- Email: [email protected]
Magnetic capture of superparamagnetic nanoparticles in a constant pressure microcapillary flow
ARTICLE IN PRESS Journal of Magnetism and Magnetic Materials 321 (2009) 1571–1574
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Magnetic capture of superparamagnetic nanoparticles in a constant pressure microcapillary flow Nicholas J. Darton , Bart Hallmark, Tom James, Pulkit Agrawal, Malcolm R. Mackley, Nigel K.H. Slater Department of Chemical Engineering, University of Cambridge, Pembroke Street, CB2 3RA, UK
a r t i c l e in fo
abstract
Available online 21 February 2009
Superparamagnetic nanoparticles were synthesised and their in-flow magnetic capture behaviour studied within transparent plastic microcapillary arrays (MicroCapillary Film or MCF). This system represents an in vitro analogue of capillary vasculature and facilitates easy optical observation of capture phenomenon. A dispersion of nanoparticles was delivered at a constant pressure to an array of capillaries sited adjacent to a 0.5 T permanent magnet. The spatial position of trapped nanoparticles relative to the position of the magnet was analysed. The position of nanoparticle capture appears to be dependent on both spatial location and fluid flow rate and suggests two zones in the magnetic field in which nanoparticles are acted upon differently; a ‘steering’ zone and a ‘capture’ zone. & 2009 Elsevier B.V. All rights reserved.
Keywords: Superparamagnetic Nanoparticle Capture Embolism Microcapillary
Previous research studying the entrapment of magnetic particles by magnetic fields in a single capillary tube have found that the particles can be used to embolise the flow [1–3]. In a subsequent study [4] an in vitro method was developed for studying the in-flow magnetic capture of suspensions of 330 and 520 nm superparamagnetic nanoparticle agglomerates in a single microcapillary of diameter 410 mm; these experiments were performed at a constant flow rate. It was discovered that the smaller nanoparticle agglomerates formed a stable captured layer that was more resistant to erosion resulting from the shear stress due to the surrounding flow. Further analysis of these results yielded a model to predict the degree of embolisation as a function of both the capillary diameter and of flow rate [5]. Although the study of superparamagnetic particle capture in a constant flow environment of a single microcapillary allowed preliminary observations concerning targeting dynamics to be made, the physiological flow through human blood capillary beds occurs under a constant pressure regime partly due to the limited work rate of the heart, and partly due to the continuously bifurcating and converging nature of capillary vasculature. This paper presents results that extend the previous research, investigating the phenomenon of magnetic capture of a suspension of superparamagnetic nanoparticles in a flow system containing multiple, parallel capillaries, subjected to a constant delivery pressure. A flow loop was constructed that was based upon using microcapillary film (MCF) as the capillary array within which
Corresponding author.
E-mail address: [email protected] (N.J. Darton). 0304-8853/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2009.02.088
nanoparticle capture would be observed. MCFs are a novel class of extrusion processed, plastic microcapillary arrays [6,7] that consist of a thin, flexible, polymer film with an embedded array of parallel microcapillaries. The mean hydraulic diameters of the capillaries can be tailored between 30 and 500 mm and the extrusion materials can be chosen such that the array is optically transparent. A cross section of a typical MCF is shown in the inset in Fig. 1. The flow loop, shown in Fig. 1, was designed such that digital imaging of superparmagnetic nanoparticle capture within a capillary array at different flow rates could be easily carried out. Deionised, degassed, MilliQTM water was delivered via a small displacement piston pump commonly used for high-performance liquid chromatography (HPLC) separations (Kontron 422, Kontron Instruments, Milan, Italy) and the nanoparticle suspension was introduced into the flow via an electromechanical injection valve (VICI Valco, Houston, TX). The resulting fluid was then delivered into an MCF, roughly 400 mm long with an internal mean hydraulic diameter of 210 mm, extruded in-house from a commercially available polyolefin plastomer resin (Dow Affinitys Plastomer, Dow Chemical Company Inc.). A 0.5 T NdFeB permanent magnet of dimensions 50 50 25 mm (e-magnets, Sheffield, UK) was placed half way along the MCF such that a spatially varying magnetic field existed across the capillary array. The distance of the magnet from each of the seven microcapillaries is given in Table 1. Observations relating to the capture of the magnetic nanoparticles could then be carried out by viewing the top surface of the MCF and imaging with a digital camera. Superparamagnetic magnetite nanoparticles were synthesised by aqueous precipitation upon mixing an iron chloride, and an ammonia solution following an existing method [8]. The resulting nanoparticles were found to be superparamagnetic by SQUID
ARTICLE IN PRESS 1572
N.J. Darton et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 1571–1574
Fig. 1. Schematic diagram of the flow loop for the analysis of superparamagnetic nanoparticle capture.
Table 1 Flow chamber setup with distances between the magnet and the seven microcapillaries. Capillary number
Distance from magnet (pixels)
Distance from magnet (mm)
1 2 3 4 5 6 7 Error
62 80 97 114 130 148 166 72
1.6 2.1 2.6 3.0 3.4 3.9 4.4 70.05
magnetometry. The mean hydrodynamic diameter of the nanoparticle agglomerates was measured as 50076 nm by zeta-sizing (ZetaPALS sizer, Brookhaven, Holtsville, New York). These agglomerates were found to be composed of 10 nm nanoparticles as observed by transmission electron microscopy (100 kV Philips CM100) and high-resolution electron microscopy (Jeol 4000EX TEM, 400 kV acceleration voltage). X-ray diffraction analysis (Philips PW1820) and lattice measurements in high-resolution electron microscopy confirmed these nanoparticles were magnetite with stoichiometry Fe3O4. The experimental protocol consisted of setting the HPLC pump to a flow rate of 0.2 ml/min and introducing a pulse of approximately 2 ml of the nanoparticle suspension via the injection valve. Observation of the location of nanoparticle capture was made by imaging at regular intervals through the top surface of the film using a digital camera and by identifying the location of the captured nanoparticle slug within the capillary array. The system was considered to have reached a steady state when the location of the captured nanoparticles remained unchanged for a period of 10 min. The MCF was then purged with deionised water at a flow rate where nanoparticle capture did not occur (approximately 10 ml/min) and the experiment repeated at a higher flow rate. Experiments were carried out at flow rates between 0.2 and 2.0 ml/min in increments of 0.2 ml/min.
The series of images shown in Fig. 2 illustrate typical observations that were made during the course of a set of experiments, and show that it is possible to capture a slug of nanoparticles (circled with a dotted line). The exact location of this captured slug depends on both the spatial position of the capillary through which the fluid is flowing and the magnitude of the flow rate delivered by the HPLC pump. The images were subsequently analysed to determine the location of the ‘start’ point and ‘end’ point of the slug of captured nanoparticles. In this sense, the ‘start’ has been defined as the furthest upstream location that nanoparticle capture is observed and the ‘end’ the most downstream point. For the images shown in Fig. 2, the most upstream point is the left-hand edge of the captured slug and the most downstream point corresponds to the right-hand edge of the captured slug. Results from this image analysis are presented for four capillaries in Fig. 3 with the upstream location presented in Fig. 3A and the downstream location in Fig. 3B. Capillary numbers 1 and 2 are the two closest capillaries to the magnet and capillary numbers 6 and 7 are the furthest away. In each case, the origin of the co-ordinate system has been defined as the most upstream point on the edge of the magnet that lies closest to the MCF (see Fig. 1), with the x-coordinate being positive in the direction of flow. Such data provides insight into how superparamagnetic nanoparticles are captured in a flow geometry that contains a parallel array of capillaries. Firstly, capture was observed in the two capillaries closest to the magnet over the full range of flow rates that were used, whereas capture in the two capillaries furthest away from the magnet ceased at 0.6 ml/min. This observation is expected since there is significant variation in the magnetic field strength as a function of location, with capillaries 1 and 2 experiencing a significantly stronger magnetic field than capillaries 6 and 7. When this spatially dependant magnetic field is considered in terms of the net force experienced by a nanoparticle, there is a set of locations within the MCF at a given flow rate where hydraulic forces dominate magnetic forces and hence capture will not occur. These observations follow on logically from previous work [4,5].
ARTICLE IN PRESS N.J. Darton et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 1571–1574
1573
60
60
50
50
40
40
x co-ordinate (mm)
x co-ordinate (mm)
Fig. 2. Sequence of images illustrating the position of nanoparticle capture within the MCF at fluid flow rates of (A) 0.2 ml/min, (B) 0.6 ml/min, and (C) 1.0 ml/min. The flow is from left to right and the location of the captured slug of nanoparticles is denoted by the dotted ellipse in each image. The direction of flow through each of the seven microcapillaries used is indicated by white arrows. Capillaries number 1 and 7 are labelled.
30 20 10
Capillary one Capillary two Capillary six Capillary seven
0 -10
0
0.5
1
1.5
2
30 20 10
Capillary one Capillary two Capillary six Capillary seven
0 -10 2.5
Flowrate (ml/min)
0
0.5
1
1.5
2
2.5
Flowrate (ml/min)
Fig. 3. Plot of (A) the most upstream edge and (B) the most downstream edge of the captured nanoparticle slug in the two closest and two furthest capillaries from the magnet as a function of fluid flow rate.
An unexpected trend in the analysed data is the apparent existence of two different regimes of capture. This finding is most clearly seen in the data presented for the spatial location of the most downstream point of capture, Fig. 3B. At flow rates up to 0.8 ml/min, the downstream position of the captured nanoparticle slug shows a very strong, possibly linear, dependence on the flow rate used. The position of the captured slug for any given flow rate in this range progresses further downstream as the capillaries get further away from the magnet and the magnetic force experienced by the nanoparticles decreases. Surprisingly, above flow rates of 0.8 ml/min, the position of the captured slug of nanoparticles shows no dependence on the flow rate that was used. One of two phenomena seem to occur: either no nanoparticles are captured in the capillaries further from the magnet (capillaries 6 and 7) or the location of the captured slug remains constant and independent of flow rate in the capillaries nearest the magnet (capillaries 1 and 2). One hypothesis that could explain this observation is that the magnetic force acting on the nanoparticles serves either to steer
the particles or to capture the particles. Assuming that the nanoparticle dispersion is initially distributed evenly across the cross-section of the capillary, the majority of nanoparticles must be steered by the magnetic field in a direction perpendicular to the flow, such that they first of all come into contact with the capillary wall closest to the magnet. For half of the nanoparticles present in the flow this will mean traversing across the highest velocity part of the flow, which is located in the centre of the capillary. Once the nanoparticles have been moved into the slowmoving region of fluid close to the capillary wall immobilisation may or may not occur; this will depend on how far the nanoparticles have travelled downstream to achieve wall contact. If the magnetic field at this location is strong enough to overcome hydraulic shear forces immobilisation will occur, whereas if the magnetic force experienced by the nanoparticles is weak when compared to the shear forces then immobilisation will not occur. Initial numerical modelling work in the literature, for example that of Furlani and Furlani [9] show particle trajectories that are consistent with this explanation.
ARTICLE IN PRESS 1574
N.J. Darton et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 1571–1574
A key factor that will govern the eventual location of the captured nanoparticles is the shape of the magnetic field along the length of the MCF. If there is a magnetic field concentration at one point that is substantially close to the origin of the defined coordinate system, then this will serve to either immediately capture the nanoparticles at low flow rates, or to steer the majority of the nanoparticles close to the capillary wall at higher flow rates. If so, then once the particles have been steered to the wall by this magnetic field peak, then lower magnetic fields present along the remainder of the length of the MCF may be sufficiently strong enough to capture and immobilise the nanoparticles. This paper has shown that it is possible to capture superparamagnetic nanoparticles from a flow within a capillary array subjected to a constant pressure gradient. The location of the captured nanoparticles has been shown to be dependent on both the spatial location of the capillaries with respect to the magnet and also on the flow rate of fluid used. Initial experimental data suggests that the shape of the magnetic field could play a pivotal role in determining the final location of the slug of captured nanoparticles. It has been postulated that the magnetic field acts in two ways—as a ‘steering field’ that brings the nanoparticles close to the capillary wall and as a ‘capture field’ that subsequently immobilises them. This hypothesis is currently being investigated. If proved to be true in future work, then this mechanism of a ‘steering field’ and a ‘capture field’ could well explain the observed trend in this preliminary data and could, therefore, have important implications for the design of magnetic
field shapes and strengths for in vivo magnetic targeting of therapeutics. Future modelling may also allow conditions to be established for magnetic nanoparticle embolisation in tumour vasculature to necrotize tumour tissue in cancer therapy [10].
Acknowledgements The authors would like to acknowledge both the BBSRC and EPSRC for funding, Mr. V. Ho for supplying the superparamagnetic nanoparticles, Dr. Adrian Ionescu (Cavendish Laboratory, Cambridge) for his assistance with the SQUID magnetometry measurements, Dr. Caterina Ducati (Department of Materials Science and Metallurgy, University of Cambridge) for the high-resolution transmission electron microscopy analysis and Mr. Alexander Barcza for the X-ray diffraction analysis. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
J. Liu, G.A. Flores, R.S. Sheng, J. Magn. Magn. Mater. 225 (2001) 209. R. Sheng, G.A. Flores, J. Liu, J. Magn. Magn. Mater. 194 (1999) 167. L.E. Udrea, N.J. Strachan, V. Badescu, et al., Phys. Med. Biol. 51 (2006) 4869. N.J. Darton, B. Hallmark, X. Han, et al., Nanomedicine: NBM 4 (2008) 19. B. Hallmark, N.J. Darton, X. Han, et al., Chem. Eng. Sci. (2008). B. Hallmark, F. Gadala-Maria, M.R. Mackley, J. Non Newton. Fluid. 128 (2005) 83. B. Hallmark, M.R. Mackley, F. Gadala-Maria, Adv. Eng. Mater. 7 (2005) 545. Z.Y. Ma, Y.P. Guan, H.Z. Liu, J. Magn. Magn. Mater. 301 (2006) 469. E.J. Furlani, E.P. Furlani, J. Magn. Magn. Mater. 312 (2007) 187. M. Sako, S. Hirota, S. Ohtsuki, Ann. Radiol. 29 (1986) 200.
Contents lists available at ScienceDirect
Journal of Magnetism and Magnetic Materials journal homepage: www.elsevier.com/locate/jmmm
Magnetic capture of superparamagnetic nanoparticles in a constant pressure microcapillary flow Nicholas J. Darton , Bart Hallmark, Tom James, Pulkit Agrawal, Malcolm R. Mackley, Nigel K.H. Slater Department of Chemical Engineering, University of Cambridge, Pembroke Street, CB2 3RA, UK
a r t i c l e in fo
abstract
Available online 21 February 2009
Superparamagnetic nanoparticles were synthesised and their in-flow magnetic capture behaviour studied within transparent plastic microcapillary arrays (MicroCapillary Film or MCF). This system represents an in vitro analogue of capillary vasculature and facilitates easy optical observation of capture phenomenon. A dispersion of nanoparticles was delivered at a constant pressure to an array of capillaries sited adjacent to a 0.5 T permanent magnet. The spatial position of trapped nanoparticles relative to the position of the magnet was analysed. The position of nanoparticle capture appears to be dependent on both spatial location and fluid flow rate and suggests two zones in the magnetic field in which nanoparticles are acted upon differently; a ‘steering’ zone and a ‘capture’ zone. & 2009 Elsevier B.V. All rights reserved.
Keywords: Superparamagnetic Nanoparticle Capture Embolism Microcapillary
Previous research studying the entrapment of magnetic particles by magnetic fields in a single capillary tube have found that the particles can be used to embolise the flow [1–3]. In a subsequent study [4] an in vitro method was developed for studying the in-flow magnetic capture of suspensions of 330 and 520 nm superparamagnetic nanoparticle agglomerates in a single microcapillary of diameter 410 mm; these experiments were performed at a constant flow rate. It was discovered that the smaller nanoparticle agglomerates formed a stable captured layer that was more resistant to erosion resulting from the shear stress due to the surrounding flow. Further analysis of these results yielded a model to predict the degree of embolisation as a function of both the capillary diameter and of flow rate [5]. Although the study of superparamagnetic particle capture in a constant flow environment of a single microcapillary allowed preliminary observations concerning targeting dynamics to be made, the physiological flow through human blood capillary beds occurs under a constant pressure regime partly due to the limited work rate of the heart, and partly due to the continuously bifurcating and converging nature of capillary vasculature. This paper presents results that extend the previous research, investigating the phenomenon of magnetic capture of a suspension of superparamagnetic nanoparticles in a flow system containing multiple, parallel capillaries, subjected to a constant delivery pressure. A flow loop was constructed that was based upon using microcapillary film (MCF) as the capillary array within which
Corresponding author.
E-mail address: [email protected] (N.J. Darton). 0304-8853/$ - see front matter & 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.jmmm.2009.02.088
nanoparticle capture would be observed. MCFs are a novel class of extrusion processed, plastic microcapillary arrays [6,7] that consist of a thin, flexible, polymer film with an embedded array of parallel microcapillaries. The mean hydraulic diameters of the capillaries can be tailored between 30 and 500 mm and the extrusion materials can be chosen such that the array is optically transparent. A cross section of a typical MCF is shown in the inset in Fig. 1. The flow loop, shown in Fig. 1, was designed such that digital imaging of superparmagnetic nanoparticle capture within a capillary array at different flow rates could be easily carried out. Deionised, degassed, MilliQTM water was delivered via a small displacement piston pump commonly used for high-performance liquid chromatography (HPLC) separations (Kontron 422, Kontron Instruments, Milan, Italy) and the nanoparticle suspension was introduced into the flow via an electromechanical injection valve (VICI Valco, Houston, TX). The resulting fluid was then delivered into an MCF, roughly 400 mm long with an internal mean hydraulic diameter of 210 mm, extruded in-house from a commercially available polyolefin plastomer resin (Dow Affinitys Plastomer, Dow Chemical Company Inc.). A 0.5 T NdFeB permanent magnet of dimensions 50 50 25 mm (e-magnets, Sheffield, UK) was placed half way along the MCF such that a spatially varying magnetic field existed across the capillary array. The distance of the magnet from each of the seven microcapillaries is given in Table 1. Observations relating to the capture of the magnetic nanoparticles could then be carried out by viewing the top surface of the MCF and imaging with a digital camera. Superparamagnetic magnetite nanoparticles were synthesised by aqueous precipitation upon mixing an iron chloride, and an ammonia solution following an existing method [8]. The resulting nanoparticles were found to be superparamagnetic by SQUID
ARTICLE IN PRESS 1572
N.J. Darton et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 1571–1574
Fig. 1. Schematic diagram of the flow loop for the analysis of superparamagnetic nanoparticle capture.
Table 1 Flow chamber setup with distances between the magnet and the seven microcapillaries. Capillary number
Distance from magnet (pixels)
Distance from magnet (mm)
1 2 3 4 5 6 7 Error
62 80 97 114 130 148 166 72
1.6 2.1 2.6 3.0 3.4 3.9 4.4 70.05
magnetometry. The mean hydrodynamic diameter of the nanoparticle agglomerates was measured as 50076 nm by zeta-sizing (ZetaPALS sizer, Brookhaven, Holtsville, New York). These agglomerates were found to be composed of 10 nm nanoparticles as observed by transmission electron microscopy (100 kV Philips CM100) and high-resolution electron microscopy (Jeol 4000EX TEM, 400 kV acceleration voltage). X-ray diffraction analysis (Philips PW1820) and lattice measurements in high-resolution electron microscopy confirmed these nanoparticles were magnetite with stoichiometry Fe3O4. The experimental protocol consisted of setting the HPLC pump to a flow rate of 0.2 ml/min and introducing a pulse of approximately 2 ml of the nanoparticle suspension via the injection valve. Observation of the location of nanoparticle capture was made by imaging at regular intervals through the top surface of the film using a digital camera and by identifying the location of the captured nanoparticle slug within the capillary array. The system was considered to have reached a steady state when the location of the captured nanoparticles remained unchanged for a period of 10 min. The MCF was then purged with deionised water at a flow rate where nanoparticle capture did not occur (approximately 10 ml/min) and the experiment repeated at a higher flow rate. Experiments were carried out at flow rates between 0.2 and 2.0 ml/min in increments of 0.2 ml/min.
The series of images shown in Fig. 2 illustrate typical observations that were made during the course of a set of experiments, and show that it is possible to capture a slug of nanoparticles (circled with a dotted line). The exact location of this captured slug depends on both the spatial position of the capillary through which the fluid is flowing and the magnitude of the flow rate delivered by the HPLC pump. The images were subsequently analysed to determine the location of the ‘start’ point and ‘end’ point of the slug of captured nanoparticles. In this sense, the ‘start’ has been defined as the furthest upstream location that nanoparticle capture is observed and the ‘end’ the most downstream point. For the images shown in Fig. 2, the most upstream point is the left-hand edge of the captured slug and the most downstream point corresponds to the right-hand edge of the captured slug. Results from this image analysis are presented for four capillaries in Fig. 3 with the upstream location presented in Fig. 3A and the downstream location in Fig. 3B. Capillary numbers 1 and 2 are the two closest capillaries to the magnet and capillary numbers 6 and 7 are the furthest away. In each case, the origin of the co-ordinate system has been defined as the most upstream point on the edge of the magnet that lies closest to the MCF (see Fig. 1), with the x-coordinate being positive in the direction of flow. Such data provides insight into how superparamagnetic nanoparticles are captured in a flow geometry that contains a parallel array of capillaries. Firstly, capture was observed in the two capillaries closest to the magnet over the full range of flow rates that were used, whereas capture in the two capillaries furthest away from the magnet ceased at 0.6 ml/min. This observation is expected since there is significant variation in the magnetic field strength as a function of location, with capillaries 1 and 2 experiencing a significantly stronger magnetic field than capillaries 6 and 7. When this spatially dependant magnetic field is considered in terms of the net force experienced by a nanoparticle, there is a set of locations within the MCF at a given flow rate where hydraulic forces dominate magnetic forces and hence capture will not occur. These observations follow on logically from previous work [4,5].
ARTICLE IN PRESS N.J. Darton et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 1571–1574
1573
60
60
50
50
40
40
x co-ordinate (mm)
x co-ordinate (mm)
Fig. 2. Sequence of images illustrating the position of nanoparticle capture within the MCF at fluid flow rates of (A) 0.2 ml/min, (B) 0.6 ml/min, and (C) 1.0 ml/min. The flow is from left to right and the location of the captured slug of nanoparticles is denoted by the dotted ellipse in each image. The direction of flow through each of the seven microcapillaries used is indicated by white arrows. Capillaries number 1 and 7 are labelled.
30 20 10
Capillary one Capillary two Capillary six Capillary seven
0 -10
0
0.5
1
1.5
2
30 20 10
Capillary one Capillary two Capillary six Capillary seven
0 -10 2.5
Flowrate (ml/min)
0
0.5
1
1.5
2
2.5
Flowrate (ml/min)
Fig. 3. Plot of (A) the most upstream edge and (B) the most downstream edge of the captured nanoparticle slug in the two closest and two furthest capillaries from the magnet as a function of fluid flow rate.
An unexpected trend in the analysed data is the apparent existence of two different regimes of capture. This finding is most clearly seen in the data presented for the spatial location of the most downstream point of capture, Fig. 3B. At flow rates up to 0.8 ml/min, the downstream position of the captured nanoparticle slug shows a very strong, possibly linear, dependence on the flow rate used. The position of the captured slug for any given flow rate in this range progresses further downstream as the capillaries get further away from the magnet and the magnetic force experienced by the nanoparticles decreases. Surprisingly, above flow rates of 0.8 ml/min, the position of the captured slug of nanoparticles shows no dependence on the flow rate that was used. One of two phenomena seem to occur: either no nanoparticles are captured in the capillaries further from the magnet (capillaries 6 and 7) or the location of the captured slug remains constant and independent of flow rate in the capillaries nearest the magnet (capillaries 1 and 2). One hypothesis that could explain this observation is that the magnetic force acting on the nanoparticles serves either to steer
the particles or to capture the particles. Assuming that the nanoparticle dispersion is initially distributed evenly across the cross-section of the capillary, the majority of nanoparticles must be steered by the magnetic field in a direction perpendicular to the flow, such that they first of all come into contact with the capillary wall closest to the magnet. For half of the nanoparticles present in the flow this will mean traversing across the highest velocity part of the flow, which is located in the centre of the capillary. Once the nanoparticles have been moved into the slowmoving region of fluid close to the capillary wall immobilisation may or may not occur; this will depend on how far the nanoparticles have travelled downstream to achieve wall contact. If the magnetic field at this location is strong enough to overcome hydraulic shear forces immobilisation will occur, whereas if the magnetic force experienced by the nanoparticles is weak when compared to the shear forces then immobilisation will not occur. Initial numerical modelling work in the literature, for example that of Furlani and Furlani [9] show particle trajectories that are consistent with this explanation.
ARTICLE IN PRESS 1574
N.J. Darton et al. / Journal of Magnetism and Magnetic Materials 321 (2009) 1571–1574
A key factor that will govern the eventual location of the captured nanoparticles is the shape of the magnetic field along the length of the MCF. If there is a magnetic field concentration at one point that is substantially close to the origin of the defined coordinate system, then this will serve to either immediately capture the nanoparticles at low flow rates, or to steer the majority of the nanoparticles close to the capillary wall at higher flow rates. If so, then once the particles have been steered to the wall by this magnetic field peak, then lower magnetic fields present along the remainder of the length of the MCF may be sufficiently strong enough to capture and immobilise the nanoparticles. This paper has shown that it is possible to capture superparamagnetic nanoparticles from a flow within a capillary array subjected to a constant pressure gradient. The location of the captured nanoparticles has been shown to be dependent on both the spatial location of the capillaries with respect to the magnet and also on the flow rate of fluid used. Initial experimental data suggests that the shape of the magnetic field could play a pivotal role in determining the final location of the slug of captured nanoparticles. It has been postulated that the magnetic field acts in two ways—as a ‘steering field’ that brings the nanoparticles close to the capillary wall and as a ‘capture field’ that subsequently immobilises them. This hypothesis is currently being investigated. If proved to be true in future work, then this mechanism of a ‘steering field’ and a ‘capture field’ could well explain the observed trend in this preliminary data and could, therefore, have important implications for the design of magnetic
field shapes and strengths for in vivo magnetic targeting of therapeutics. Future modelling may also allow conditions to be established for magnetic nanoparticle embolisation in tumour vasculature to necrotize tumour tissue in cancer therapy [10].
Acknowledgements The authors would like to acknowledge both the BBSRC and EPSRC for funding, Mr. V. Ho for supplying the superparamagnetic nanoparticles, Dr. Adrian Ionescu (Cavendish Laboratory, Cambridge) for his assistance with the SQUID magnetometry measurements, Dr. Caterina Ducati (Department of Materials Science and Metallurgy, University of Cambridge) for the high-resolution transmission electron microscopy analysis and Mr. Alexander Barcza for the X-ray diffraction analysis. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]
J. Liu, G.A. Flores, R.S. Sheng, J. Magn. Magn. Mater. 225 (2001) 209. R. Sheng, G.A. Flores, J. Liu, J. Magn. Magn. Mater. 194 (1999) 167. L.E. Udrea, N.J. Strachan, V. Badescu, et al., Phys. Med. Biol. 51 (2006) 4869. N.J. Darton, B. Hallmark, X. Han, et al., Nanomedicine: NBM 4 (2008) 19. B. Hallmark, N.J. Darton, X. Han, et al., Chem. Eng. Sci. (2008). B. Hallmark, F. Gadala-Maria, M.R. Mackley, J. Non Newton. Fluid. 128 (2005) 83. B. Hallmark, M.R. Mackley, F. Gadala-Maria, Adv. Eng. Mater. 7 (2005) 545. Z.Y. Ma, Y.P. Guan, H.Z. Liu, J. Magn. Magn. Mater. 301 (2006) 469. E.J. Furlani, E.P. Furlani, J. Magn. Magn. Mater. 312 (2007) 187. M. Sako, S. Hirota, S. Ohtsuki, Ann. Radiol. 29 (1986) 200.