Armington 1 A Novel Device fo r the Characterization of Viscosity via Magnetic Particle Translation Samuel L. Armington Committee: Kyle Allen, Ph.D Jon Dobson, Ph.D Blanka Sharma, Ph.D.
Armington 2 Abstract Synovial fluid viscosity has been shown to be useful as a biomarker for the disease progression of osteoarthritis, which is a common in both human s and large mammals. Particularly in veterinary medicine, clinical practices for synovial fluid vis cosity measurement are limited at best in their precisio n. In this paper, a new concept called magnetic deflection is proposed and the developments of a device to validate it are detailed. This device is in the form of a flow chamber that create s a stream of superparamagnetic microparticles within a solution to be measured The particle stream flows past a series of fixed, permanent magnets which attract the particles while a drag force opposes the magnetic force and is scaled proportionally by the viscosity This leads to a deflecti on of the stream that is dependent on the fluid s viscosity. After the stream has passed the magnet and been deflected it is imaged for measurement The device developed was used to empirically validate t he concept using a series of glycerol/water standard viscosity solutions. A relationship between viscosity and magnetic deflection was found to be linearly dependent on the reciprocal of viscosity.
Armington 3 I ntroduction Osteoarthritis (OA) is a maladaptive disease of articular joints affecting 10% of men and 13% of women above the age of 60  I n addition to cartilage, it effects ligaments, bone, and the synovium  A s the viscosity of synovial fluid (SF) has been studied for its relevance to disease progression and has been shown to decrease in correlati on with the ,  For this reason, our la borato ry has considered SF viscosity a potential bioma rker of interest to characterize OA progression and is interested in developing new techniques for its characterization. Particularly i n equine veterinary medicine, OA is a widespread problem where an estimated 60% of all cases of lameness can be attributed to OA  For clinicians, SF viscosity is used as a measure of the degree of hyaluronic acid polymerization, where a reduction would indicate inflammation   This is useful in characterizing OA and other inflammatory diseases of the joint. Presently, clinicians either between the thumb and index finger or at the tip of th e needle used to aspirate it  Whil e these practices have been effective, it is the view of our group that an alternative which could more precisely characterize viscosity would raise the standard of care and be welcomed by veterinarians In a study by Garraud et al  investigating the feasibility of collecting magnetic particles from a high viscosity solution our laboratory investigated the translational properties of magnetic particles through highly vi sco us Newtonian fluids Analytically, it can be demonstrated that particle translation is governed by two forces, those of drag and magnetism ,  W hile the magnetic force acts as a function of the field gradient, the drag force opposes it and is scaled proportionally by the viscosity of the medium This fundamental understanding formed the basis of a subsequent empirical study by Shah et al to characterize the effect of viscosity on particle collection in vitro over a fi nite period  They demonstrated a strong correlation between the fraction of particles collected and the viscosity of the f luid through which they translated T hese findings will be used to support the premise for the device to be discussed here. While a novel technique, particularly because it r equired such small sample volumes the method ology employed by Shah et al has little practic al use in veterinary practice due to its
Armington 4 reliance on labor atory equipment for measurement Aware of these limitations, Dr. Jon Dobson proposed a microfluidic device that could measure viscosity by deflect ing in steady state a stream of magnetic p articles while visual ly measuring displacement. This measure would be a surrogate to quantify the balance of magnetic and drag forces and t hus the fluid viscosity This concept, if possible, could offer a practical and more quantitative method of measuring SF viscosity particularly for veterinary medicine In the subsequent sections, the development of such a device to demonstrate the practicality of this concept will be detailed. Methods Prototype for a Qualitati ve Proof of Concept In developing the first prototype the objective was to qualitatively demonstrate that a stream of particles c ould first be formed uniformly and then be deflected by a magnet. The first priority was to combine two separate flows, one from the fluid to be measured, and another for the stream of particles without inducing excessive turbulence After establishing a uniform flow of particle s its deflection could be attempted. With respect to deflecting the stream, the approach I elected to follow was to maximize deflection in the minimum viscosity boundary condition, that of water, assuming that if a design could maximize deflection in water, it s efficacy should translate to the other boundary condition, that of high viscosity thus achie ving the broadest possible measurable range Thanks to a suggestion from Dr. Z. Hugh Fan, the first flow chamber woul d be prototyped using two glass microscope slides and other materials scavenged from around the laboratory.
Armington 5 F igure 1 : The first flow chamber pro totype. The syringe and connected tube are used to inject a stream of parti cles, while the other tubes inlet the fluid of interest through the flow chamber. In figure 1 the first prototype built can be seen. The same silicone tubing (Cole P armer ) is used as a gasket to seal either side of the chamber as is used for the particle and fluid inlet streams. Before the fluid inlets were placed, a line of si licone sealant (GE5000 Clear S ilicone S ealant) was laid down to seal their undersi de. Then, the tubes were lined up and delicately pinned into place. Then, tubes were laid along each edge of the bottom slide and fixed with pins. Before the top slide could be placed, another line of silicone was placed along the top of the tubes. After placing the covering slide, the two slides were clamped together then the pins were removed. Along each slide of the chamber, a line of silicone was pl aced to lock the gasket into place and ensure it s seal Using a 2mm biopsy punch, int erference fittings were created in the end of a tube Finally, the particles were injected into the chamber using an insulin syring e and the target fluid was propelled via a syphon with the PVC tubing. A clamp throttled the tubing to regulate i ts f low rate. While a resourceful arrangement, this prototype h ad a variety of issues, but the most significant was the fluid entry. The para llel arrangement of tubes was intended to form a tight seal with the benefit of resembling a crude diffuser Unfo rtunately, the substantial wall thickness of the silicone tubing led to a large disparity between the height of the chamber and the ID of the silicone tubing feeding it This created region s on the top and bottom plates where bubbles congregated, thus ind ucing substantial tu rbulence through the chamber which prevented a uniform stream of particles from forming.
Armington 6 The first prototype was unable to deflect a stream because the induced turbulence made the requisite uniform particle stream impossible to achieve. In addition, a lesser problem existed, and that was the large fluid volume required. Moving forward, an improved prototype should firstly be free of turbulent flow, and secondly reduce the volumetric requirements. Figures 2,3 (respectivel y L to R ) show a revised prototype. Figure 2 shows how the chamber is attached to the fluid inlet without the use of the parallel tubing arrangement. Figure 3 shows the attachment between tubing and a 50ml tube. Figures two and three show the second prototype which was designed to resolve the turbulence associated with the inlet/chamber junction by removing the diffuser Additionally, a new approach to the gasket was devised to move beyond the outer diameter constraint imposed by usi ng tubing. More specifically, t wo slides were s tacked and staggered then a line of silicone It was formed with the pass of a f inger. After the silicone cured a scalpel was run along the edge of eac h slide (touching both staggered edges) before separating the slides This trimmed down the excess material and left a resulting molded edge with the height of the slide (1mm) that would constitute the gasket. To add the particle inlet, a n ~45 by 1mm wide groove was cut into one of the gaskets and a drop of silicone was placed in the notch. Then, a short length of 1mm OD tubing (BD Intramedic PE tubing) was laid through and time was allotted for the silicone to dry. Finally, the excess tubing (l aying on the inside of the slide which will become the flow chamber) was cut along the edge of the gasket. At this point the two formed slides were clamped together and silico ne was used to seal either edge from the outside.
Armington 7 After sealing off the sides, a slide was hot glued onto the bottom of a 50ml tube as can be seen in figure 2 The chamber was laid on top and another slide placed above to cover the o pening. Hot glue was applied liberally to seal the joint but with great care to avoid melting the P E par ticle feed line (this was learnt the hard way at a great expense of time). This desig n met the obje ctives set to improve the first version. Firstly, the bub ble induced turbulence w as overcome with a new junction thus the flow characteristics becam e far closer to optimal Secondly, the new gasket allowed for the chamber height to be reduced by half (to 1mm) thus requiring a reduced volume of fluid and magnetic particles Because of this, the second prototype provided characteristics more conducive to creat ing and deflect ing a particle stream, and indeed it could demonstrate a noticeable deflection depending on the permanent magnet configuration and flow rates Unfortunately, several problems arose Firstly, uniformity was difficult to achieve in gasket thickness when the slides were clamped, thereby producing an inconsistent chamber cross section and thus invalidating the requisite assumption of a constant linear flow rate through the chamber. Additionally, the methodology and materials employed to sea l the chamber/inlet junction were in effective causing the device to le ak, thereby preventing the precise regulation of the flow rate which will eventually be required Ultimately, this device served its purpose in of fering qu alitative verification; however its flaws made collecting repeatable and valid data impossible. Prototype for the Collection of Quantitative Data
Armington 8 Having established that a stream could in fact be deflected, the next objective was to achieve that deflect ion in a controlled manner by sealing the device and forming a geometrically uniform chamber. From this point, electronic pumps were adopted for both inlets to regulate f low rates and the new device was intended to be conducive toward imaging. For its availability and ability to be machined in our lab, this next series of prototypes would be built using acrylic sheets. With these the chamber itself could be created in two ways: either additively, with a gasket acting as a spacer to s eparate and seal t he sheets, or subtractively, with the plates fixed together and the cham ber machined into one of them. F igure 5 shows a rough sketch for the sizing of the plates and chamber The chamber is region in the center without crossing lines and the center hole r epresents the location for the elbow connector (inlet) Magnet placement is noted in the center of the chamber, and the particle inlet to the right of the chamber was never realized due to the difficulty in sealing and aligning the gasket with such a cut in it. For the first attempt, I chose the additive method. F igure 5 shows the dimensio ns and a sketch of the plates/ gasket that would be used. Unfortunately, I did not photograph this failed attempt, and the prototype would be modified in subsequent versions. It involved two 8 x 21.4 cm sheets of 6mm thick acrylic separated by a 0.5 mm silicone sheet (gasket) The top plate would have another piece of acrylic (scraps used) that were glued on top of either end. This served to provide sufficient thickness to thread x 27 NPT threads, US Plastics) into either end of the chambe r for the flow in let and F igure 6: N ote the second layer of acrylic and how the hose barb is connected. The green (dye) line represents the particle feed, and the round indents represent different locations for the deflection magnet. This image represents a subsequent version, where the leaking green liquid represents a failure, however through all versions, all inlet junctions were fabricated in the same fashion.
Armington 9 outlet of the chamber. The particle inlet was formed by drilling a 1mm hole through the top plate, and counterboring 2mm deep with a 0.0 ) to a ct as a soft adapter thereby preventing leaks and allowing the line to be easily detachable. While the inlet and outlet junction s proved to be a useful step toward meeting the objective of sealing the device and would remain, the challenge of the next few versions lay in forming a seal between the plates and gasket. Additionally forming the chamber from the gasket (by cutting it out) proved a challenge. The gasket was made from a 0.5mm thick sheet of silicone rubber, with the intention of a continued reduction in volume, but its lack of rigidity required it to be cut in place, after having been stuck to the bottom plate. After the gasket was stuck to the bottom plate and cut, a v acuum line was attached to the outlet, and the other elbow con nectors were sealed before the plates and gaskets were stuck together using the low air pressure in the flow chamber. Unfortunately, without a constant ly applied pressure, the seal was impossible to maintain, and despite all the effort in forming the ga sket and positioning the plates, the seal would fail as soon as the vacuum line was removed. A new approach would be needed, and it would follow the subtractive avenue. Figures 7,8 (L to R): Detail the two subtractive approaches taken. Note in figure 7 the failure due to a leak into the chamber (was under vacuum to clamp plates together. Note in 8 the failure d ue to grease influx. The magnet and particle holes are shown, although the fittings have been reused in subsequent prototypes. The first subtr active approach can be seen in figure 7 In this, vacuum pressure was used and 14 cm long. Vacuum grease (Dow Corning 976V) was used to help seal where the re was
Armington 10 acrylic/acrylic contact. In the first hole, PDMS (Dow Corning Sylguard 109) was injected with the intent of it curing and sealing the plates together. After failing v ia leakage into the chamber a sealant with greater viscosity was chosen (GE5000 silicone sealant). This time, as shown in figure 8 the plates together, the sealant was ap plied in to the gap as can be seen. This was the first functioning acrylic chamber in that it was sealed, however seve ral problems arose. Firstly, some of the grease in filtrated the edge of the chamber, which induced turbulence. Additionally, due to the minute dimensions required, the equipment at hand could not cut with enough precision, thus again leaving a variable channel depth in much the same way as the second prototype did In another effect, t he mill left tool marks on the bottom of the chann el with the potential to induce turbulence For these difficulties, I elected to abandon the subtractive approach and revisit the additive approach Figures 9,10: figure 9 shows the gasket placed on the bottom plate. The channel cut is under low pressure and again used to clamp and seal the chamber b etween plates. The bubbles are present because this particular gasket had been taken off and reapplied for the photo. Figure 10 is annotated to show each part of the prototype. Above, fig ures 9 and 10 show the next prototype. In this, a useful bit of advice from Dr. Peter McFetridge was applied such that a separate channel was created for vacuum pressure. This allowed the clamping force to re main while the flow chamber operated The vacuum channel w figure 9 the gasket is laid onto the bottom plate. Using a scalpel, the part covering the low pressure channel is cut away as is the 2 cm wide c hamber itself. The top plate was sealed in the same way as the previous prototype, but instead of using the exhaust line, a purpose vacuum line is used. This approach, featuring an additively formed channel via a silicone sheet gasket and low pressure seal succeeded in meeting the two objectives d escribed to seal the chamber and to create a uniform channel. Unfortunately, while these two objectives are necessary to deflect a
Armington 11 stream of magnetic particles in a controlled manner, they are not sufficient to do so. This was illustrated by the diffic ulties had with the particle stream, whereby preventing pulsation and particle accumulation on the magnet became the primary objective moving forward. Having realized this, the first and most obvious factor contributing to the pulsation was the proximity of the magnet to the particle inlet which can be seen in figure 10 Particle a ccumulation was visible inside the tube on the side closest to the magnet. Figure 11 shows the next prototype. T his version is 10 cm longer than the previous, and the particle stream flows through the center of the chamber. A d ditionally, the low pressure channel was not machined out, but was widened, allowing for more clamping force on a smaller area of gasket ther eby improving the seal. To remedy this, more space was needed between the magnet and particles to prevent this type of interference. In the next prototype, seen in figure 11 the chamber was lengthened by 10 cm and the particle inlet was moved from the ed ge to the center of the chamber. T ogether, these prevented interference, but also would allow increased flexibility in magnet placeme nt which was yet to be determined Additionally, the machined pressure groove was foregone (it was only present be cause the bottom plate was reused from a previous generation of prototype) thus expediting the manufacturing process. After further testing, it quickly became clear that pulsation was greatly improved, but the stream could not be deflected because the particles appeared to be settling on the bottom and accumulating near the magnet This caused them to move slowly regardless of the flow rate and inhibited to formation of a steady state stream At this point, having mostly overcome the pulsation, the next objective became preventing the particles from settling. While seemingly trivial, meeting this objective required a fresh look at the particles behavior. Firstly, with the magnet placed on top of the acrylic sheet, the field gradient, and thus B force direction had a depth component ( denoted by the Z direction where Z =0 at the center of the chamber ) This Z component of force would pull particles out of t he plane of the center of the channel ( X,Y with X being the direction of deflection and Y being along the channel in the direction of flow) and into the acrylic sheet forming its cover.
Armington 12 which drastically slowed the speed of any particles not centered exactly vertically (Z) in the stream (assuming laminar flow) giving them the appearance of having settled on the bottom This served to increase the amount of time they spend passing the magnet, thus increasing the impulse delivered (in the x direction) and therefore leading to accumulation below the magnet Because of the previously stated desire to minimize requisite fluid volumes, I had reduced the chamber s thickness repeatedly while holding the linear flow rate constant, with no consideration for the shear rate, which is halved with each ha l ving of thickness. Th is leads into the final factor confounding these troubles which is the effect of gravity. It causes the particles to settle in the channel (in the negative z direction) and thus slow relative to the flow in the center plane To meet this objective, three changes were implemented. First the magnet(s) were moved from the surface of the acrylic to a groove machined between the t wo plates, which centered the magnet and thu s positioned its field gradient in the X,Y plane at Z=0 (or toward Z =0 when deviating from it ) This created a theoretically stable equilibrium for the particle stream in the z direction The second change was to double the thickness (0.5mm 1mm gasket) thus reducing the shear rate by half The final change was to orient the chamber such that the flow direction ( Y ) was pointed vertically, thereby preventing gravity from exerting a force on the particles in th e z direction (which confounded the settling/slowing problem). These three changes succeeded in meeting the set objective of preventing the particles from settling, and for the first time allowed for a uniform particle stream to be created in a sealed, ge ometrically uniform device that could (hopefully) control relevant parameters and produce valid data. Unfortunately, with the magnet in place, even two to double their effects, the deflection did not appear to be measurable, thus setting another objective increase the magnetic force on the particles. To increase the B force, and thus deflection, three routes were available: increase the particles iron oxide loading, strengthen the deflection magnet, or reduce the distance between the magnet and particle stream as the most feasible It was achieved by halving the channel direction) to 1cm (from 2c m) which increased the force substantially. This change demonstrated its merit by markedly defl ecting the
Armington 13 stream, without allowing for the accumulation of particles on the magnet w hich afflicted the previous generation of the device. Protocol for Use Because of the design evolution, th e usage protocol was fluid as well and will be described in this section in its final form which is the one used to collect data for figure s 16 &17 The complete setup is shown beside in figure 1 3 It involves two syringe pumps (Cole Parmer) one for each the particle stream and main flow. The particle pump is run using a 1 ml HSW Norm Ject syringe (item # 4010.200V0 ) containing water with the pump set to a diameter of 4.66 mm and rate of 45 l/m in The second pump used to power the main flow uses a 30 ml BD syringe (catalog # 309650 ) with the diameter set to 20.5 mm, and rate set to 6.825 ml/min. The standard solutions were made (for the final data set, see figures for details on others) by combining glycerol (Fisher Chemical, catalog # G33 4) and water by volume in aliquots of 50 ml, enough for 2 trials each requiring 25 ml. The viscosity of the standard solutions was calculated using an empirical formula developed by Nian Sheng Cheng  For each viscosity standard, a particle solution must also be made. Each includes 100 g of Invitro gen D ynabeads MyOne Streptavidin C1 (ref # 65002) partic l es suspended in a 40 l solution of its corresponding viscosity to achieve a concentration of 2.5 g/l Aft er aliquoting, the particles were sonicate d, Figure 13 shows the experimental setup used. The clamps and aluminum bars are used to clamp and iPhone (camera). Note the tape marks on the table used to replicate the alignment. The particle pump is left of the frame and was omitted for the sake of clarity. Figure 12 shows the particle stream being deflected by two permanent magnets in water. The image on the right is inverted and enlarged with enhanced contrast for visibility. The success of this design lies in the magnitude of deflection achieved as well as the uniformity of the particle stream.
Armington 14 and used promptly after to avoid particle aggregation Additiona lly, a negative control of water/food coloring is aliquoted of the same volume With each trial, the chamber is first emptied of fluid. Next, the particles are mixed with a vortex mixer Using the 1 ml syringe, a small bubble is drawn (< 1cm long) into the particle feedline to separate the particle solution from the water used to push it. Then, the 40 l particle solution is withdrawn, and again a bubble should be withdrawn, this time ~5 cm long to ensure the particle solution is not wasted in the event the of the plunger being inadvertently bumped. The feedline is then plugged into the chamber and the pump is used to push out the first b ubble. in to the chamber, the particle pump is turned off. This will prevent air from entering the chamber during the trial which would induce turbulence and disrupt the stream. Next, the 30 ml syringe is connected to its feedline and filled with care being taken to keep its tip as low as po ssible while filling. This will ensure that the initial air in the feedline can travel upwards and not bubble After the feedline has been filled and the standard solution has entered the chamber, the syringe is attached to its pump and started. Once th e viscous solution front has reached the top of the chamber, the particle pump is started and the trial can commence. For its duration, pictures are taken approximately every 2 seconds. Results To take measurements the raw images from each trial are ana lyzed using ImageJ First, they must be visually inspected to determine when steady state has been reached and particle deflection maximized. This occurs near the end of each sequence. Having selected an example from each tr ail, they are imported to Ima ge J and the measurement standard is taken as 100 mm on the ruler to the right. The image is then zoomed and inverted to enhance visibility and contrast. The deflection measurement is taken from the edge of the ruler at the 4 cm mark to the far edge of th e particle stream horizontally (180 in ImageJ ) The measurement taken is then subtracted by the measurement taken from the negative control (dye sample) to gain the displacement of the stream due to magnetic deflection.
Armington 15 The data displayed in figure 14 devia tes from the protocol as described in the figure label. Being the first data obta ined, it served to verify the trend of decreasing deflection as a function of increasing viscosity. Unfortunately, a steady state could not be achieved, thereby necessitating changes in the subsequent trials. Figure 15: shows data taken in the second full trial run. In this, the syringe pump was adopted with the parameters as described in the protocol for use section to drive the particle flow with the hope of s teadying the flow. Again, MagnaBind particles were used, this time suspended in their corre sponding viscous standards In figure 15 data from the second trial can be seen. Changes from the first trial are described in the figure label. While this data demonstrated a stronger linear correlation between the measured deflection and log of viscosity, the variability suggests that a steady state assumption cannot be made, and indeed when examining the images that is confirmed y = 4.1382x + 2.3339 R = 0.7247 0 0.5 1 1.5 2 2.5 3 3.5 -0.1 0 0.1 0.2 0.3 0.4 0.5 Deflection Measured [mm] log(viscosity) [mPa*s] y = 5.3457x + 1.7646 R = 0.5832 0 0.5 1 1.5 2 2.5 -0.1 -0.05 0 0.05 0.1 0.15 0.2 Deflection Measured [mm] log(viscosity) [mPa*s] Figure 14: the measurement was taken as shown to the right. To the left shows the data collected from the first working trial of the device using the previously described protocol. The particles used were MagnaBind Goat Anti Mouse IgG Magnetic Beads (Product # 21354) particles at 2 g /l. Note that the particle solutions were all water and standard solutions included 0%, 5%, 10% and 15% glycerol. They were driven by a Flow Peristaltic Pump (Catalog # 13 876 4 ) set to 28.
Armington 16 Figure 16 shows the measured deflection of the particles with a strong correlation to the log of the 10%, 20%, and 30% glycerol standards were used with particle solutions and pump parameters as described in the pro tocol for usage section. Figure 16 shows the third trial The strong correlation implies that the steady state assumption should for the first time be validated, and when examining the raw images that claim can be supported. As such, a further trail should be run to collect measurements over a wider range of viscosities to better characterize the relationship. In the besi de plots of figure 17, a broader range of solutions are tested and a more robust model of the trend can be found by linearizing the data via an inverse plot as opposed to a semi log plot. Note the negative deflection measurement of the 50% glycerol soluti on which suggests the maximum viscosity for this device to detect would be nearly that of the 50% magnetic particles are attract ed to each other to a greater extent than they are to the magnet; y = 3.6626x + 2.1325 R = 0.9956 0 0.5 1 1.5 2 2.5 -0.1 0 0.1 0.2 0.3 0.4 0.5 Deflection Measured [mm] log(viscosity) [mPa*s] Deflection vs log y = 2.1995x + 1.5152 R = 0.9436 -0.5 0 0.5 1 1.5 2 -0.2 0 0.2 0.4 0.6 0.8 1 Measured Deflection [mm] log() [mPa*s] Deflection vs log y = 2.0265x 0.3797 R = 0.9947 -0.5 0 0.5 1 1.5 2 0 0.2 0.4 0.6 0.8 1 1.2 Measured Deflection [mm] 1/ [mPa*s] ^ 1 Deflection vs 1/ Figure 17 shows the measured deflection as a function of viscosity. Standard solutions used were again separated by increments of 10% glycerol, and included groups from 0% 50% glycerol. The above plot again attempts to linear ize the data with the log of viscosity, however the data suggests otherwise. In the plot below, linearization appears to be achieved using an inverse plot
Armington 17 however more testing should be conducted to determine whether this a result of experimental error or some other phenomenon. D iscussion In the methodology section, a great deal was done to describe the efforts to build a device which could create a stream of magnetic particles and deflect them with a permanent magnet. In this section, I will delve further into control ling the stream in su ch a way as to isolate the effects of displaceme nt before then discussing future directions for the project. The first and perhaps most fundamental assumption is that the stream of particles will remain uniform and not be altered except by the magnetic and drag forces. The first potential challenge to meet this assumption is particulate diffusion. Because diffusion of the particles can be assumed to be uniform, unavoidable within the constraints of this device, and occurr ing over a relatively small timescale, its effects will be assumed negligible. The next challenge to achieving uniformity is turbulence in the flow. Below in figure 1 8 a brief calculation demonstrating that at the flow rates utilitzed in this device are an order of magnitude fro m their transition to turbulent and as such can be assumed laminar. The other potential source of turbulence is the inlet of the particle stream which flows orthogonally into the main flow at a linear rate of 0.19 cm/sec. This is approximately an order of magnitude below the main flow rate, which along with the qualitativ e data (images in figures 12, 14, 17 ) will be used to justify the assumption that this induced turbulence is minimal and can be neglected. The final flow characteristic to be considered is pulsation which would preclude a Figure 18: Number rearranged to solve for linear velocity. Beside it is the equation for the hydraulic diameter of a rectangular condu it, where a = 1 mm and b = 10 mm. For the R E 2300 was used as the boundary condition for laminar flow. The dynamic viscosity of water was used as 8.9E 4 Pa*s, with a density of 1000 kg/m 3 This calculation determined the maximum flow rate of 61.4 cm/s with water (the boundary condition), while the linear flow rate used was approximately 1.3 cm/s. In the beside photo, the requisite flow conditions are demonstrated using a green dye.
Armington 18 steady state from forming Flow rate pulsation was eliminated largely by switching to a second syringe pump from the peristal tic pump (after the second trial). The final consideration in achieving steady state is the behavior of the particles themselves as they enter the device. P rimarily, aggregation and separation should be considered. As particles aggregate, the cumulative magnetization (of the aggregate) increases with volume, wh ile the drag increases only as a function of the aggregate s increasing diameter. As such, these larger aggregates will have a larger ratio of magnetic force to drag force, thus translating more than an individual. Following the same logic, monodispersity of these particles is also essential Between the two particle types used, the first (MagnaB ind ) were used for their lower cost and immediate availability. However, i n handling them, it became clear that aggregation was a much more significant problem than with the DynaBeads. Additionally, the D yna B eads are far more monodisperse with a diameter of 1 m and CV of <3%, while the MagnaB ind are specified only as between 1 and 4 m in diameter This leads to the next issue, separation. As the particle solution flows through the tubing, its concentration changes spatially, such that the particles move toward the back of the stream and thus concentration increases in the stream as the trial progresses. The effect of this heightened concentration is an increase in deflection, which is thus also time dependent and contradicts the requisite steady state a ssumption for the device. For this issue, the switch to DynaBeads again helped as their reduced size should hypothetically increase their diffusability thus counterin g their tendenc y to separate With so many factors a ffecting the state of the particle stream, more work will be required to sufficiently control them to the extent that the steady state assumption can be fully justified. Firstly, improvements must be made to the parti cle stream to remove its time dependence of concentration (separation) which was still present in the final device tested This may be remedied by further slowing the diameter. This will require t he manufacturing of a new chamber Another a venue to reduce these effects may be to drastically reduce the particle concentration in the stream, thereby limiting the interparticle interactions that may lead to the on. This change will require improveme nt s in lighting and camera to detect the stream thus a complete
Armington 19 redesign of the experimental setup would be required If interactions persist, it may be necessary to record the translation of fluorescen tly tagged particles which could drastically reduce the requisite stream concentration. Having improved the stability of the stream, it will become necessary to quantitatively confirm the steady state assumption such that it can be validated. This may take the form of a MATLAB code used to process a stream of images taken autonomously at a prescribed interval to select one representative of the steady state and then make the measurement. Conclusion In this paper, the concept of magnetic deflection has been proposed tested and empirically validated by dev eloping a device and methodology capable of creating regulating deflecting, and measuring a stream of magnetic particles Through this paper, a series of devices has been developed, trialed, and improved upon. From the results of figures 16 and 17 t he empirically determined relationship between deflection a nd viscosity can be shown. Moving forward, further refinements to the device should be made to fully achieve a steady state deflection, and to quantitatively determine when that state has been rea ched Keeping in mind the original objective, the lessons learned in developing these prototypes should be combined with a quantitative model to downscale this technology into a microfluidic chip. If one could be affordably built at minimal complexity, t his technology could see the clinical use it was originally intended for.
Armington 20 References  E. Losina et al. Ann Intern Med vol. 26, no. 154, pp. 217 226, 2011.  Buckland existing Osteoarthr. Cartil. vol. 7, no. 4, pp. 430 433, 1999.  B. P. Conrad, S. O. Canapp, A. R. Cross, C. E. Levy, M. Horodyski, and R. Tran son tay, Ca n Synovial Fluid Viscosity Be Used As a Phys. Marker Osteoarthr. Sev. no. 3, pp. 1157 1158, 2003.  E. H. Jebens and M. E. Monk J. Bone Joint Surg. Br. vol. 41 B, no. 2, pp. 388 4 00, 1959.  Natl. Anim. Heal. Monit. Syst. no. April, p. 1 34 #N318.0400, 2000.  Vet. Clin. North Am. Equine Pract. vol. 24, no. 2, pp. 437 454, 2008. [7 ] A. Garraud et al. viscosity IEEE Trans. Biomed. Eng. vol. 63, no. 2, pp. 372 378, 2016.  assisted nano patterning of m agnetic core shell Phys. Chem. Chem. Phys. vol. 16, no. 26, pp. 13306 13317, 2014.
Armington 21  Am. J. Phys. vol. 56, no. 8, pp. 688 692, 1988.  Y. Y. Shah et al. e translation as a surrogate measure for synovial fluid J. Biomech. vol. 60, pp. 9 14, 2017.  Ind. Eng. Chem. Res. vol. 47, no. 9, pp. 3285 3288, 2008.