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Magnetic field driven actuation of sessile ferrofluid droplets in the presence of a time dependent magnetic field
Journal Pre-proof Magnetic field driven actuation of sessile ferrofluid droplets in the presence of a time dependent magnetic field Sudip Shyam, Mohammed Asfer, Balkrishna Mehta, Pranab K. Mondal, Zeyad A Almutairi
PII:
S0927-7757(19)31108-2
DOI:
https://doi.org/10.1016/j.colsurfa.2019.124116
Reference:
COLSUA 124116
To appear in:
Colloids and Surfaces A: Physicochemical and Engineering Aspects
Received Date:
5 August 2019
Revised Date:
29 September 2019
Accepted Date:
14 October 2019
Please cite this article as: Shyam S, Asfer M, Mehta B, Mondal PK, Almutairi ZA, Magnetic field driven actuation of sessile ferrofluid droplets in the presence of a time dependent magnetic field, Colloids and Surfaces A: Physicochemical and Engineering Aspects (2019), doi: https://doi.org/10.1016/j.colsurfa.2019.124116
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Magnetic field driven actuation of sessile ferrofluid droplets in the presence of a time dependent magnetic field Sudip Shyam1, Mohammed Asfer2*, Balkrishna Mehta 3*, Pranab K. Mondal1, Zeyad A Almutairi4 Department of Mechanical Engineering, IIT Guwahati, Guwahati, India
2
Department of Mechanical Engineering, College of Engineering, Dawadmi, Shaqra University, KSA
3
Department of Mechanical Engineering, IIT Bhilai, Bhilai, India
4
Department of Mechanical Engineering, College of Engineering, King Saud University, KSA
*
Corresponding author: E-mail: [email protected], Tel: +91-361-258-3439 Corresponding author: E-mail: [email protected], Tel: +966-50-900-4912
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Graphical Abstract
ABSTRACT The present paper reports actuation of sessile ferrofluid droplets over a hydrophobic substrate in the presence of a time-dependent magnetic field generated by an electromagnet. The internal hydrodynamics of the ferrofluid droplet in the presence of magnetic field are measured using both bright field visualization and micro-particle image velocimetry (µ-PIV) techniques. During ON
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cycle of the magnetic field, bright field visualizations show the migration of nanoparticles towards the contact line near the vicinity of the electromagnet resulting in aggregation of nanoparticles
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inside the droplet. Similarly aggregated nanoparticles at the contact line from the ON cycle are
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observed to disperse from the cluster of nanoparticles during the OFF cycle of the magnetic field. Both migration and dispersion of nanoparticles result in bulk motion inside the ferrofluid droplet
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during the ON and OFF cycle of the magnetic field. Velocity measurements from µ-PIV technique successfully validate the qualitative measurements of flow field from bright field visualization
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technique. A critical frequency is observed for the applied magnetic field above which negligible dispersion of nanoparticles resulted inside the ferrofluid droplet during the OFF cycle of the
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magnetic field.
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Keywords: Ferrofluid; Magnetic field; Droplet; Micro particle image Velocimetry.
Nomenclature: 𝑎𝑐𝑜𝑖𝑙
Cross sectional area of coil (𝑚)
𝐴𝑚
Magnetic vector potential
𝐴𝑠
Surface area of the droplet (𝑚2 ) 2
Magnetic flux density (𝑇)
𝐶𝑑
Drag coefficient
𝐷
Diameter of seeding particle (𝑚)
𝑓
Frequency (𝐻𝑧)
𝐹d
Drag force (𝑁), 𝐹𝑑 = 3𝜋𝜂𝐷𝑝 (𝑈𝑝 − 𝑈𝑓𝑓 )𝐶𝑑
𝐹 mp
Magnetophoresis Force (𝑁), 𝐹𝑚𝑝 = −𝑉𝜇0 (𝑀 ∙ ∇𝐻)𝐻
𝐻
Magnetic field (𝐴/𝑚)
𝐼
Current (𝐴)
𝐽𝑒
Current density (𝐴/𝑚)
𝑀
Magnetization (𝐴/𝑚)
𝑁
Number of turns
NA
Numerical Aperture
𝑅
Radius of the droplet (𝑚)
𝑇
Time period of one cycle (𝑠)
𝑡𝜈 𝑡𝑚
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𝑈
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𝑡𝑎
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𝐵
Advective time scale (𝑠), 𝑡𝑎 = 2𝑅/𝑈𝐵=0 Viscous/diffusion time scale (𝑠), 𝑡𝑑 = (2𝑅)2 /𝜈 Magnetic perturbation time scale (𝑠), 𝑡𝑚 = 0.5𝑓 Velocity (𝑚/𝑠)
𝑉
Volume of seeding particle (𝑚3 )
𝜔𝑦
Vorticity (1/𝑠), 𝜔𝑦 = ( 𝜕𝑥 − 𝜕𝑧 )
𝜕𝑤
𝜕𝑢
Symbols
3
Kinematic viscosity (m2 s)
𝜇
Permeability (m kg s-2 A-2)
𝜌
Density (Kg/m3)
𝜎
Electrical conductivity of coil (s/m)
Surface tension (N/m)
𝜃
Contact angle (degree)
𝜁
Time (𝑠)
𝜒
Magnetic susceptibility
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𝜈
Subscript Critical
𝑑
Drag
𝑚
Magnetic
mp
Magnetophoresis
𝑝
Particle
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𝑓𝑓
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𝑐𝑟
ferrofluid
Non-dimensional numbers
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Bo
Magnetic Bond Number, 𝐵𝑜 = 2𝜇0 𝐻 2 𝑅/𝛾
U*
Non-diemnsionalized velocity, 𝑈 ∗ = 𝑈/𝑈𝑚𝑎𝑥
We
Weber number 𝑊𝑒 = 𝜇0 |𝑀2 |𝑈/𝛾𝐴𝑠 ,
Z*
Non-dimensional length along Z-direction, 𝑍 ∗ = 𝑍/𝑅
X*
Non-dimensional length along X-direction, 𝑋 ∗ = 𝑋/𝑅
Constants 𝜇0
Permeability of free space 4
1. INTRODUCTION Controlled actuation of droplets on a planar surface using different actuation concepts such as electrostatic forces [1, 2], thermocapillarity [3], acoustics [4], and magnetism [5, 6] have been the subject of theoretical and experimental investigations among the researchers for the last decade.
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Compared to different actuation concepts, droplet manipulation using magnetism offers several
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advantages. Droplets can be manipulated from a distance using magnetic field which is not in contact with the liquid. Furthermore, magnetic field based manipulation are relatively more
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tolerable to liquid properties compared to electric field based manipulation which are found to highly dependent on the conductivity and permittivity of the liquid that forms the droplet [7].
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Ferrofluids because of its magnetic properties provide a viable option for the choice of fluid for
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the magnetic based platforms for manipulation of droplets. Ferrofluids are synthesized as a stable colloidal suspension of iron oxide (Fe3O4) nanoparticles dispersed in a carrier liquid such as water or oil [8]. Nanoparticles in ferrofluid are normally coated with a surfactant in order to prevent
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agglomeration by overcoming the attractive van der Waals forces between the nanoparticles. The presence of iron oxide nanoparticles in ferrofluid provides the ability to control/actuate the droplet using a magnetic field. In the absence of magnetic field, nanoparticles in ferrofluid are randomly
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oriented with the overall magnetization of ferrofluid being zero. With the application of magnetic field, nanoparticles in ferrofluid exhibit super - paramagnetic characteristics with a magnetic moment oriented in the direction of applied magnetic field. Over the past decade, several studies related to ferrofluid based mixing [9-14], spreading/wetting on a substrate [15-17], evaporation or drying pattern [18, 19] in the presence of magnetic field or no magnetic field are reported in literature. For ferrofluid based phenomenon as discussed above, 5
the hydrodynamics of ferrofluid in the presence of magnetic field plays an important role, where nanoparticles of ferrofluid migrate in the direction of magnetic field which in turn induces a flow called magnetoconvetion in ferrofluid. This magnetoconvection may result in enhanced mixing between fluids or controlled spreading or evaporation of ferrofluids in the presence of magnetic field. Quantitative measurements of convection or velocity of nanofluids (e.g. ferrofluids) can be obtained experimentally using either µ-PIV or PTV technique. µ-PIV technique provides the
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velocity information by tracing seeding particles added to nanofluid whereas PTV technique
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provides the velocity information by tracing the individual nanoparticles of nanofluid. Very few studies related to velocity measurements of nanofluids using µ-PIV or PTV technique are available
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in literature [20-23]. However velocity measurements of nanofluids in particular for ferrofluids in
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the presence of magnetic field is not available till date. With this background, the present study reports the internal hydrodynamics of a sessile ferrofluid droplet subjected to a time dependent
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magnetic field using µ-PIV technique. Both bright field visualizations and µ-PIV measurements were carried out in order to understand the internal hydrodynamics of the ferrofluid droplet in the
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presence of magnetic field. Time dependent magnetic field with different actuation frequencies were applied in order to study the effect of actuation frequency on the internal hydrodynamics of the ferrofluid droplet.
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2. MATERIALS AND METHODS
2.1 Preparation and Characterization of Ferrofluid Iron oxide nanoparticle (IONPs) were synthesized chemically by the co-precipitation reaction from an aqueous mixture of Fe+3/Fe+2 in the molar ratio of 2:1 by using concentrated ammonium hydroxide solution in an inert atmosphere of nitrogen. After the co-precipitation of magnetic nanoparticles, oleic acid (5–50% (w/w), related to the weight of IONPs) was added as a stabilizer 6
for the synthesis of OA-IONPs. After 30 min of reaction, the temperature was elevated to 100-110 °C in order to remove excess of water and ammonium hydroxide. One gram of OA-IONPs as received above was added to 6.0 g of n-hexane to form an organic dispersion. For the aqueous phase transfer of the above dispersion, 20 mL of aqueous solution of sodium lauryl sulphate (10– 60% (w/w) was added to it at 500 rpm for 1 hour. The added sodium lauryl sulphate act as a surfactant which prevents agglomeration of nanoparticles. The mixture was then subjected to
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sonication twice for 2 min at 90% amplitude with a sonicator (Branson Sonifier W450) in an ice-
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cooled bath followed by the evaporation of n-hexane under continuous stirring at 80 °C for 3 hour. The water loss was compensated by addition of 2 mL of water in every 30 min in order to obtain
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a stable water-based ferrofluid of OA-IONPs (0.5% w/v) as shown in Fig. 1(a). The detailed
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procedure for the synthesis of water-based ferrofluid can be found in our earlier work [24, 25]. Ferrofluid with such a low volume fraction of nanoparticles (0.5%) was used in the present study
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as the non-transparent nature of ferrofluid affects the visibility of seeding particles added to ferrofluid during the µ-PIV measurments [26]. Secondly ferrofluids with such a low volume
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fraction of nanoparticles is assumed as a single phase fluid where nanoparticles are freely suspended in the carrier liquid. The various thermophysical properties of the ferrofluid are mentioned in Table 1. The magnetization curve of the water-based ferrofluid as measured by the vibration sample magnetometer (VSM) is shown in Fig. 1(b). This data illustrates the super-
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paramagnetic characteristic of the ferrofluid. The nanoparticles have an average size of around 50 ± 2 nm as shown in Fig 1(c) as measured by dynamic light scattering (DLS) technique. The absolute zeta potential of the ferrofluid was found to be 53 mV (Fig. 1(d)) and for an absolute value of zeta potential higher than 25 – 30 mV, it is generally accepted that the particles are electrostatically stable [27].
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Table 1: Thermophysical properties of water and prepared ferrofluid (at 30 °C) Specific heat
Thermal conductivity
Viscosity
(Kg m-3)
(J (Kg K)-1)
(W (m K)-1)
(Pa s)
Water
995
4180
0.6
0.0009 0.00001
Ferrofluid
1022
3425
0.7
0.00106 0.00001
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Density
Fig 1. (a) Prepared ferrofluid sample, (b) magnetization curve of ferrofluid, (c) particle size distribution of ferrfluid and (d) zeta potential of ferrofluid.
2.2 Fabrication of hydrophobic substrate and electromagnet
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The hydrophobic substrate used in the present experiments was fabricated by coating a thin layer of PDMS on a glass slide using a spin coater (EZspin-ADV). PDMS was poured directly on the glass slide mounted on the spin coater rotating at 2000 rpm for 50 seconds. The PDMS coated glass slide was then kept at 80 º C in an oven for 1 hour in order to cure PDMS. The PDMS coated glass slide was then tested for hydrophobicity towards water and ferrofluids. The PDMS layer on the glass slide was found to be chemically insensitive as no absorption was observed for ferrofluid
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and water on PDMS layer. For the contact angle measurements of droplets, a goniometer imaging
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set up was used as shown in Fig. 2(a). Droplets were kept on the substrate using a droplet dispensing module (Acam-NSC). A CMOS camera (Nikon, D5200) was used to capture the
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images and a white light source along with a diffuser was used to illuminate the droplet. Image J
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software was used to calculate the contact angle and diameter of the droplets. The contact angle of water on PDMS coated glass slide was found to be 105 ± 0.8° whereas for untreated surface i.e.
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for glass slide it was found to be 44 ± 0.6°. Similarly the contact angle was found to be 63 ± 2.05° and 34 ± 2.15° for ferrofluid on the PDMS coated glass slide and the untreated glass slide
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respectively. An electromagnet was fabricated by winding 26 SWG enamel coated copper wires ( ~ 20 turns per cm) over a 6 mm diameter and 100 mm long iron core and was kept at a distance of 𝑥𝑚𝑎𝑔 = 1.5 mm from the droplet as shown in Fig 2(b). The electromagnet was activated by supplying current from a DC power source (32 V/ 5 A). For generating alternating magnetic field,
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an in-house built digital circuit was used to supply a pulse current to the electromagnet. Alternating magnetic field of strength 𝐵 = 340 G and actuation frequencies 𝑓 = 0.1, 0.5, 1.0 and 3 Hz were applied to the ferrofluid droplet. Fig 2(c) shows the evaporation of the ferrofluid droplet in the presence of no magnetic field up to 𝜁 = 400 seconds. It can be observed that the rate of evaporation of ferrofluid droplet was very slow for initial period of time up to 𝜁 < 30 seconds,
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whereas the rate of evaporation became significant for later period of time i.e. for 𝜁 > 100
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seconds.
Fig 2. (a) Goniometric imaging set up for contact angle measurment, (b) schematic of droplet -
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electromagnet arrangement and (c) images showing rate of evaporation of ferrofluid droplet in the absence of magnetic field. 2.3 Bright field imaging and µ-PIV system Bright field visualisations of internal convection or bulk flow of ferrofluid droplet were carried out using an inverted microscope (Leica: DM IL LED) as shown in Fig 3. The droplet –
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electromagnet set up was kept over the stage of the inverted microscope and the droplet was illuminated from below the microscope stage though a 10X objective lens (NA = 0.25) using a mercury lamp. Under bright field visualizations mode, nanoparticles of ferrofluid were appeared as black particles with a white background. In order to visualize the chain like cluster of nanoparticles during aggregation, a higher magnification objective lens 20X (NA = 0.4) was used. Similarly, during µ-PIV measurements of internal convection of ferrofluid droplet, an inverted
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microscope with a florescent light source was used as shown in Fig 3. Fig 3 shows the schematic
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of the µ-PIV system. It consists of three main components: (a) an inverted microscope (Leica: DM IL LED), (b) a florescent light source and (c) a CCD camera. For µ-PIV measurements the
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ferrofluid droplet was seeded with 1 µm diameter fluorescent microspheres (Molecular Probes
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Inc.) with a dilution of 1:200 (v/v). The above seeding particle concentration was chosen as it provided acceptably low noise levels under the present illumination conditions. The droplet –
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electromagnet set up was kept over the stage of the inverted microscope and the droplet was illuminated by a green light of wavelength of 530 nm from below the microscope stage though a
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10X objective lens (NA = 0.25). The fluorescent seeding particles in the ferrofluid droplet were then excited with green light, which emitted light at a peak wavelength of 590 nm. An epi – fluorescent prism filter was used on the optical path in order to eliminate the background light such that only the emitted light from seeding particles reached the CCD camera of the µ-PIV system.
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Under fluorescent visualization mode, seeding particles added to ferrofluid were appeared as fluorescent particles with a black background. Fluorescent images of seeding particles were captured using a 12 bit 1344 × 1244 pixels2 CCD camera and then transferred to a computer for further image processing. Double images were captured per realization in such a way that seeding particles moved approximately 1/4th size of the interrogation window used for correlation between
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two consecutive images. Before carrying out cross correlation algorithm raw µ-PIV images were overlapped using Image J software. Image overlapping prior to correlation was carried out to increase the number of seeding particles per interrogation window resulting in easy peak detection during cross correlation algorithm. A cross correlation algorithm with interrogation size 64 × 64 pixels2 and 50% overlapping between interrogation windows was used to calculate the
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instantaneous velocity vector field inside the droplet using PIVLab plugin by Matlab V 12 [28].
Fig 3: Schematic of the bright field imaging/µ-PIV set up
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3. RESULTS AND DISCUSSIONS
3.1 Magnetic flux density distribution
The distribution of magnetic flux density (𝐵) in the droplet region was simulated using the COMSOL Multiphysics V 5.3 software. The governing equations and parameters used for the simulation of magnetic field are presented in Table 2. Free tetrahedral mesh of maximum element 12
size of 1 mm, with a total of 2.1 × 106 elements, was used in the present simulations. A stationary MUMPS solver with absolute tolerance of 10-6 was used for simulating the magnetic field generated by the electromagnet. Fig. 4(b) shows the simulated magnetic flux density distribution around the droplet. Along the diameter 𝑍 − 𝑍´ of the droplet, the magnetic flux density was found to be nearly constant, whereas a magnetic field gradient was present along the diameter 𝑋 − 𝑋´ of
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the droplet as shown in Fig. 4(c). In order to validate the simulation results, the magnetic flux density produced by the electromagnet was measured using a gauss meter and was compared with
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the simulation results as shown in Fig. 4(d). A good match between the two validates the various
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parameters and equations used for the simulation of magnetic field.
Table 2. Governing equations and parameters used for COMSOL simulation of magnetic field
Am 1 1 ( 0 r B) B J e t
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Governing Equations
NI Je acoil
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Current (𝐼)
1.5 A
2.82 × 10-5 m2
Number of turns (𝑁)
200
Electrical conductivity of coil (𝜎)
5.96 × 107 s/m
Relative permeability of air (𝜇𝑟 )
1
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Cross section area of coil (𝑎𝑐𝑜𝑖𝑙 )
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Fig. 4: (a) Meshing of computational domain for magnetic field (b) Distribution of magnetic flux
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density (𝐵) around the droplet region (c) variation of magnetic flux density along the diameters (𝑋 − 𝑋´ and 𝑍 − 𝑍´) of the droplet and (d) validation of simulation results with measurements from gauss meter.
3.2 Scaling analysis
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Various scaling analysis were carried out in the present work. First scaling analysis was carried out for translational motion of the ferrofluid droplet towards the electromagnet from the position where it was originally deposited on the PDMS coated glass slide. In the presence of magnetic field, the resultant of surface tension and magnetic force acting on the droplet determines the translational motion of the droplet towards the electromagnet. For the present study above two forces were evaluated by calculating the Weber number (𝑊𝑒𝑚 ) and magnetic Bond number 14
(𝐵𝑜) respectively. Weber number was found to be 𝑊𝑒𝑚 ~ 10−3 as compared to magnetic Bond number 𝐵𝑜 ~ 0.96 indicating higher dominance of surface tension compared to the magnetic force resulting in negligible change in spherical shape of the droplet with no translational velocity towards the electromagnet. The droplet was therefore observed to actuate at the same position in the presence of magnetic field where the droplet was initially deposited on the PDMS coated glass
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slide. The details of calculations of Weber and magnetic Bond number are mentioned in the nomenclature section.
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A second scaling analysis was carried out to find the amount of negative magnetophoresis acting
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on seeding particles in ferrofluid in the presence of magnetic field during µ-PIV measurements. The negative magnetophoresis is usually encountered by a non-magnetic body like seeding
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particles dispersed in a magnetic medium like ferrofluid in the presence of a magnetic field [29, 30]. Zhu et al. carried out analytical study on transport of non-magnetic particles in a diluted
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ferrofluid in the presence of magnetic field produced by a permanent magnet [31]. They reported that deflection of non-magnetic particles due to negative magnetophoresis can be minimized with
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the use of diluted ferrofluids and a low strength of applied magnetic field. The negative magnetophoretic force (𝐹𝑚𝑝 ) and viscous drag force (𝐹𝑑 ) acting on seeding particles under the present experimental conditions were calculated and the ratio between the two was found to be 𝐹𝑚𝑝
~ 10−7, indicating negligible deflection of seeding particles due to negative magnetophoresis.
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𝐹𝑑
Therefore seeding particles were observed to follow the bulk flow faithfully inside the droplet in the presence of magnetic field during the µ-PIV measurements.
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3.3 Internal hydrodynamics of ferrofluid droplet in absence of magnetic field Before conducting experiments in the presence of magnetic field, the internal convection or bulk flow present inside the ferrofluid droplet was measured in the absence of magnetic field using µPIV measurements. Ferrofluid in the absence of magnetic field behaves like any other nanofluid with nanoparticles freely dispersed in carrier fluid. Several studies have been carried out on
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internal hydrodynamics of a sessile liquid droplet over a hydrophobic surface, where buoyancy driven Rayleigh convection results in downward motion of fluid along the interface and an upward
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plume like flow at the center region of the droplet [19, 32-34]. Fig 5(a) shows the velocity field
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inside the ferrofluid droplet in the absence of magnetic field which shows a radial inward motion towards the center region of the droplet similar to the studies as discussed above. The inward
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motion of the fluid resulted in a plume like flow in the center region which was subsequently travelled towards the contact line region near the air – liquid interface of the droplet. In order to
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validate our study, a comparison of 𝑈 ∗ - velocity profile along the diameter of the ferrofluid droplet is carried out with the literature as shown in Fig 5(b). A good match between the two validates the
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present study and confirms the feasibility of using µ-PIV technique for velocity measurements of
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nanofluids like ferrofluids.
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Fig. 5: (a) Velocity field inside the ferrofluid droplet in the absence of magnetic field, and (b) comparison
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of 𝑈 ∗ velocity profile along the diameter (𝑍 − 𝑍 ´ ) of the droplet with the literature.
3.4 Internal hydrodynamics of droplet in the presence of magnetic field
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As the rate of evaporation of droplet was observed to be negligible for 𝜁 < 30 seconds as discussed in section 2.2, it indicates that bright field visualizations and µ-PIV measurements of internal hydrodynamics of ferrofluid in the presence of magnetic field can be conducted precisely up to time scale 𝜁 < 30 seconds considering negligible evaporation from the ferrofluid droplet. The
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maximum time scale corresponding to actuation frequency 𝑓 = 0.1 Hz of applied magnetic field was calculated to be 𝜁 = 10 seconds, which was found to be less than the time scale for negligible evaporation i.e. 𝜁 < 30 seconds.
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3.4.1 Bright field visualizations The ferrofluid droplet was subjected to an alternating magnetic field of strength 𝐵 = 340 G and actuation frequencies 𝑓 = 0.1, 0.5, 1 and 3 Hz. Bright field visualizations were carried out for each case (see the supplementary videos) and are shown in Fig. 6 respectively. For each case, bright field images are shown at time intervals 𝜁 = 0+, /4, 𝑇/2, 3𝑇/4, and 𝑇 respectively as shown
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in Fig 6(a). The time stamp 𝜁 = 0+ represents the instant when the magnetic field was just ON resulting in actuation of the ferrofluid droplet in the direction of the applied magnetic field. During
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the ON cycle of the operation of the electromagnet (𝜁 = 0+ – 𝑇/4), IONPs in ferrofluid were
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observed to migrate through the droplet towards the magnetic zone near the vicinity of the electromagnet. Migration of nanoparticles resulted in bulk motion of ferrofluid towards the contact
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line near the vicinity of the electromagnet (See the bright field videos). In the presence of magnetic field, the inter particle dipole – dipole interaction resulted in chain like cluster of nanoparticles
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within the aggregate near the contact line as shown in the zoomed view in Fig 6(b) [35]. In the absence of magnetic field, random orientation of magnetic moments of nanoparticles resulting in
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negligible dipolar attraction between the nanoparticles. However in the presence of magnetic field, magnetic moments of nanoparticles are orientated in the direction of applied magnetic field resulting in chain like clusters of nanoparticles as shown in Fig 6(b). During the OFF cycle of the
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electromagnet (𝜁 = 𝑇/2, 3𝑇/4, 𝑇), nanoparticles were observed to disintegrate from the chain like clusters and were dispersed freely within the droplet as shown in Fig 6(b). This was because of random orientation of magnetic moments of nanoparticles in the absence of magnetic field as discussed above. Similar to the migration of nanoparticles, dispersion of nanoparticles during the OFF cycle resulted in bulk motion of ferrofluid in the direction opposite to the ON cycle as visualized from the supplementary videos. 18
In order to study the effect of actuation frequencies on the migration and dispersion of IONPs in the droplet, various time scales involved with the present study were evaluated such as; advective time scale (𝑡𝑎 ), diffusion/viscous time scale (𝑡𝜈 ), and magnetic perturbation time scale (𝑡𝑚 ). All the above timescales were calculated for each case of actuation frequency and are mentioned in Table 3. As the advective time scale 𝑡𝑎 was found to be very high and constant for
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all the cases, the effect of advective time scale is not discussed further. Therefore, the migration, aggregation at the contact line and then dispersion of nanoparticles during one complete cycle of
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operation of the electromagnet were found to depend on the balance between the diffusion time scale 𝑡𝜈 and magnetic perturbation time scale 𝑡𝑚 . During the ON cycle of magnetic field
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aggregation of nanoparticles was observed in the droplet for time interval 𝜁 = 0 to 𝑇/4 as shown
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in Fig 6(a) and 6(b). This is because during time interval 𝜁 = 0 to 𝑇/2, nanoparticles experienced higher magnetic force compared to viscous force resulting in aggregation of nanoparticles in the
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droplet. The time interval 𝜁 = 𝑇/2 corresponds to case when the magnetic field was just OFF. During the OFF cycle i.e. from 𝜁 = 𝑇/2 to 3𝑇/4, strong dominance of the viscous force compared
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to the magnetic force acting on nanoparticles resulted in release/disperse of nanoparticles from the cluster of nanoparticles as shown in Fig 6(a) and 6(b). Both migration and dispersion of nanoparticles during the ON and OFF cycle of the magnetic field resulted in a bulk motion of ferrofluid in the droplet.
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It can be clearly observed that as the magnetic perturbation time scale increases (with the
decrease in actuation frequency), the amount of aggregation of nanoparticles in the droplet increases as shown in Fig 6. This is because at lower actuation frequencies, the magnetic perturbation time scale was found to be higher as compared to viscous time scale resulting in migration of more nanoparticles towards the contact line during the ON cycle. Similarly, during
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the OFF cycle in case of lower actuation frequencies, aggregated nanoparticles from the ON cycle experienced higher viscous time scale resulting in either complete or partial dispersion of nanoparticles from clusters of aggregated nanoparticles as shown in Fig 6. A critical actuation frequency was observed (𝑓𝑐𝑟 = 0.5 Hz), above which no dispersion of nanoparticles from the aggregated nanoparticles at the contact line was observed during the OFF cycle of magnetic field. This is because magnetic perturbation time scale 𝑡𝑚 corresponding to frequencies above the critical
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aggregated nanoparticles during the OFF cycle of magnetic field.
Diffusion timescale (2 R)2 /
5 Hz 300
2.413
2.413
2.413
2.413
5
1
0.5
0.166
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Magnetic perturbation timescale (0.5 f )
Actuation frequencies (𝑓) 0.1 Hz 0.5 Hz 1 Hz 300 300 300
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Advective timescale 2 R / U B0
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Table 3: Calculation of various time scales Time scale (𝑠)
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frequency 𝑓𝑐𝑟 results in less relaxation time available for dispersion of nanoparticles from the
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of ro -p re lP ur na Jo Fig 6: (a) Bright field visualizations of the aggregation and dispersion of nanoparticles inside the ferrofluid droplet in the presence of magnetic field and (b) zoomed view of aggregation and dispersion of nanoparticles at the contact line of the droplet.
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3.4.2 µ-PIV measurements Fig 7 represent the temporal variation of the flow field inside the ferrofluid droplet in the presence of alternating magnetic field with actuation frequencies 𝑓 = 0.1, 0.5, 1 and 3 Hz respectively. It can be clearly observed that on the activation of magnetic field, a bulk motion towards the direction of the electromagnet was observed inside the droplet as evident from the velocity vectors (Left →
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Right) as shown in Fig 7 (see the supplementary videos). This is because of migration of nanoparticles towards the contact line near the vicinity of the electromagnet during the ON cycle
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as discussed in the previous section. Similarly, during the OFF cycle a bulk motion was observed
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inside the droplet in the direction opposite to the ON cycle as shown by the velocity vectors (Right → Left) in Fig 7. This bulk motion inside the droplet was resulted from dispersion of nanoparticles
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from the aggregated nanoparticles during the OFF cycle as discussed in the previous section. For all the cases of actuation frequencies, the magnitude of velocity of bulk flow inside the droplet was
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observed to decrease from time instant 𝜁 = 0+ to 𝜁 = 𝑇/4 during the ON cycle as shown in Fig 7. This is because of continuous aggregation of nanoparticles at the contact line from 𝜁 = 0+ – 𝜁 =
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𝑇/4, which reduces the strength of magnetic field inside the droplet resulting in lower magnetic force acting on nanoparticles at 𝜁 = 𝑇/4. During the OFF cycle, the magnitude of bulk motion inside the droplet was observed to be less as compared to the ON cycle as shown in Fig 7. This is
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because of weak dominance of magnetic force over the viscous force acting on nanoparticles during the OFF cycle. The black arrow in each velocity plot clearly indicates that two opposite bulk motion exist across the line of symmetry of the droplet during the ON and OFF cycle as shown in Fig 7. In order to quantify the strength of the circulation of the flow inside the droplet, we calculated the vorticity of the velocity field (𝜔𝑦 ) and is shown in Fig 8. The corresponding streamlines are also superimposed on the vorticity plot as shown in Fig 8. It can be clearly observed 22
that for all the cases of actuation frequencies, at 𝜁 = 0+ two opposite directed vorticity were generated inside the droplet due to the motion of bulk flow towards the electromagnet during the ON cycle. From 𝜁 = 0+ – 𝜁 = 𝑇/4, vorticity was observed to affected by the continuous aggregation of nanoparticles at the contact line as evident from the stream lines as shown in Fig 8. Similarly, during the OFF cycle dispersion of nanoparticles resulted in two opposite directed
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vorticity inside the droplet as compared to ON cycle as shown in Fig 8.
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of ro -p re lP ur na Jo Fig. 7: Instantaneous velocity field inside the ferrofluid droplet in the presence of magnetic field for different actuation frequencies. 24
of ro -p re lP ur na Jo Fig. 8: Instantaneous vorticity and corresponding streamlines inside the ferrofluid droplet in the presence of magnetic field of different actuation frequencies. 25
Fig 9 shows the variation of the total velocity (𝑈) along the diameter 𝑋 − 𝑋´ and 𝑍 − 𝑍´ of the droplet at different time instants for each case of actuation frequency respectively. In order to compare the effect of magnetic field, the total velocity in the absence of magnetic field (𝐵 = 0) is also superimposed in each plot as shown in Fig 9. It can be clearly observed that the magnitude of total velocity 𝑈 along the diameters 𝑋 − 𝑋´ and 𝑍 − 𝑍´ increased in the presence of magnetic
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field for a complete cycle (𝜁 = 0+ , 𝑇/4, 𝑇/2, 3𝑇/4) as compared to the case of no magnetic field. This is because of migration and dispersion of nanoparticles in the presence of magnetic field
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which resulted in a strong bulk motion inside the droplet as compared to negligible bulk motion in case of no magnetic field. For each case of actuation frequency, the velocity magnitude was found
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to decrease from time instant 𝜁 = 0+ to 𝜁 = 𝑇/4 because of the continuous aggregation of
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nanoparticles at the contact line as discussed in the previous section. During the OFF cycle (𝜁 = 𝑇/2 – 3𝑇/4), the velocity magnitude was found to decrease for all the cases of actuation
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frequencies as shown in Fig 9. This is because of dispersion of nanoparticles from the aggregated nanoparticles at the contact line resulting from strong viscous force acting on nanoparticles during
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the OFF cycle. An increase in velocity magnitude was observed with increase in actuation frequency as shown in Fig 9. This is resulted because with increase in actuation frequency, the magnetic perturbation time scale was found to be lower as compared to viscous time scale. Lower magnetic perturbation time scale with increasing actuation frequency resulted in partial retention
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of bulk flow from the previous ON cycle of magnetic field with no dispersion of nanoparticles at the contact line.
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of ro -p re lP ur na Jo Fig 9. Variation of the total velocity (𝑈) along the diameters 𝑋 − 𝑋´ and 𝑍 − 𝑍´ of the ferrofluid droplet at different time instants in the presence of magnetic field. 27
4. CONCLUSION The internal hydrodynamics of ferrofluid droplets plays an important role towards the magnetic field assisted evaporation or spreading or mixing of ferrofluid droplets. Though the opaqueness of ferrofluid limits the use of various velocity measurement techniques, the present study reports the possibility of using µ-PIV technique to measure the velocity field of ferrofluid flow in the presence
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of magnetic field. The present study reports the internal hydrodynamics of a sessile ferrofluid droplet in the presence of a time dependent magnetic field of different actuation frequencies.
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Application of magnetic field leads to migration of nanoparticles in the direction of magnetic field
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which in turn results in internal convection or bulk flow inside the ferrofluid droplet. The magnitude of internal convection is found to be a function of strength and frequency of applied
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magnetic field. A critical frequency of applied magnetic field is observed above which negligible dispersion of nanoparticles is observed at the contact line of the droplet during the OFF cycle of
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the magnetic field. Negligible dispersion of nanoparticles at critical frequency results in stagnant layers of nanoparticles near the contact line, which can be explored in future for the study of
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separation of cells or proteins using various markers/antibodies attached magnetic nanoparticles. As the strength of circulation of internal convection of the droplet is observed to be higher in the presence of magnetic field, such flow circulation can be effective for magnetic assisted mixing of
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reagents or fluids.
Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
ACKNOWLEDGEMENT The authors acknowledges the CIF, IIT Guwahati for the support in characterization of ferrofluid.
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The 3rd and 4th author acknowledges the financial grants obtained from DST-SERB through project
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No ECR/2016/000611 and ECR/2016/000702/ES respectively.
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051502-1--10.
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PII:
S0927-7757(19)31108-2
DOI:
https://doi.org/10.1016/j.colsurfa.2019.124116
Reference:
COLSUA 124116
To appear in:
Colloids and Surfaces A: Physicochemical and Engineering Aspects
Received Date:
5 August 2019
Revised Date:
29 September 2019
Accepted Date:
14 October 2019
Please cite this article as: Shyam S, Asfer M, Mehta B, Mondal PK, Almutairi ZA, Magnetic field driven actuation of sessile ferrofluid droplets in the presence of a time dependent magnetic field, Colloids and Surfaces A: Physicochemical and Engineering Aspects (2019), doi: https://doi.org/10.1016/j.colsurfa.2019.124116
This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2019 Published by Elsevier.
Magnetic field driven actuation of sessile ferrofluid droplets in the presence of a time dependent magnetic field Sudip Shyam1, Mohammed Asfer2*, Balkrishna Mehta 3*, Pranab K. Mondal1, Zeyad A Almutairi4 Department of Mechanical Engineering, IIT Guwahati, Guwahati, India
2
Department of Mechanical Engineering, College of Engineering, Dawadmi, Shaqra University, KSA
3
Department of Mechanical Engineering, IIT Bhilai, Bhilai, India
4
Department of Mechanical Engineering, College of Engineering, King Saud University, KSA
*
Corresponding author: E-mail: [email protected], Tel: +91-361-258-3439 Corresponding author: E-mail: [email protected], Tel: +966-50-900-4912
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Graphical Abstract
ABSTRACT The present paper reports actuation of sessile ferrofluid droplets over a hydrophobic substrate in the presence of a time-dependent magnetic field generated by an electromagnet. The internal hydrodynamics of the ferrofluid droplet in the presence of magnetic field are measured using both bright field visualization and micro-particle image velocimetry (µ-PIV) techniques. During ON
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cycle of the magnetic field, bright field visualizations show the migration of nanoparticles towards the contact line near the vicinity of the electromagnet resulting in aggregation of nanoparticles
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inside the droplet. Similarly aggregated nanoparticles at the contact line from the ON cycle are
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observed to disperse from the cluster of nanoparticles during the OFF cycle of the magnetic field. Both migration and dispersion of nanoparticles result in bulk motion inside the ferrofluid droplet
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during the ON and OFF cycle of the magnetic field. Velocity measurements from µ-PIV technique successfully validate the qualitative measurements of flow field from bright field visualization
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technique. A critical frequency is observed for the applied magnetic field above which negligible dispersion of nanoparticles resulted inside the ferrofluid droplet during the OFF cycle of the
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magnetic field.
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Keywords: Ferrofluid; Magnetic field; Droplet; Micro particle image Velocimetry.
Nomenclature: 𝑎𝑐𝑜𝑖𝑙
Cross sectional area of coil (𝑚)
𝐴𝑚
Magnetic vector potential
𝐴𝑠
Surface area of the droplet (𝑚2 ) 2
Magnetic flux density (𝑇)
𝐶𝑑
Drag coefficient
𝐷
Diameter of seeding particle (𝑚)
𝑓
Frequency (𝐻𝑧)
𝐹d
Drag force (𝑁), 𝐹𝑑 = 3𝜋𝜂𝐷𝑝 (𝑈𝑝 − 𝑈𝑓𝑓 )𝐶𝑑
𝐹 mp
Magnetophoresis Force (𝑁), 𝐹𝑚𝑝 = −𝑉𝜇0 (𝑀 ∙ ∇𝐻)𝐻
𝐻
Magnetic field (𝐴/𝑚)
𝐼
Current (𝐴)
𝐽𝑒
Current density (𝐴/𝑚)
𝑀
Magnetization (𝐴/𝑚)
𝑁
Number of turns
NA
Numerical Aperture
𝑅
Radius of the droplet (𝑚)
𝑇
Time period of one cycle (𝑠)
𝑡𝜈 𝑡𝑚
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𝑈
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𝑡𝑎
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𝐵
Advective time scale (𝑠), 𝑡𝑎 = 2𝑅/𝑈𝐵=0 Viscous/diffusion time scale (𝑠), 𝑡𝑑 = (2𝑅)2 /𝜈 Magnetic perturbation time scale (𝑠), 𝑡𝑚 = 0.5𝑓 Velocity (𝑚/𝑠)
𝑉
Volume of seeding particle (𝑚3 )
𝜔𝑦
Vorticity (1/𝑠), 𝜔𝑦 = ( 𝜕𝑥 − 𝜕𝑧 )
𝜕𝑤
𝜕𝑢
Symbols
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Kinematic viscosity (m2 s)
𝜇
Permeability (m kg s-2 A-2)
𝜌
Density (Kg/m3)
𝜎
Electrical conductivity of coil (s/m)
Surface tension (N/m)
𝜃
Contact angle (degree)
𝜁
Time (𝑠)
𝜒
Magnetic susceptibility
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𝜈
Subscript Critical
𝑑
Drag
𝑚
Magnetic
mp
Magnetophoresis
𝑝
Particle
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𝑓𝑓
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𝑐𝑟
ferrofluid
Non-dimensional numbers
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Bo
Magnetic Bond Number, 𝐵𝑜 = 2𝜇0 𝐻 2 𝑅/𝛾
U*
Non-diemnsionalized velocity, 𝑈 ∗ = 𝑈/𝑈𝑚𝑎𝑥
We
Weber number 𝑊𝑒 = 𝜇0 |𝑀2 |𝑈/𝛾𝐴𝑠 ,
Z*
Non-dimensional length along Z-direction, 𝑍 ∗ = 𝑍/𝑅
X*
Non-dimensional length along X-direction, 𝑋 ∗ = 𝑋/𝑅
Constants 𝜇0
Permeability of free space 4
1. INTRODUCTION Controlled actuation of droplets on a planar surface using different actuation concepts such as electrostatic forces [1, 2], thermocapillarity [3], acoustics [4], and magnetism [5, 6] have been the subject of theoretical and experimental investigations among the researchers for the last decade.
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Compared to different actuation concepts, droplet manipulation using magnetism offers several
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advantages. Droplets can be manipulated from a distance using magnetic field which is not in contact with the liquid. Furthermore, magnetic field based manipulation are relatively more
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tolerable to liquid properties compared to electric field based manipulation which are found to highly dependent on the conductivity and permittivity of the liquid that forms the droplet [7].
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Ferrofluids because of its magnetic properties provide a viable option for the choice of fluid for
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the magnetic based platforms for manipulation of droplets. Ferrofluids are synthesized as a stable colloidal suspension of iron oxide (Fe3O4) nanoparticles dispersed in a carrier liquid such as water or oil [8]. Nanoparticles in ferrofluid are normally coated with a surfactant in order to prevent
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agglomeration by overcoming the attractive van der Waals forces between the nanoparticles. The presence of iron oxide nanoparticles in ferrofluid provides the ability to control/actuate the droplet using a magnetic field. In the absence of magnetic field, nanoparticles in ferrofluid are randomly
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oriented with the overall magnetization of ferrofluid being zero. With the application of magnetic field, nanoparticles in ferrofluid exhibit super - paramagnetic characteristics with a magnetic moment oriented in the direction of applied magnetic field. Over the past decade, several studies related to ferrofluid based mixing [9-14], spreading/wetting on a substrate [15-17], evaporation or drying pattern [18, 19] in the presence of magnetic field or no magnetic field are reported in literature. For ferrofluid based phenomenon as discussed above, 5
the hydrodynamics of ferrofluid in the presence of magnetic field plays an important role, where nanoparticles of ferrofluid migrate in the direction of magnetic field which in turn induces a flow called magnetoconvetion in ferrofluid. This magnetoconvection may result in enhanced mixing between fluids or controlled spreading or evaporation of ferrofluids in the presence of magnetic field. Quantitative measurements of convection or velocity of nanofluids (e.g. ferrofluids) can be obtained experimentally using either µ-PIV or PTV technique. µ-PIV technique provides the
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velocity information by tracing seeding particles added to nanofluid whereas PTV technique
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provides the velocity information by tracing the individual nanoparticles of nanofluid. Very few studies related to velocity measurements of nanofluids using µ-PIV or PTV technique are available
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in literature [20-23]. However velocity measurements of nanofluids in particular for ferrofluids in
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the presence of magnetic field is not available till date. With this background, the present study reports the internal hydrodynamics of a sessile ferrofluid droplet subjected to a time dependent
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magnetic field using µ-PIV technique. Both bright field visualizations and µ-PIV measurements were carried out in order to understand the internal hydrodynamics of the ferrofluid droplet in the
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presence of magnetic field. Time dependent magnetic field with different actuation frequencies were applied in order to study the effect of actuation frequency on the internal hydrodynamics of the ferrofluid droplet.
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2. MATERIALS AND METHODS
2.1 Preparation and Characterization of Ferrofluid Iron oxide nanoparticle (IONPs) were synthesized chemically by the co-precipitation reaction from an aqueous mixture of Fe+3/Fe+2 in the molar ratio of 2:1 by using concentrated ammonium hydroxide solution in an inert atmosphere of nitrogen. After the co-precipitation of magnetic nanoparticles, oleic acid (5–50% (w/w), related to the weight of IONPs) was added as a stabilizer 6
for the synthesis of OA-IONPs. After 30 min of reaction, the temperature was elevated to 100-110 °C in order to remove excess of water and ammonium hydroxide. One gram of OA-IONPs as received above was added to 6.0 g of n-hexane to form an organic dispersion. For the aqueous phase transfer of the above dispersion, 20 mL of aqueous solution of sodium lauryl sulphate (10– 60% (w/w) was added to it at 500 rpm for 1 hour. The added sodium lauryl sulphate act as a surfactant which prevents agglomeration of nanoparticles. The mixture was then subjected to
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sonication twice for 2 min at 90% amplitude with a sonicator (Branson Sonifier W450) in an ice-
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cooled bath followed by the evaporation of n-hexane under continuous stirring at 80 °C for 3 hour. The water loss was compensated by addition of 2 mL of water in every 30 min in order to obtain
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a stable water-based ferrofluid of OA-IONPs (0.5% w/v) as shown in Fig. 1(a). The detailed
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procedure for the synthesis of water-based ferrofluid can be found in our earlier work [24, 25]. Ferrofluid with such a low volume fraction of nanoparticles (0.5%) was used in the present study
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as the non-transparent nature of ferrofluid affects the visibility of seeding particles added to ferrofluid during the µ-PIV measurments [26]. Secondly ferrofluids with such a low volume
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fraction of nanoparticles is assumed as a single phase fluid where nanoparticles are freely suspended in the carrier liquid. The various thermophysical properties of the ferrofluid are mentioned in Table 1. The magnetization curve of the water-based ferrofluid as measured by the vibration sample magnetometer (VSM) is shown in Fig. 1(b). This data illustrates the super-
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paramagnetic characteristic of the ferrofluid. The nanoparticles have an average size of around 50 ± 2 nm as shown in Fig 1(c) as measured by dynamic light scattering (DLS) technique. The absolute zeta potential of the ferrofluid was found to be 53 mV (Fig. 1(d)) and for an absolute value of zeta potential higher than 25 – 30 mV, it is generally accepted that the particles are electrostatically stable [27].
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Table 1: Thermophysical properties of water and prepared ferrofluid (at 30 °C) Specific heat
Thermal conductivity
Viscosity
(Kg m-3)
(J (Kg K)-1)
(W (m K)-1)
(Pa s)
Water
995
4180
0.6
0.0009 0.00001
Ferrofluid
1022
3425
0.7
0.00106 0.00001
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Density
Fig 1. (a) Prepared ferrofluid sample, (b) magnetization curve of ferrofluid, (c) particle size distribution of ferrfluid and (d) zeta potential of ferrofluid.
2.2 Fabrication of hydrophobic substrate and electromagnet
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The hydrophobic substrate used in the present experiments was fabricated by coating a thin layer of PDMS on a glass slide using a spin coater (EZspin-ADV). PDMS was poured directly on the glass slide mounted on the spin coater rotating at 2000 rpm for 50 seconds. The PDMS coated glass slide was then kept at 80 º C in an oven for 1 hour in order to cure PDMS. The PDMS coated glass slide was then tested for hydrophobicity towards water and ferrofluids. The PDMS layer on the glass slide was found to be chemically insensitive as no absorption was observed for ferrofluid
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and water on PDMS layer. For the contact angle measurements of droplets, a goniometer imaging
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set up was used as shown in Fig. 2(a). Droplets were kept on the substrate using a droplet dispensing module (Acam-NSC). A CMOS camera (Nikon, D5200) was used to capture the
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images and a white light source along with a diffuser was used to illuminate the droplet. Image J
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software was used to calculate the contact angle and diameter of the droplets. The contact angle of water on PDMS coated glass slide was found to be 105 ± 0.8° whereas for untreated surface i.e.
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for glass slide it was found to be 44 ± 0.6°. Similarly the contact angle was found to be 63 ± 2.05° and 34 ± 2.15° for ferrofluid on the PDMS coated glass slide and the untreated glass slide
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respectively. An electromagnet was fabricated by winding 26 SWG enamel coated copper wires ( ~ 20 turns per cm) over a 6 mm diameter and 100 mm long iron core and was kept at a distance of 𝑥𝑚𝑎𝑔 = 1.5 mm from the droplet as shown in Fig 2(b). The electromagnet was activated by supplying current from a DC power source (32 V/ 5 A). For generating alternating magnetic field,
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an in-house built digital circuit was used to supply a pulse current to the electromagnet. Alternating magnetic field of strength 𝐵 = 340 G and actuation frequencies 𝑓 = 0.1, 0.5, 1.0 and 3 Hz were applied to the ferrofluid droplet. Fig 2(c) shows the evaporation of the ferrofluid droplet in the presence of no magnetic field up to 𝜁 = 400 seconds. It can be observed that the rate of evaporation of ferrofluid droplet was very slow for initial period of time up to 𝜁 < 30 seconds,
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whereas the rate of evaporation became significant for later period of time i.e. for 𝜁 > 100
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seconds.
Fig 2. (a) Goniometric imaging set up for contact angle measurment, (b) schematic of droplet -
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electromagnet arrangement and (c) images showing rate of evaporation of ferrofluid droplet in the absence of magnetic field. 2.3 Bright field imaging and µ-PIV system Bright field visualisations of internal convection or bulk flow of ferrofluid droplet were carried out using an inverted microscope (Leica: DM IL LED) as shown in Fig 3. The droplet –
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electromagnet set up was kept over the stage of the inverted microscope and the droplet was illuminated from below the microscope stage though a 10X objective lens (NA = 0.25) using a mercury lamp. Under bright field visualizations mode, nanoparticles of ferrofluid were appeared as black particles with a white background. In order to visualize the chain like cluster of nanoparticles during aggregation, a higher magnification objective lens 20X (NA = 0.4) was used. Similarly, during µ-PIV measurements of internal convection of ferrofluid droplet, an inverted
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microscope with a florescent light source was used as shown in Fig 3. Fig 3 shows the schematic
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of the µ-PIV system. It consists of three main components: (a) an inverted microscope (Leica: DM IL LED), (b) a florescent light source and (c) a CCD camera. For µ-PIV measurements the
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ferrofluid droplet was seeded with 1 µm diameter fluorescent microspheres (Molecular Probes
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Inc.) with a dilution of 1:200 (v/v). The above seeding particle concentration was chosen as it provided acceptably low noise levels under the present illumination conditions. The droplet –
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electromagnet set up was kept over the stage of the inverted microscope and the droplet was illuminated by a green light of wavelength of 530 nm from below the microscope stage though a
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10X objective lens (NA = 0.25). The fluorescent seeding particles in the ferrofluid droplet were then excited with green light, which emitted light at a peak wavelength of 590 nm. An epi – fluorescent prism filter was used on the optical path in order to eliminate the background light such that only the emitted light from seeding particles reached the CCD camera of the µ-PIV system.
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Under fluorescent visualization mode, seeding particles added to ferrofluid were appeared as fluorescent particles with a black background. Fluorescent images of seeding particles were captured using a 12 bit 1344 × 1244 pixels2 CCD camera and then transferred to a computer for further image processing. Double images were captured per realization in such a way that seeding particles moved approximately 1/4th size of the interrogation window used for correlation between
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two consecutive images. Before carrying out cross correlation algorithm raw µ-PIV images were overlapped using Image J software. Image overlapping prior to correlation was carried out to increase the number of seeding particles per interrogation window resulting in easy peak detection during cross correlation algorithm. A cross correlation algorithm with interrogation size 64 × 64 pixels2 and 50% overlapping between interrogation windows was used to calculate the
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instantaneous velocity vector field inside the droplet using PIVLab plugin by Matlab V 12 [28].
Fig 3: Schematic of the bright field imaging/µ-PIV set up
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3. RESULTS AND DISCUSSIONS
3.1 Magnetic flux density distribution
The distribution of magnetic flux density (𝐵) in the droplet region was simulated using the COMSOL Multiphysics V 5.3 software. The governing equations and parameters used for the simulation of magnetic field are presented in Table 2. Free tetrahedral mesh of maximum element 12
size of 1 mm, with a total of 2.1 × 106 elements, was used in the present simulations. A stationary MUMPS solver with absolute tolerance of 10-6 was used for simulating the magnetic field generated by the electromagnet. Fig. 4(b) shows the simulated magnetic flux density distribution around the droplet. Along the diameter 𝑍 − 𝑍´ of the droplet, the magnetic flux density was found to be nearly constant, whereas a magnetic field gradient was present along the diameter 𝑋 − 𝑋´ of
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the droplet as shown in Fig. 4(c). In order to validate the simulation results, the magnetic flux density produced by the electromagnet was measured using a gauss meter and was compared with
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the simulation results as shown in Fig. 4(d). A good match between the two validates the various
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parameters and equations used for the simulation of magnetic field.
Table 2. Governing equations and parameters used for COMSOL simulation of magnetic field
Am 1 1 ( 0 r B) B J e t
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B Am
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Governing Equations
NI Je acoil
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Current (𝐼)
1.5 A
2.82 × 10-5 m2
Number of turns (𝑁)
200
Electrical conductivity of coil (𝜎)
5.96 × 107 s/m
Relative permeability of air (𝜇𝑟 )
1
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Cross section area of coil (𝑎𝑐𝑜𝑖𝑙 )
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Fig. 4: (a) Meshing of computational domain for magnetic field (b) Distribution of magnetic flux
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density (𝐵) around the droplet region (c) variation of magnetic flux density along the diameters (𝑋 − 𝑋´ and 𝑍 − 𝑍´) of the droplet and (d) validation of simulation results with measurements from gauss meter.
3.2 Scaling analysis
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Various scaling analysis were carried out in the present work. First scaling analysis was carried out for translational motion of the ferrofluid droplet towards the electromagnet from the position where it was originally deposited on the PDMS coated glass slide. In the presence of magnetic field, the resultant of surface tension and magnetic force acting on the droplet determines the translational motion of the droplet towards the electromagnet. For the present study above two forces were evaluated by calculating the Weber number (𝑊𝑒𝑚 ) and magnetic Bond number 14
(𝐵𝑜) respectively. Weber number was found to be 𝑊𝑒𝑚 ~ 10−3 as compared to magnetic Bond number 𝐵𝑜 ~ 0.96 indicating higher dominance of surface tension compared to the magnetic force resulting in negligible change in spherical shape of the droplet with no translational velocity towards the electromagnet. The droplet was therefore observed to actuate at the same position in the presence of magnetic field where the droplet was initially deposited on the PDMS coated glass
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slide. The details of calculations of Weber and magnetic Bond number are mentioned in the nomenclature section.
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A second scaling analysis was carried out to find the amount of negative magnetophoresis acting
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on seeding particles in ferrofluid in the presence of magnetic field during µ-PIV measurements. The negative magnetophoresis is usually encountered by a non-magnetic body like seeding
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particles dispersed in a magnetic medium like ferrofluid in the presence of a magnetic field [29, 30]. Zhu et al. carried out analytical study on transport of non-magnetic particles in a diluted
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ferrofluid in the presence of magnetic field produced by a permanent magnet [31]. They reported that deflection of non-magnetic particles due to negative magnetophoresis can be minimized with
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the use of diluted ferrofluids and a low strength of applied magnetic field. The negative magnetophoretic force (𝐹𝑚𝑝 ) and viscous drag force (𝐹𝑑 ) acting on seeding particles under the present experimental conditions were calculated and the ratio between the two was found to be 𝐹𝑚𝑝
~ 10−7, indicating negligible deflection of seeding particles due to negative magnetophoresis.
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𝐹𝑑
Therefore seeding particles were observed to follow the bulk flow faithfully inside the droplet in the presence of magnetic field during the µ-PIV measurements.
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3.3 Internal hydrodynamics of ferrofluid droplet in absence of magnetic field Before conducting experiments in the presence of magnetic field, the internal convection or bulk flow present inside the ferrofluid droplet was measured in the absence of magnetic field using µPIV measurements. Ferrofluid in the absence of magnetic field behaves like any other nanofluid with nanoparticles freely dispersed in carrier fluid. Several studies have been carried out on
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internal hydrodynamics of a sessile liquid droplet over a hydrophobic surface, where buoyancy driven Rayleigh convection results in downward motion of fluid along the interface and an upward
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plume like flow at the center region of the droplet [19, 32-34]. Fig 5(a) shows the velocity field
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inside the ferrofluid droplet in the absence of magnetic field which shows a radial inward motion towards the center region of the droplet similar to the studies as discussed above. The inward
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motion of the fluid resulted in a plume like flow in the center region which was subsequently travelled towards the contact line region near the air – liquid interface of the droplet. In order to
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validate our study, a comparison of 𝑈 ∗ - velocity profile along the diameter of the ferrofluid droplet is carried out with the literature as shown in Fig 5(b). A good match between the two validates the
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present study and confirms the feasibility of using µ-PIV technique for velocity measurements of
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nanofluids like ferrofluids.
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Fig. 5: (a) Velocity field inside the ferrofluid droplet in the absence of magnetic field, and (b) comparison
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of 𝑈 ∗ velocity profile along the diameter (𝑍 − 𝑍 ´ ) of the droplet with the literature.
3.4 Internal hydrodynamics of droplet in the presence of magnetic field
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As the rate of evaporation of droplet was observed to be negligible for 𝜁 < 30 seconds as discussed in section 2.2, it indicates that bright field visualizations and µ-PIV measurements of internal hydrodynamics of ferrofluid in the presence of magnetic field can be conducted precisely up to time scale 𝜁 < 30 seconds considering negligible evaporation from the ferrofluid droplet. The
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maximum time scale corresponding to actuation frequency 𝑓 = 0.1 Hz of applied magnetic field was calculated to be 𝜁 = 10 seconds, which was found to be less than the time scale for negligible evaporation i.e. 𝜁 < 30 seconds.
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3.4.1 Bright field visualizations The ferrofluid droplet was subjected to an alternating magnetic field of strength 𝐵 = 340 G and actuation frequencies 𝑓 = 0.1, 0.5, 1 and 3 Hz. Bright field visualizations were carried out for each case (see the supplementary videos) and are shown in Fig. 6 respectively. For each case, bright field images are shown at time intervals 𝜁 = 0+, /4, 𝑇/2, 3𝑇/4, and 𝑇 respectively as shown
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in Fig 6(a). The time stamp 𝜁 = 0+ represents the instant when the magnetic field was just ON resulting in actuation of the ferrofluid droplet in the direction of the applied magnetic field. During
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the ON cycle of the operation of the electromagnet (𝜁 = 0+ – 𝑇/4), IONPs in ferrofluid were
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observed to migrate through the droplet towards the magnetic zone near the vicinity of the electromagnet. Migration of nanoparticles resulted in bulk motion of ferrofluid towards the contact
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line near the vicinity of the electromagnet (See the bright field videos). In the presence of magnetic field, the inter particle dipole – dipole interaction resulted in chain like cluster of nanoparticles
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within the aggregate near the contact line as shown in the zoomed view in Fig 6(b) [35]. In the absence of magnetic field, random orientation of magnetic moments of nanoparticles resulting in
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negligible dipolar attraction between the nanoparticles. However in the presence of magnetic field, magnetic moments of nanoparticles are orientated in the direction of applied magnetic field resulting in chain like clusters of nanoparticles as shown in Fig 6(b). During the OFF cycle of the
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electromagnet (𝜁 = 𝑇/2, 3𝑇/4, 𝑇), nanoparticles were observed to disintegrate from the chain like clusters and were dispersed freely within the droplet as shown in Fig 6(b). This was because of random orientation of magnetic moments of nanoparticles in the absence of magnetic field as discussed above. Similar to the migration of nanoparticles, dispersion of nanoparticles during the OFF cycle resulted in bulk motion of ferrofluid in the direction opposite to the ON cycle as visualized from the supplementary videos. 18
In order to study the effect of actuation frequencies on the migration and dispersion of IONPs in the droplet, various time scales involved with the present study were evaluated such as; advective time scale (𝑡𝑎 ), diffusion/viscous time scale (𝑡𝜈 ), and magnetic perturbation time scale (𝑡𝑚 ). All the above timescales were calculated for each case of actuation frequency and are mentioned in Table 3. As the advective time scale 𝑡𝑎 was found to be very high and constant for
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all the cases, the effect of advective time scale is not discussed further. Therefore, the migration, aggregation at the contact line and then dispersion of nanoparticles during one complete cycle of
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operation of the electromagnet were found to depend on the balance between the diffusion time scale 𝑡𝜈 and magnetic perturbation time scale 𝑡𝑚 . During the ON cycle of magnetic field
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aggregation of nanoparticles was observed in the droplet for time interval 𝜁 = 0 to 𝑇/4 as shown
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in Fig 6(a) and 6(b). This is because during time interval 𝜁 = 0 to 𝑇/2, nanoparticles experienced higher magnetic force compared to viscous force resulting in aggregation of nanoparticles in the
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droplet. The time interval 𝜁 = 𝑇/2 corresponds to case when the magnetic field was just OFF. During the OFF cycle i.e. from 𝜁 = 𝑇/2 to 3𝑇/4, strong dominance of the viscous force compared
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to the magnetic force acting on nanoparticles resulted in release/disperse of nanoparticles from the cluster of nanoparticles as shown in Fig 6(a) and 6(b). Both migration and dispersion of nanoparticles during the ON and OFF cycle of the magnetic field resulted in a bulk motion of ferrofluid in the droplet.
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It can be clearly observed that as the magnetic perturbation time scale increases (with the
decrease in actuation frequency), the amount of aggregation of nanoparticles in the droplet increases as shown in Fig 6. This is because at lower actuation frequencies, the magnetic perturbation time scale was found to be higher as compared to viscous time scale resulting in migration of more nanoparticles towards the contact line during the ON cycle. Similarly, during
19
the OFF cycle in case of lower actuation frequencies, aggregated nanoparticles from the ON cycle experienced higher viscous time scale resulting in either complete or partial dispersion of nanoparticles from clusters of aggregated nanoparticles as shown in Fig 6. A critical actuation frequency was observed (𝑓𝑐𝑟 = 0.5 Hz), above which no dispersion of nanoparticles from the aggregated nanoparticles at the contact line was observed during the OFF cycle of magnetic field. This is because magnetic perturbation time scale 𝑡𝑚 corresponding to frequencies above the critical
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aggregated nanoparticles during the OFF cycle of magnetic field.
Diffusion timescale (2 R)2 /
5 Hz 300
2.413
2.413
2.413
2.413
5
1
0.5
0.166
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Magnetic perturbation timescale (0.5 f )
Actuation frequencies (𝑓) 0.1 Hz 0.5 Hz 1 Hz 300 300 300
re
Advective timescale 2 R / U B0
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Table 3: Calculation of various time scales Time scale (𝑠)
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frequency 𝑓𝑐𝑟 results in less relaxation time available for dispersion of nanoparticles from the
20
of ro -p re lP ur na Jo Fig 6: (a) Bright field visualizations of the aggregation and dispersion of nanoparticles inside the ferrofluid droplet in the presence of magnetic field and (b) zoomed view of aggregation and dispersion of nanoparticles at the contact line of the droplet.
21
3.4.2 µ-PIV measurements Fig 7 represent the temporal variation of the flow field inside the ferrofluid droplet in the presence of alternating magnetic field with actuation frequencies 𝑓 = 0.1, 0.5, 1 and 3 Hz respectively. It can be clearly observed that on the activation of magnetic field, a bulk motion towards the direction of the electromagnet was observed inside the droplet as evident from the velocity vectors (Left →
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Right) as shown in Fig 7 (see the supplementary videos). This is because of migration of nanoparticles towards the contact line near the vicinity of the electromagnet during the ON cycle
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as discussed in the previous section. Similarly, during the OFF cycle a bulk motion was observed
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inside the droplet in the direction opposite to the ON cycle as shown by the velocity vectors (Right → Left) in Fig 7. This bulk motion inside the droplet was resulted from dispersion of nanoparticles
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from the aggregated nanoparticles during the OFF cycle as discussed in the previous section. For all the cases of actuation frequencies, the magnitude of velocity of bulk flow inside the droplet was
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observed to decrease from time instant 𝜁 = 0+ to 𝜁 = 𝑇/4 during the ON cycle as shown in Fig 7. This is because of continuous aggregation of nanoparticles at the contact line from 𝜁 = 0+ – 𝜁 =
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𝑇/4, which reduces the strength of magnetic field inside the droplet resulting in lower magnetic force acting on nanoparticles at 𝜁 = 𝑇/4. During the OFF cycle, the magnitude of bulk motion inside the droplet was observed to be less as compared to the ON cycle as shown in Fig 7. This is
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because of weak dominance of magnetic force over the viscous force acting on nanoparticles during the OFF cycle. The black arrow in each velocity plot clearly indicates that two opposite bulk motion exist across the line of symmetry of the droplet during the ON and OFF cycle as shown in Fig 7. In order to quantify the strength of the circulation of the flow inside the droplet, we calculated the vorticity of the velocity field (𝜔𝑦 ) and is shown in Fig 8. The corresponding streamlines are also superimposed on the vorticity plot as shown in Fig 8. It can be clearly observed 22
that for all the cases of actuation frequencies, at 𝜁 = 0+ two opposite directed vorticity were generated inside the droplet due to the motion of bulk flow towards the electromagnet during the ON cycle. From 𝜁 = 0+ – 𝜁 = 𝑇/4, vorticity was observed to affected by the continuous aggregation of nanoparticles at the contact line as evident from the stream lines as shown in Fig 8. Similarly, during the OFF cycle dispersion of nanoparticles resulted in two opposite directed
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vorticity inside the droplet as compared to ON cycle as shown in Fig 8.
23
of ro -p re lP ur na Jo Fig. 7: Instantaneous velocity field inside the ferrofluid droplet in the presence of magnetic field for different actuation frequencies. 24
of ro -p re lP ur na Jo Fig. 8: Instantaneous vorticity and corresponding streamlines inside the ferrofluid droplet in the presence of magnetic field of different actuation frequencies. 25
Fig 9 shows the variation of the total velocity (𝑈) along the diameter 𝑋 − 𝑋´ and 𝑍 − 𝑍´ of the droplet at different time instants for each case of actuation frequency respectively. In order to compare the effect of magnetic field, the total velocity in the absence of magnetic field (𝐵 = 0) is also superimposed in each plot as shown in Fig 9. It can be clearly observed that the magnitude of total velocity 𝑈 along the diameters 𝑋 − 𝑋´ and 𝑍 − 𝑍´ increased in the presence of magnetic
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field for a complete cycle (𝜁 = 0+ , 𝑇/4, 𝑇/2, 3𝑇/4) as compared to the case of no magnetic field. This is because of migration and dispersion of nanoparticles in the presence of magnetic field
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which resulted in a strong bulk motion inside the droplet as compared to negligible bulk motion in case of no magnetic field. For each case of actuation frequency, the velocity magnitude was found
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to decrease from time instant 𝜁 = 0+ to 𝜁 = 𝑇/4 because of the continuous aggregation of
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nanoparticles at the contact line as discussed in the previous section. During the OFF cycle (𝜁 = 𝑇/2 – 3𝑇/4), the velocity magnitude was found to decrease for all the cases of actuation
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frequencies as shown in Fig 9. This is because of dispersion of nanoparticles from the aggregated nanoparticles at the contact line resulting from strong viscous force acting on nanoparticles during
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the OFF cycle. An increase in velocity magnitude was observed with increase in actuation frequency as shown in Fig 9. This is resulted because with increase in actuation frequency, the magnetic perturbation time scale was found to be lower as compared to viscous time scale. Lower magnetic perturbation time scale with increasing actuation frequency resulted in partial retention
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of bulk flow from the previous ON cycle of magnetic field with no dispersion of nanoparticles at the contact line.
26
of ro -p re lP ur na Jo Fig 9. Variation of the total velocity (𝑈) along the diameters 𝑋 − 𝑋´ and 𝑍 − 𝑍´ of the ferrofluid droplet at different time instants in the presence of magnetic field. 27
4. CONCLUSION The internal hydrodynamics of ferrofluid droplets plays an important role towards the magnetic field assisted evaporation or spreading or mixing of ferrofluid droplets. Though the opaqueness of ferrofluid limits the use of various velocity measurement techniques, the present study reports the possibility of using µ-PIV technique to measure the velocity field of ferrofluid flow in the presence
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of magnetic field. The present study reports the internal hydrodynamics of a sessile ferrofluid droplet in the presence of a time dependent magnetic field of different actuation frequencies.
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Application of magnetic field leads to migration of nanoparticles in the direction of magnetic field
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which in turn results in internal convection or bulk flow inside the ferrofluid droplet. The magnitude of internal convection is found to be a function of strength and frequency of applied
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magnetic field. A critical frequency of applied magnetic field is observed above which negligible dispersion of nanoparticles is observed at the contact line of the droplet during the OFF cycle of
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the magnetic field. Negligible dispersion of nanoparticles at critical frequency results in stagnant layers of nanoparticles near the contact line, which can be explored in future for the study of
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separation of cells or proteins using various markers/antibodies attached magnetic nanoparticles. As the strength of circulation of internal convection of the droplet is observed to be higher in the presence of magnetic field, such flow circulation can be effective for magnetic assisted mixing of
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reagents or fluids.
Declaration of interests The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
28
The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
ACKNOWLEDGEMENT The authors acknowledges the CIF, IIT Guwahati for the support in characterization of ferrofluid.
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The 3rd and 4th author acknowledges the financial grants obtained from DST-SERB through project
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No ECR/2016/000611 and ECR/2016/000702/ES respectively.
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