Microfluidic transport in magnetic MEMS and bioMEMS

(a) Two modes of magnetic relaxation of nanoparticles: Brownian(top) and Néelian (bottom) with the Larmor time constant τ₀∼10⁻⁹ s. The effective relaxation time due to the combined action of both relaxations is . (b) Magnetization curves for ferrofluids containing different particle sizes. A qualitative comparison of the magnetization of a paramagnetic substance is also shown on the same plot.

(a) Rotating chains of magnetic beads in a rotating (ω = 5 revolutions per minute (RPM) ) magnetic field (size of the scale on the left is 10 µm). (b) Mixing of a blue dye due to the clockwise rotation of bead chains due to a rotating magnetic field (size of the scale on the left is 500 µm). (c) Time evolution of the mixing index, showing an improvement in mixing with a rotating field. (d) Variation of t_1/2 with the field rotational speed for different Ma. The mixing half‐life attains a minimum value near a critical , (Reprinted with permission from Ref 126. Copyright 2009 American Institute of Physics).

Basic steps of immunomagnetic separation (IMS) in a microfluidic configuration. (a) Introduction of the beads and the analyte mixture, (b) mixing of analytes and binding of the target analyte on the bead surfaces, (c) magnetic separation of the bead and target analyte conjugates, (d) washing of the nontarget entities and background fluid by buffer, followed by collection of the target analyte–bead conjugates.

Single particle dynamics in a microfluidic channel. (a) The microchannel geometry and the flow arrangement, and (b) the computational domain. (c) The experimentally observed and computed particle trajectories for a combination of the dipole strength m = 2.28 × 10⁻⁷ A m², m, Re ∼1, and a = 1 µm. (d) Experimentally observed temporal growth rate of the particle aggregates during the ‘buildup phase’ for a = 2 µm, I = 0.5 A, U = 1 mm/s, c = 10¹² m⁻³, inside a 200 µm × 1000 µm cross‐section microchannel. (e) Simulated growth rate of the aggregate volume fraction, showing the ‘buildup’ and the ‘washaway’ phases. (Frames (a), (d), and (e) are reprinted with permission from Ref 75. Copyright 2009 Elsevier. Frames (b) and (c) reprinted with permission from Ref 76. Copyright 2007 American Institute of Physics).

Dipole–dipole interaction of magnetic microspheres in an externally imposed magnetic field (a), leading to the formation of long chains (b), packed aggregates (c), or a combination of both (d).

(a) Magnetically induced three‐dimensional temporary ferrofluid structures produced on a flat substrate, (b) orientations of these structures with respect to the magnetic lines of force. (c) Permanent ferrofluid structures made by mixing a curing agent (Sylgard^®) with the ferrofluid and then curing under a magnetic field. (d) Patterns exhibited by an oil‐based ferrofluid on water surface. (e) Labyrinthine ferrofluid structures formed in a Hele Shaw cell. (Reproduced with permission from Ref 38. Copyright 2007 Elsevier).