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Summary of effects in magnetophoresis due to magnetic and hydrodynamic interactions beyond the classical model. The cartoon indicates the physical interactions behind the cooperative effect and the magnetic-induced convection, illustrated by the images

The challenge of understanding low-gradient magnetic separation

Low-gradient magnetic separation (LGMS) is a complex phenomena with a behaviour so contradictory with classic magnetophoresis models that it was considered to be almost paradoxical. An Editor’s Choice feature article at the Langmuir journal, co-authored by ICMAB Researcher Jordi Faraudo, proposes a unified theoretical framework to understand and control this helpful separation technique.

While there are more stablished and understood methods for colloid separation like electrophoresis and dielectrophoresis, the development of new magnetic particles has rekindled an interest in magnetophoresis, a technique that allows for colloid separation through the use of magnetic fields. While there are many applications for these method, like drug delivery, removal of heavy ions from water or the removal of microalgae, sorting as well as detection of cells, amongst others, a particular challenge appears in some applications, particularly in the biomedical field. 

The common technique for magnetiphoresic separation, High-gradient magnetic separation (HGMS), requires the magnetic field to be created within the solution through a separation column. However, some applications depend on distal control of the particle motion in non-contact mode, and thus the ideal methodology would be the creation of the field with permanent magnets located outside the particle suspension. When considering classic theory, an issue arrises: permanent magnets create too small a gradient (< 100 T/m), which enters the field of low-gradient magnetic separation. The problem with implementing LGMS is that it requires a macroscopic time and length of movement through magnetic forces that work at the nanoscale. 

However, this is not always a problem in application. With changing parameters in different applications, the same process has been observed to take from seconds to hours. This disparity between the classic theory on magnetophoresis and the observed results has been considered to be paradoxical. The various factors and parameters that affect this strange behaviour have been studied for years, but a new publication is defining a unified theory for LGMS. 

Understanding the anomalies

The article, entitled “Unified View of Magnetic Nanoparticle Separation under Magnetophoresis”, has been published on Langmuir journal. The article authors, amongst which is ICMAB Researcher Jordi Faraudo, from the Soft Matter Theory Group, have used many of the available studies on the topic to design an holistic view of the behaviour of this technique. Langmuir has considered this article an Editor’s Choice for their latest issue. 

The article uses two observed novel effects of LGMS to explain the increase of speed. One is cooperative magnetophoresis, which can be identified in the strong dependence on particle concentration observed in the kinetics of magnetophoresis. When considering larger magnetic particles, the magnetic field causes them to align in self-assembled elongated structures that move faster than individual particles. 

The other is magnetophoresis-induced convection, a phenomena defined by the creation of convective current within the solution that is trying to relax a mechanical instability provoked by the solution having different particle concentrations in different sections of the fluid as a result of being within an inhomogeneous magnetic gradient. This phenomena can be seen in action in these samples that use dye as tracers and showcase how the motion maintains a uniform concentration of magnetic particles along the sample.

Figure 6. (a) Sketch of a simple setup for observing convection-induced magnetophoresis with a single permanent magnet. Typical values of magnetic field gradients are indicated. The red arrows indicate the spontaneous motion of the fluid. (b) Visualization of convective flow in one of the experiments reported in Figure 4b (a very dilute dispersion of magnetic nanoparticles under the effect of a magnet) using a blue dye. This hydrodynamic instability is induced by a magnet which produces an inhomogeneous magnetic gradient and therefore an inhomogeneous magnetic force, strong in the bottom near the magnet and weak at the top. Reproduced with permission from ref 53. Copyright 2015 Royal Society of Chemistry.

The combined effect of these two phenomena can accelerate the process and make it 30 to 50 times faster than expected, depending of many variables. These dependences are expressed in this new unified view through two dimensionless numbers: the Aggregation Parameter N*, which relates to how the separation is affected by cooperative magnetophoresis and involves the magnetic properties of the particles and also thermodynamic quantities, such as concentration and temperature, and the Magnetic Grashof Number Grm, which informs to what degree the separation is affected by magnetophoresis-induced convection. Through the use of these dimensionless parameters, the article establishes four distinct regimes that indicate which mechanisms will affect the solution.Plot of Grm against N* for the general magnetophoresis process with four distinct regimes characterized by different flow mechanisms.

This diagram plots these regimes, indicating weather the solution is accelerated through cooperative magnetophoresis, magnetophoresis-induced convection, both or neither, and it is the key to understand the process's behaviour and find in which ways a particular LGMS can be optimized and implemented for different engineering applications.

More information:

The video in this article was created by Dr. Juan Camacho and Dr. Jordi Faraudo. You can find more simulations and helpful resources by all the members of the Soft Matter Theory Group in their new YouTube channel!

Unified View of Magnetic Nanoparticle Separation under Magnetophoresis
Sim Siong Leong, Zainal Ahmad, Siew Chun Low, Juan Camacho, Jordi Faraudo, and JitKang Lim
Langmuir, 36 (28), 8033-8055, 2020
DOI: 10.1021/acs.langmuir.0c00839

Cover image: Summary of effects in magnetophoresis due to magnetic and hydrodynamic interactions beyond the classical model. The cartoon indicates the physical interactions behind the cooperative effect and the magnetic-induced convection, illustrated by the images.

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