Transport of a sessile aqueous droplet over spikes of oil based

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Transport of a sessile aqueous droplet over spikes of oil based ferrofluid in presence of a magnetic field Chiranjit Mandal, UTSAB BANERJEE, and Ashis K. Sen Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.9b00631 • Publication Date (Web): 29 May 2019 Downloaded from http://pubs.acs.org on May 31, 2019

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Transport of a sessile aqueous droplet over spikes of oil based ferrofluid in presence of a magnetic field C. Mandal, U. Banerjee, A. K. Sen* Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai-600036, India *Author to whom correspondence should be addressed. Email: [email protected] Both first and second authors have contributed equally.

ABSTRACT Droplets can be used as carrier vehicles for the transportation of biological and chemical reagents. Manipulation of waterand oil- based ferromagnetic droplets in presence of magnetic field have been well-studied. Here, we elucidate the transport of a sessile aqueous (diamagnetic) droplet placed over spikes of oil-based ferrofluid (FF) in presence of a non-uniform magnetic field. An oil-based FF droplet, dispensed over a rigid oleophilic surface, interacts with a magnetic field to get transformed into an array of spikes which then act as a carrier for the transportation of the aqueous droplet. Our study reveals that transportation phenomena is governed by the interplay of three different forces – magnetic force , frictional force ) and magnetic Bond and interfacial tension force , which is expressed in terms of the magnetic Laplace number 1 1 ) as =( =( ) and ). Based on the values of the dimensionless numbers, three number ( different regimes – steady droplet transport, spike extraction and magnet disengagement, are identified. It is found that steady 1 1 1 1 and 1, whereas extraction of spikes is observed for 1 and droplet transport is observed for 1 1 > 1, and magnet disengagement is observed for > 1. In the steady droplet transport regime, velocity of the ~ aqueous droplet was found to be dependent on the volumes of the aqueous droplet and FF droplet following 0.19 0.36 . A simple model is presented that accurately predicts the aqueous droplet velocity within 5% of the corresponding experimental data. In the spike extraction regime, the spike extraction distance was found to vary with , and the magnet velocity following ~ 1.75 0.75 1.56. INTRODUCTION Precise manipulation of aqueous droplets is receiving enormous attention from the microfluidic community due to its unique features such as low sample volume and cost effectiveness and various applications such as cell sorting1 and biochemical analysis2. Moreover, droplets can be used as the carrier vehicle for the transportation of biological3 and chemical reagents4. The area of droplet microfluidics can be classified as open and closed channel microfluidics5. Droplets in open geometries deal with the manipulation of individual droplets (of volume nL to µL) on engineered surfaces. On the other hand, in closed geometries, droplets (of volume pL to nL) are continuously generated and manipulated in a confined space such as inside a microchannel6–9. Drop manipulation techniques can be classified into active and passive methods. Active methods involve external fields to facilitate droplet manipulation e.g. electrowetting10, magnetic field11,12 and optical force13, whereas passive methods employ the surface morphology to execute manipulations e.g. Laplace pressure gradient14 and surface wettability14,15, chemically heterogeneous surfaces16. Magnetic field-based manipulation being non-contact and biocompatible, exhibits prodigious advantages over other active manipulation techniques. Depending on magnetic behaviour of objects, magnetic manipulation can be classified as positive and negative magnetophoresis. Positive magnetophoresis17 embraces manipulation of paramagnetic or ferromagnetic objects inside a diamagnetic medium. In contrary, negative magnetophoresis18 demonstrates manipulation of diamagnetic objects inside a paramagnetic or ferromagnetic medium. Magnetic medium can be synthesised by mixing magnetic particles or paramagnetic salts into a non-magnetic medium (oil/water/organic solvents). Microdroplets containing magnetic particles19 or magnetic marbles20 can be manipulated on superhydrophobic (SH) surfaces using magnetic fields. It was found that at concentrations ranging between 0.1-10% (by weight), these microparticles form chains, which is responsible for the droplet manipulation. Manipulation of droplets containing paramagnetic salts on SH surfaces using permanent magnets has been studied21, where several kinds of paramagnetic salts of different molar magnetic susceptibilities have been used to show a parametric comparison. A detailed study22 reported magnetic manipulation of oil coated aqueous droplets in which magnetic beads are internalized; three important operating regimes were found which delineates droplet motion. These magnetic particles can also be used to fabricate magnetic platforms for droplet manipulation on open surfaces. A recent study12 reports the fabrication of a soot-wax coated SH surface in which iron particles are embedded in PDMS. A local deformation created due to the interaction between the permanent magnet and the iron particles drives the droplets on the surface. Due to the large size, magnetic particles agglomerate in presence of magnetic field, and may get completely extracted from the carrier fluid, which is undesirable for practical applications. This issue can be conquered using ferrofluids in which magnetic nanoparticles are stabilized by surfactants to restrict the inter-particle interactions.

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Ferrofluids (FF) are the colloidal suspensions of ferromagnetic particles (~10 nm) suspended in oil or water exhibiting magnetization in presence of a magnetic field. The high affinity of ferrofluids toward magnetic field opens up opportunity for several microfluidic applications23–25. A detailed study26 reports the effect of magnetic field on shape, contact angle and motion of ferrofluid droplets on a planar surface. The apparent contact angle is found to reduce with increase in magnetic flux. Shape evolution and subsequent splitting of aqueous ferrofluid droplets on hydrophobic surface has been experimentally studied27. Interplay between the magnetic force and surface tension force governs the shape change and splitting of FF droplets in the presence of a permanent magnet. Aqueous FF droplets dispensed on a superhydrophobic surface get splitted28,29 when a perpendicular magnetic field (above a critical value) is applied. The droplets self-assemble (simple patterns) under a static magnetic field and can be switched to complicated patterns by applying a time varying magnetic field. A similar behaviour is found where an oil based ferrofluid droplet splits30 into daughter droplets when a perpendicular magnetic field is applied at the bottom of the droplet. Since most of the techniques demonstrate manipulation of water- or oil- based ferrofluid droplets or droplets containing magnetic particles, the manipulation of aqueous droplets using magnetic fluids has not been addressed. Although several techniques32 have been reported for the manipulation of droplets using magnetic fields on various surfaces, from the practical application point of view, manipulation of aqueous droplets without the inclusion of magnetic particles in the aqueous medium is desired to prevent contamination31. A recent study reported controlled motion of aqueous droplets33 immersed in oil based ferrofluid using two orthogonal rotating magnetic fields. The in-plane rotating magnetic field magnetizes the magnetic tracks which results in local magnetic field gradients, while the orthogonal field magnetizes the bulk ferrofluid. Kinematics of aqueous droplet motion and bulk fluid flow of ferrofluid was studied. However, the amount of bulk ferrofluid used in the above study is much higher thus making recovery of the aqueous droplets or contents present therein extremely challenging. Although, manipulation of aqueous droplets using aqueous based ferrofluid has been reported34, in that case recovery of aqueous droplets is challenging. Here, we report the transport of aqueous droplets over spikes of oil-based FF in presence of a normal magnetic field. We study the various forces that contribute toward the droplet motion and identify the various regimes based on the relative magnitudes of these forces. The effects of different parameters such as aqueous droplet volume, ferrofluid droplet volume and magnet velocity on the droplet transport behavior is studied. THEORETICAL ANALYSIS A schematic of the model system used for the present study is depicted in Fig. 1(a-d). A droplet of an oil-based ferrofluid (FF) of volume is dispensed on a rigid oleophilic substrate. Under the influence of an external magnetic field (due to the presence of a permanent magnet at a distance of # from the substrate), when the magnetic force overcomes the surface tension force, the FF droplet splits into an array of FF spikes30. Since, the substrate is oleophilic, there is always a thin layer of oil (the base medium for the FF nanoparticles) between the FF spikes and the substrate. Next, an aqueous droplet of volume is placed over the FF spikes that encapsulate the FF spikes. Further, when the magnet is moved horizontally at some velocity , the array of FF spikes tend to move along with it owing to the magnetic pull that carries the aqueous droplet placed over the spikes. We now analyze the various forces involved in the transport of the array of FF spikes and the aqueous droplet. The array of FF spikes present in a non-uniform magnetic field experiences magnetic force35 , which is expressed as =

$%&'

(0

)*

(1)

where, $% is the total volume of the nanoparticles present inside the array of FF spikes, which is calculated from the FF ' is the difference in magnetic susceptibility of droplet volume and the nanoparticle concentration (11.8%), &' = ' aqueous droplet and ferrofluid ~ ( 10 5 6.79) - 6.79, is the magnetic flux density (. and * is the flux gradient (Tm 1) and (0 is the permeability of vacuum (12 × 10 7H/m). To estimate the magnetic force , the magnetic flux density is obtained from the COMSOL multiphysics simulations, as presented in the Supplementary Information (section S.1). The angle 6 is defined as the angle between the axis of magnetization (magnet) and the axis of the droplet as shown in Fig. 1 (c). Since the aqueous droplet encapsulates the FF spikes, the aqueous droplet can be carried with the FF spikes that are driven by the magnetic force. There will be a friction force, which is mainly attributed to the contact line pinning22, acting at the contact line between the array of FF spikes (and the thin oil-layer) with the substrate, which is expressed as, 78 9 (

(2)

where, 8 is the friction constant, 9 is the base radius of the array of ferrofluid spikes present inside the aqueous droplet (shown in Fig. 1 (c)), ( - 8 mPa s is the viscosity of the ferrofluid, and is the steady velocity of the aqueous droplet, which will be equal to the FF steady spike velocity in the stable droplet transport regime. The friction constant 8 is estimated


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balance for the respective system in various regimes (e) Various manipulation regimes based on the force ratios acting on the system. EXPERIMENTAL In our experiments, oil based ferrofluid (EMG901, Ferrotec, USA) of particle (Fe3O4) concentration = = 11.8% (by volume), density ^ = 1430 kg/m3, viscosity ( = 8 mPa s was used. The initial susceptibility of EMG 901 is ' = 6.79. A neodymium iron boron magnet (NdFeB, N52, K&J Magnetics Inc., USA) of dimension a = = b = 0.47 cm, and of residual flux d = 1.48 T was used to provide the non-uniform magnetic field. To demonstrate our study, we have used an oleophilic and superhydrophobic substrate37 having oil contact angle > = 70° for our experiments. In short, the PDMS monomer and curing agent (Sylgard 184, Silicone Elastomer Kit, Dow Corning, USA) at a ratio of 10:1 (by weight) were mixed and degassed, and following that n-hexane (10% by weight) was stirred into the degassed mixture. Then, this mixture was spin coated at 4000 rpm for 10 s on a glass slide (sonicated in isopropyl alcohol followed by drying in N2) and was allowed to cure at 85 °C for 10 min. After curing, the glass slide was coated with soot particles using candle flame for a duration of 5 min. The substrate was then cleaned by high speed water-jet to achieve a transparent superhydrophobic surface. The permanent magnet was mounted on a moving rack which was driven by a stepper motor through a pinion. The linear velocity of the rack was controlled by a linear speed regulator connected to the stepper motor. The permanent magnet was positioned by maintaining a gap # from the substrate using a non-metallic e - stage (Thorlabs, Inc.). Micropipette (Eppendorf, Germany) of required capacity was used for dispensing various volumes of ferrofluid droplets (1 to 5 µL) and aqueous droplets (2 to 12 µL). Motion of ferrofluid, magnet and aqueous droplets were captured by a USB camera (Dinolite, Taiwan) and a high-speed camera (FASTCAM SA3 model, Photron, USA, Inc.) interfaced with a PC. To analyse the captured videos and images, Image J and PFV softwares were used. The surface tension of the oil-based FF and the aqueous phase and the interfacial tension between the two are measured as: 1 G = 23 mNm 1, Gb = 72.8 mNm 1, G , respectively. When an aqueous droplet is placed over the oilb = 48 mNm G ) > 0), the aqueous based FF spikes, due to positive spreading parameter of the oil-based FF (f = (Gb G b droplet is covered by a thin layer of oil-based FF. However, after the manipulation, the aqueous droplet can be easily recovered by using a polydimethyl siloxane (PDMS) – coated sponge, as illustrated from our experiments in the Supplementary Information (Fig. S.2) and decribed in detail elsewhere38. RESULTS AND DISCUSSION In this section, we first elucidate the various manipulation regimes exhibited by the aqueous droplet and FF system due to the motion of the magnet and illustrate the same based on the relevant forces acting on the FF spikes and aqueous droplet. Further, the effect of FF droplet volume , aqueous droplet volume b and the magnet velocity on the velocity of the aqueous droplet is illustrated. Comparison between the predictions of a simple theoretical model for the aqueous droplet velocity and the corresponding experimental data is presented . Finally, the extraction of spikes from the aqueous droplet is characterized in terms of spike extraction distance and the magnet disengagement is briefly outlined. Magnetic manipulation of the FF spike – aqueous droplet system – different regimes An aqueous droplet of volume that needs to be transported is gently placed on top of the array of ferrofluid spikes. When the magnet is moved in the horizontal direction at some velocity , depending on the competition between the various forces, namely, the magnetic force , interfacial tension force and the frictional force , different regimes are observed. Contribution of the different forces on the magnetic maniplation of the system is already introduced in theoretical section. 1 1 =( ) and As discussed, the various regimes are characterized based on the dimensionless numbers, =(

).

Fig. 2 (a) shows time-lapse experimental images illustrating the various manipulation regimes. For a FF droplet volume = 3 gh, aqueous droplet volume = 4 gh and magnet velocity = 10.56 cm/s, steady transport of aqueous droplet is = 1.4 mN, interfacial force = 0.69 mN and observed as shown in Fig. 2 (a), (i). In this case, the magnetic force = = 0.46 mN. The variation of angle 6 with time i is shown in Fig. S.4 in the Supplementary frictional force Information. Here, we have used the smallest value of the angle i.e. 6 = 4° for the estimation of the minimum magnetic force required for the manipulation. We will discuss in the next sectrion that that the velocity of the FF spike (which is equal to the aqueous droplet velocity) increases with time i (or distance ) until it becomes equal to the magnet velocity . Here, we have considered the maximum velocity of the FF spikes (from experiments) for calculating the frictional force . Our force calculations clearly show that the magnetic force is adequate to overcome the frictional force between the FF spikes and the surface. Also, the interfacial tension force offered by the aqueous and FF interface is higher than the 1 frictional force at the contact line of the aqueous droplet and the FF spikes. For the present case, we calculate


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FF spikes and the aqueous droplet will gradually increase with time and attain a steady velocity , which is equal to the magnet velocity . Fig. 3(a) shows the variation of the magnet velocity and aqueous droplet velocity (which is same as the FF spike velocity) with time i. The stepper motor used in our experiments for driving the magnet has rather a large = 22 cm/s only at i7 time constant j = 0.02 due to which the magnet attains its set velocity of . The aqueous = 22 cm/s only at i7 droplet (and the FF spikes) attains the steady velocity of . The variation of the locations of the magnet and the aqueous droplet (and the FF spikes) with time i are shown in in the inset of Fig. 3(a). The results show that, in the steady droplet transport regime, the aqueous droplet (and then FF spikes) safely follows the magnet. Next, we study the effect of aqueous droplet volume and FF droplet volume on the maximum droplet velocity , which is same as the maximum allowable magnet velocity in the steady droplet transport regime. Obviously, this velocity would correspond to the points lying on the boundary of the regime 91. Fig. 3(b) shows that for a fixed volume of the FF droplet , the maximum aqueous droplet velocity decreases with increase in the volume of the aqueous droplet . In 1 1 needs to be satisfied and the fact that does not depend the steady droplet transport regime, considering that 78 9J( on the aqueous droplet volume , the value of the frictional force should not vary with . However, the base radius of the aqueous droplet 9J will increase when increases (i.e. for a larger aqueous droplet) thus theoretically, the droplet velocity should decrease, which is observed in our experiments. It is also seen that for a fixed volume of aqueous droplet , the maximum droplet velocity is higher for a larger volume of FF droplet . This is because; for a larger FF droplet, the magnetic force becomes higher and thus the droplet velocity will increase in order to ensure 1 1. From the experimental data, the maximum steady velocity of the aqueous droplet is correlated with the ~ 0.19 0.36. volumes of the aqueous droplet and the ferrofluid droplet as Using the simple model (i.e. equation 1 to 3) presented in theoretical section, we predict the maximum droplet velocity by equating the minimum of the magnetic and interfacial force i.e. min ( , ) with frictional force . For a system with = 1 gh, for different aqueous droplet volume in the range = 2 to 8 gh, a comparison between a FF droplet volume the maximum droplet velocity predicted using the simple model and measured in our experiments is also depicted in Fig. 3(b). A very good match, within 5%, is obtained indicating the validity of the simple model. (a) 300

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Fig. 3 (a) Variation of the magnet velocity and aqueous droplet ( = 1( velocity (which is same as the FF spike = 3 gh i velocity) for with time , variation of the locations of the magnet and the aqueous droplet (and the FF spikes) with time i are shown in the inset, (b) Variation of maximum velocity of aqueous droplets with aqueous droplet volume = 3 gh a comparison between the model predictions and experimental data , for different ferrofluid volumes , for is also shown, > = 70°.

1 1 1 and > 1 indicates the spike extraction regime (i.e. regime 92). As the velocity of the magnet The region is increased from zero to a steady value , if at some intermediate velocity, the drag force exceeds the interfacial tension force , the FF spikes will get extracted out of the aqueous droplet and follow the magnet leaving the aqueous droplet = 3 gh, aqueous droplet volume = 4 gh and behind, which is indicated by the regime 92. For a FF droplet volume


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Fig. 4 (a) Variation in the velocity of the magnet (which is same as that of the FF spikes) and the aqueous droplet with = 3 gh, = 4 gh and = 24 cm/s, inset shows the variation of location of the magnet (and FF spike) and time i, the aqueous droplet with time i, (b) Variation of spike extraction distance with velocity of the magnet for different = 4 gh, (c) Variation of spike extraction distance volumes of ferrofluid , with velocity of the magnet for = 1 gh different volumes of aqueous droplets , , (d) Variation in the velocity of the magnet and the FF spikes = 3 gh, = 4 gh and steady magnet velocity = 44 cm/s (which is same as that of the aqueous droplet) with time i, , inset shows the variation of location of the magnet and the FF spike (aqueous droplet) with time i, > = 70°. CONCLUSION We studied the transport of aqueous droplet placed on top of an array of oil-based ferrofluid (FF) spikes in presence of a magnetic field. The spikes are formed when a FF droplet is placed on a rigid oleophilic substrate and exposed to a nonuniform normal magnetic field, due to the competition between surface tension and magnetic forces. Our experiments revealed that the behavior of the FF spikes – aqueous droplet system is governed by the competition between the magnetic force , interfacial tension force and the frictional force . It was found that depending on the values of the magnetic 1 1 =( =( ) and ), different regimes – steady Laplace number and the magnetic Bond number, droplet transport, spike extraction and magnet disengagement, are observed. Our results show that steady droplet transport 1 1 1 1 1 and 1, whereas extraction of spikes is observed for 1 and > 1, and is observed for 1 > 1. Among the different regimes observed, the steady droplet transport regime magnet disengagement is observed for would be of relevance for practical applications. We also demonstrated that the thin film of oil-based FF that covers the aqueous droplet surface can be easily cleaned using a PDMS – coated sponge to recover the aqueous droplet. In steady droplet transport regime, aqueous droplet velocity was found to be higher for a larger FF droplet but lower for a larger 0.19 0.36 ~ aqueous droplet, following the correlation . A simple model was able to accurately predict the aqueous droplet velocity within 5% of the corresponding experimental data. In the spike extraction regime, the spike extraction distance was found to be higher for a larger FF droplet but lower for a larger aqueous droplet and higher magnet velocity, following the correlation ~ 1.75 0.75 1.56. SUPPLEMENTARY CONTENT See supplementary information for distribution of magnetic flux density of magnet (Fig. S.1), recovery of ferrofluid coated aqueous droplet using a PDMS coated sponge (Fig. S.2), Variation of number of spikes $ with magnetic Bond number , variation of the maximum height of the FF spike m and the critical gap # with FF droplet volume and pictorial representation of ferrofluid spikes (Fig. S.3), variation of 6 vs i (Fig. S.4). Video S1 – different regimes for the magnetic manipulation of the FF spike – aqueous droplet system. AUTHOR INFORMATION Corresponding Author: Dr. Ashis Kumar Sen Email: [email protected]


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Notes: The authors declare no competing interest. ACKNOWLEDGEMENTS The authors would like to thank I.I.T. Madras (MEE/15-16/843/RFTP/ASHS) for providing the financial support which enabled this work. REFERENCES (1)

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Long, Z.; Shetty, A. M.; Solomon, M. J.; Larson, R. G. Fundamentals of Magnet-Actuated Droplet Manipulation


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Transport of a sessile aqueous droplet over spikes of oil based ferrofluid in presence of a magnetic field C. Mandal, U. Banerjee, A. K. Sen* Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai-600036, India * Author to whom correspondence should be addressed. Email: [email protected] Both first and second authors have contributed equally.

Oil based ferrofluid droplet

(a)

Magnetization (b)

(e)

Regime 2, R2 – Spikes extraction

Ferrofluid spikes

Oleophilic surface (d)

System for R1

Aqueous droplet dispensed

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1

(c)

System for R2

System for R3

Magnet motion

Regime 3, R3 – Magnet disengagement

Magnet

Regime 1, R1– Steady droplet transport Aqueous droplet

Magnet 1

Fig. 1 (a) Schematic of an oil-based ferrofluid (FF) droplet dispensed on a rigid oleophilic substrate, (b) Formation of an array of FF spikes after incorporation of a normal magnetic field, (c) Aqueous droplet dispensed over the array of FF spikes, encapsulating the FF spikes, 𝜙 is the angle between the axis of magnetization (magnet) and the axis of the droplet, (d) Force balance for the respective system in various regimes (e) Various manipulation regimes based on the force ratios acting on the system.

(b)

(a) ()

( ) (

)

Fig. 2 (a) Time-lapse experimental images showing the different regimes for the magnetic manipulation of the FF spike – aqueous droplet system, (b) Plot showing the different manipulation regimes based on magnetic Laplace number 𝐿𝑎𝑚 and magnetic Bond number 𝐵𝑜𝑚 , 𝜃 = 70°.


Langmuir

(a) 300

30 VFF = 1L, expt, VFF = 3L, expt VFF = 5L, expt

Uds (cm/s)

24

200

18

150

Xmag Xdroplet

60

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30

6

15

50

24

12

45

Uds (cm/s)

75

X (mm)

Velocity (mm/s)

(b)

Ud - droplet & spikes Um- magnet

250

0 0.00 0.08 0.16 0.24 0.32 0.40

0.1

0.2

0.3

0

0.4

0

Experiment Model R2 = 0.99

21 18 15 12

t (s)

0 0.0

3

6

9

Vw (L)

2

t (s)

4

6

Vw (L)

8

10

Fig. 3 (a) Variation of the magnet velocity 𝑈𝑚 and aqueous droplet (𝑉𝑤 = 4𝜇𝐿) velocity 𝑈𝑑 (which is same as the FF spike velocity) for 𝑉𝐹𝐹 = 3 μL with time 𝑡, variation of the locations 𝑥 of the magnet and the aqueous droplet (and the FF spikes) with time 𝑡 are shown in the inset, (b) Variation of maximum velocity of aqueous droplets 𝑈𝑑𝑠 with aqueous droplet volume 𝑉𝑤 , for different ferrofluid volumes 𝑉𝐹𝐹 , for 𝑉𝐹𝐹 = 3 μL a comparison between the model predictions and experimental data is also shown, 𝜃 = 70°.

300 250

(b)

Um - magnet & spikes

8

VFF = 1L

Ud - droplet

VFF = 3L VFF = 5L

6

50

150

40

100 50

Xmag Xdrop

4

30

2

20 10 0 0.00

0 0.00

Lse (cm)

200

X (mm)

(a)

Velocity (mm/s)

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0.08

t (s)

0.16

0.08

0.24

0

0.16

0.24

t (s)


6

12

18

24

Um (cm/s)

30

36

5

Vw=4L Vw=6L

4

(d)

500 400

Vw=12L

Velocity (mm/s)

(c)

Lse (cm)

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3

2

1

Um- magnet Ud - droplet and spikes

300

40 32

200

X (mm)

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100

24 16 8 0 0.00

0

0

8

16

24

32

40

0 0.00

Um (cm/s)

Xmag Xdrop

0.04

0.04

t (s)

0.08

0.08

t (s)

Fig. 4 (a) Variation in the velocity of the magnet (which is same as that of the FF spikes) and the aqueous droplet 𝑈𝑑 with time 𝑡, 𝑉𝐹𝐹 = 3 μL, 𝑉𝑤 = 4 μL and 𝑈𝑚𝑠 = 24 cm/s, inset shows the variation of location 𝑥 of the magnet (and FF spike) and the aqueous droplet with time 𝑡, (b) Variation of spike extraction distance 𝐿𝑠𝑒 with velocity of the magnet 𝑈𝑚 for different volumes of ferrofluid 𝑉𝐹𝐹 , 𝑉𝑤 = 4 μL, (c) Variation of spike extraction distance 𝐿𝑠𝑒 with velocity of the magnet 𝑈𝑚 for different volumes of aqueous droplets 𝑉𝑤 , 𝑉𝐹𝐹 = 1 μL, (d) Variation in the velocity of the magnet and the FF spikes 𝑈𝑑 (which is same as that of the aqueous droplet) with time 𝑡, 𝑉𝐹𝐹 = 3 μL, 𝑉𝑤 = 4 μL and steady magnet velocity 𝑈𝑚𝑠 = 44 cm/s, inset shows the variation of location 𝑥 of the magnet and the FF spike (aqueous droplet) with time 𝑡, 𝜃 = 70°.


0.12

0.12

Transport of a sessile aqueous droplet over spikes of oil based

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