CB-03 1 Diamagnetic levitation with permanent magnets for contactless guiding and trapping of microdroplets and particles in air and liquids H. Chetouani, C. Jeandey, V. Haguet, H. Rostaing, C. Dieppedale, G. Reyne Abstract— Diamagnetic levitation was applied to micro- positioning and trapping of diamagnetic micron-sized particles and micro-droplets. Scale reduction laws for magnetism indicate that diamagnetism is highly efficient for magnetic MEMS. We demonstrate here that diamagnetic bodies can be contactless guided along magnetic grooves or trapped in magnetic wells both in air and in liquids. Levitation of water, ethanol and oil microdroplets was achieved within a 1.6 mm bore of a cylindrical magnet and in micromachined bulk magnets. Thick permanent micromagnets were also electroplated above silicon wafers in various matrix configurations. Diamagnetic levitation on micromagnet arrays was tested with 3μm-large diamagnetic latex beads in a paramagnetic buffered solution. Trapping and arraying of microparticles in stable spatial levitation within magnetic wells were successfully achieved. Index Terms— Magnetic Micro-actuators and Systems, Lab- on-chip, Magnetophoresis, Diamagnetic Levitation, Permanent Magnets, Contactless Manipulation, Microparticles, Droplets. I. INTRODUCTION OVING and positioning small particles and low liquid volumes are important tasks in miniaturized bio- analytical and biomedical systems, where decreased sample sizes can reduce analysis costs and times. Particularly, the manipulation of liquids in small discrete volumes (microdroplets) provides an amazing alternative solution, compared to microchannels, for the design of new promising labs-on-chip [1]. Moreover, the ability to handle particles and cells using magnetophoresis is currently under investigation for biotechnology applications, including separation of particles [2,3] and cell trapping [4-6]. Current magnetic approaches to organize and pattern particles fall into two categories. The first method involves paramagnetic or superparamagnetic particles, or para-/superparamagnetic labeling of the target particles [2-4,6,7]. However, the microdroplets and particles are in contact with labelling materials, magnets or surfaces [7]. Adsorption and contamination of the manipulated bodies are thus possible. The second approach reported herein provides passive contactless manipulation, trapping and arraying of micro- droplets and particles within magnetic traps created through a precise configuration of permanent magnets. Diamagnetic particles are guided and maintained in wells without any magnetic labeling and without any surface contact [5,8]. Here, we show that droplets and particles can be trapped and guided by diamagnetic levitation both in air and in liquids. Permanent magnets act as magnetic field sources without energy dissipation and heating. Diamagnetism allows passive spatial stability of levitating bodies [9]. Furthermore, when considering scale reduction laws for magnetism [10], it appears that diamagnetism is more efficient when the dimensions of magnets decrease. In other words, what is difficult and complex at macroscopic scale may become effortless and simple in the micron-sized world. Manuscript received March 13, 2006. H. Chetouani, H. Rostaing and G. Reyne are with Laboratoire d’Electrotechnique de Grenoble, ENSIEG, Domaine Universitaire, BP46, F- 38402 SMH, France (e-mail: hichem.chetouani@leg.ensieg.inpg.fr). C. Jeandey, V. Haguet and C. Dieppedale are with Commissariat à l’Energie Atomique (CEA), 17 rue des Martyrs, F-38054 Grenoble Cedex 9, France. II. MAGNETOPHORESIS PRINCIPLE AND FORMULATION A diamagnetic particle with a magnetic moment M, placed into a magnetic field B, has energy B M U r r ⋅ − = and experiences a torque B M r r r × = τ . If the field is inhomogeneous, the diamagnetic particle experiences a magnetic force ) ( B M U Fm r r r r r ⋅ ∇ = ∇ − = , as illustrated in Fig. 1. The force experienced by a volume segment of the particle can be expressed, considering as constant the magnetization within this volume segment, by . After integration over the whole volume of the particle, magnetophoretic force components are then given by: dv dv B M F d m ). ( r r r r ∇ ⋅ = ( ) ∫∫∫ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ Δ = ∫∫∫ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ + ∂ ∂ + ∂ ∂ − = v v m p mx dv x B μ dv x Bz Bz x By By x Bx Bx μ F . 2 . 2 0 0 χ χ χ (1) ( ) ∫∫∫ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ Δ = ∫∫∫ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ + ∂ ∂ + ∂ ∂ − = v v m p my dv y B μ dv y Bz Bz y By By y Bx Bx μ F . 2 . 2 0 0 χ χ χ (2) ( ) ∫∫∫ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ∂ ∂ Δ = ∫∫∫ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ ∂ ∂ + ∂ ∂ + ∂ ∂ − = v v m p mz dv z B μ dv z Bz Bz z By By z Bx Bx μ F . 2 . 2 0 0 χ χ χ (3) where χ Δ is the susceptibility contrast between magnetic susceptibility of the particle χ p and the one of the medium χ m , and is the vacuum magnetic permeability. 0 μ Direction and velocity of particle movement in a magnetic field gradient are determined by magnetic (F m ), drag (F d ), gravitational (F g ), and Archimedes (F a ) forces. Thus a stable M