High-Sensitivity Measurement of Density by Magnetic Levitation

Abstract

This paper presents methods that use Magnetic Levitation (MagLev) to measure very small differences in density of solid diamagnetic objects suspended in a paramagnetic medium.Previous work in this field has shown that, while it is a convenient method, standard MagLev cannot resolve differences in density < 0.0001 g/mm 3 for macroscopic objects (> mm) because i) objects close in density prevent each other from reaching equilibrium height due to hard contact and excluded volume and ii) using weaker magnets or reducing the magnetic susceptibility of the medium destabilizes the magnetic trap. The present work investigates ways to increase the sensitivity of MagLev without destabilization by i) rotating the standard configuration relative to the gravitational field, and therefore, exploiting the weak magnetic gradients along alternative axes of measurement, and ii) tuning the sensitivity by manipulating the geometries of the magnets. These modifications enable an improvement in the resolution up to 1300 over the standard configuration, and measurements with resolution down to 10 -6 g/cm 3 . Three examples of characterizing the small differences density among "identical" samples of materials-Nylon spheres, PMMA spheres, and drug spheres-demonstrate the applicability of high-sensitivity, rotated Maglev to measure the density of small (0.1 -1 mm) objects with high sensitivity, for use in materials science, separations, and quality control of manufactured products.2

Magnetic Levitation in Chemistry, Materials Science, and Biochemistry

“…This capability leads to applications of MagLev in density-based separations. [20,22,101,123,41,42,93,[95][96][97][98]100] MagLev also provides au nique environment in which diamagnetic objects can be levitated and manipulated, without contacting the walls of the container,f or 3D assembly.T his capability,inconjunction with densitybased levitation, opens unexplored domains of research, and enables new applications of MagLev in emerging areas such as advanced manufacturing, quality control, and 3D self-assembly of both hard and soft, fragile components. [21,135À139]…”

“…Air bubble mm~0N dFeB 0.4 MnCl 2 in water [22,93] Polymer particles (PMMA, PS, Nylon, etc.) mm-mm 0.9-2.3 NdFeB 0.4 MnCl 2 /GdCl 3 in water and alcohol [20,42,44,74,86,[93][94][95] Organic liquids (e.g.,chlorobenzene, 2-nitrotoluene, dichloromethane, 3-bromotoluene, and chloroform. )…”

“…Polymorphsofcrystals (e.g.,sulfathiazole and trans-cinnamic acid), enantiomers (S-/RS-ibuprofen), cocrystals (e.g.,c arbamazepine/salicylic acid) mm-mm 1.093-1.580 NdFeB 0.4 MnCl 2 in water [97][98][99] Drug microspheres from drug capsules mm 1.3284 NdFeB 0.4 GdCl 3 in water [95] Powders containing illicit drugs (e.g.,f entanyls) mm-mm 1.10-1.58 NdFeB 0.4 Gd(DPM) 3 TOPO [b] or Gd(acac) 3 TOPO [c] in organic solvents [100] Forensic evidence:" glitter" and gunpowder mm-mm 1.226-1.395 NdFeB 0.4 MnCl 2 in water [101] Water and Foods:vegetable oils, milk, cheese, peanut butter,grains mm 0.9-1.4 NdFeB 0.4 MnCl 2 /GdCl 3 in water; Gd-DTAD [d] in organic solvents [41] Si, Diamond, Al 2 O 3 ,v arious minerals mm 2.33-6.55 NdFeB 0.4 MnCl 2 in water [93] Al, brass, Hg, Sn, In, Cu, Ag, Pb, Au, Ir,Os mm-mm 2.7-22.6 NdFeB 0.4 MnCl 2 in water [93] Graphite, Graphene, Bismuth --NdFeB 0.4 Air [102][103][104] Organic liquids (e.g.,pentane, toluene, nitrobenzene, bromoethane, carbon tetrachloride) mm 0.6-1.6 Electromagnet 1.9 MnCl 2 or MnBr 2 in water [105] KCl, Si, GaAs, Pb, Au mm-cm -S uper-conducting electromagnet…”

Evaluation of polymer injection molded parts via density‐based magnetic levitation

“…Nemiroski et al mentioned that pycnometer and densitometer require costly devices to achieve high accuracy (up to 0.0001 g cm −3 ) and are usually difficult to use. 18 The work of Davidson and Perkin reported that the density gradient column has the following disadvantages: the device is overly large (usually a column height of over 2 m is necessary) and the density gradient is difficult to prepare. 19 Nevertheless, the most significant disadvantage that is common among these methods is that they cannot detect the density distribution of interior parts.…”

Self‐Contained Handheld Magnetic Platform for Point of Care Cytometry in Biological Samples

“…At equilibrium between these two forces, the object will levitate at a height which is proportional to its volumetric mass density. Magnetic levitation has been proposed for a wide range of applications, including self‐assembly and arrangement of objects, monitoring of chemical reactions and substrate binding, material characterization, bottom‐up tissue engineering, and quality control based on the volumetric mass density of the levitated object . This method allows measurements of the intrinsic cell densities and, compared to other label‐free approaches, active sorting using a magnetic field formed by two permanent magnets and does not require peripheral equipment to generate the field, reducing the overall cost.…”