], and is thus tangential to F_NL. Particles (represented by yellow spheres) are driven away from the core of the flow toward regions of high stress, but are simultaneously kept away from the walls by asymmetric wake effects. In a straight rectangular channel (panels a and b), competition between these lift forces ultimately leads to particle aggregation along streamlines near the middle of the broad walls. In a curved channel (panel c), the induced secondary flow (indicated by arrows) contributes to the net lateral force and drives particles toward an apparent streamline near the midpoint of the inner wall of the turn. Here, and in all subsequent figures, the low end of the relevant scale (speed, force, etc) is mapped onto the colour blue.</p

Calculated map of the magnetic field strength H, in units of A/m.

<p>The microfluidic channel is shown as a white spiral (upper panel; plan view) and a white line (lower panel; side view). Spatial coordinates are specified relative to its centre, in units of mm. The dashed line indicates the intersection of the two orthogonal views.</p

Fraction of (a) large (12 μm diameter) and (b) small (2 μm diameter) MMS extracted from the two outlets during experiments in which a 1:1 mixture of the two components was injected into the spiral.

<p>Data acquired without the octupole [<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0169919#pone.0169919.ref043" target="_blank">43</a>] are shown for reference.</p

Photographs of MMS distributions in the microfluidic spiral at (a) low (5 μL/min), (b) medium (30 μL/min), and (c) high (60 μL/min) flow rates.

<p>The view is from above the spiral, looking down toward the magnet array. The full vertical extent of the channel lies within the optical depth of field.</p

Geometry of a curved microfluidic channel, illustrating the relationship between the primary (downstream) and induced secondary flows.

<p>Geometry of a curved microfluidic channel, illustrating the relationship between the primary (downstream) and induced secondary flows.</p