- Email: [email protected]
Observation of water droplets oscillation due to laser induced Marangoni convection
Optics and Laser Technology 120 (2019) 105749
Contents lists available at ScienceDirect
Optics and Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Full length article
Observation of water droplets oscillation due to laser induced Marangoni convection
T
Zahra Saeedian Tareiea, Hamid Latifia,b, , Saeid Parcheganib, Kobra Soltanloub ⁎
a b
Laser and Plasma Research Institute, Shahid Beheshti University, Evin, Tehran 1983969411, Iran Department of Physics, Shahid Beheshti University, Evin, Tehran 1983969411, Iran
HIGHLIGHTS
the first time, the oscillatory behaviour of water droplets by Marangoni force was observed. • For velocity and oscillation frequency of the droplets were measured. • The relationship between droplet diameter versus oscillation frequency and amplitude are observed. • Linear • This method is suitable for separation according to the size and refractive index. ARTICLE INFO
ABSTRACT
Keywords: Fiber laser Manipulation Temperature gradient Convection Thermocapillary Marangoni force Oscillation frequency
In this paper, using experimental characterizations, we explore the motion of water droplets suspended in mineral oil under exposure of a focused continuous wave (CW) fiber laser beam. The laser beam exposure heats the surrounding oil medium as well. The temperature gradient generates thermocapillary (or Marangoni) convection flows. This approach uses infrared laser-induced thermocapillary-driven flow for manipulation of droplets in the range of 10 to 30 µm in diameter. The droplets are trapped in the convection flow and travel with thermocapillary convection flow (depending on the droplet sizes) along the streamline with high speed. This motion is observed at a certain critical power of the laser. The behavior of a droplet in response to thermally induced convection can be consider. we also examined the oscillatory behavior of the droplet on the x y plane. As expected, oscillation frequency/amplitude are linearly correlated to the droplet size.
1. Introduction The micro-object manipulation (e.g. particle and droplet manipulation) is an important technique required for many chemical, biological and medical applications [1–6]. Many methods have been utilized to manipulate particles and droplets in an aqueous solution, using electric, magnetic, acoustic, Marangoni, thermophoresis and optical forces[7–18] .Among different techniques mensioned above, the need for a technique capable of manipulating larger objects (above 10 μm) is critical. Optical manipulation can be carried out either through optical forces exerted upon micro-objects or through the temperature gradient induced nearby the objects [19,20]. The optical manipulation is noncontact and contamination-free as well as having higher precision in the manipulation process but the energy required to displace the objects larger than 10 μm is much higher than radiation pressure can achieve (a few pN ). The laser induced convection flows (Marangoni) is an intresting ⁎
method to achieve better manipulation of micro objects (1–200 μm) in a liquid medium [21]. Over the past few years, some studies on laser induced complex convection in liquids have been reported [22]. By local strong heating of a free surface between either liquid and air or two liquids by high-power lasers, Marangoni (or thermocapillary) convection in liquids can be generated [23]. Marangoni force is an external force applied on the droplets causing them to move [24,25]. The important factors in the interaction between the Marangoni force and objects are size, wavelength and power of the laser beam as described by different models [26]. In this study, we explored the motion of droplets in presence of Marangoni (thermophoresis) force induced by a localized focused infrared laser beam. While the infrared laser exposure resulted in exertion of a temperature gradient in the oil medium. The induced temperature gradient changed the surface tension nearby the localized heated point and thus, the Marangoni convection was resulted as well. As we observed experimentally, at an appropriate wavelength, and adequate
Corresponding author. E-mail address: [email protected] (H. Latifi).
https://doi.org/10.1016/j.optlastec.2019.105749 Received 6 April 2019; Received in revised form 14 July 2019; Accepted 1 August 2019 Available online 21 August 2019 0030-3992/ © 2019 Elsevier Ltd. All rights reserved.
Optics and Laser Technology 120 (2019) 105749
Z. Saeedian Tareie, et al.
power of the laser, existence of Marangoni and flow convections, resulted in droplets exhibiting oscillatory motions. With regard to the experimental and simulation results and the small movement of the droplet in z diredction (13–17 μm), we examined the oscillatory behavior of the droplet on the x y plane. Analysis of experimental data revealed that the characteristics of this oscillatory motion (e.g. frequency and amplitude) were linearly correlated to the droplet size as well as its location relative to the laser spot. The findings of this paper may shed new lights on our understanding of droplet manipulation that is for instance very essential to new biological technologies in microfluidics.
droplets, we assumed that the movement of droplets were in the same direction as the vortices that were created by the Marangoni effect in the mineral oil and therefore we did not introduce the droplet in the simulation process. The effect of droplets interactions on thermocapillary motion in general is weak, unless the droplets are nearly touching [30], the intractions between droplets are not taken into account in our simulation. In this paper, the fluid flow is modeled using the continuum equation off mass, momentum and energy conservation that in the following section, the details of them are provided. 3.1.1. Energy equation In this section, we assumed that the fluid is incompressible which provide the energy conservation equation:
2. Theory The presence of a temperature gradient at a liquid/air or liquid/ liquid interface creates a net force in the fluid called Marangoni force that can be exploited for manipulating the droplet. Conventional thermocapillary devices typically use micro-fabricated electrical resistors to generate temperature gradient for transporting and trapping the droplets and sorting them on the trajectories of pre-patterned structures [27,28]. Another way for producing the temperature gradient is to use localized laser heating such as a Gaussian laser beam profile shaping at the droplet interface. This increased local temperature produces a surface tension gradient at the heated site. This gradient gives rise to the Marangoni force which is balanced by the viscous force of the fluid. From this we can compute the liquid velocity gradient at the weld pool surface. The Marangoni force can be described by investigating the velocity field among the liquid layers induced by the thermal Marangoni effect as [29]:
u = y
T x
( Cp T )/ t +
/ t +
T
·( UU ) =
P +
·(µ U ) + SU
(5)
where is the fluid density, U is the velocity vector, P is the pressure, µ is the dynamic viscosity and SU is the external forces from spatial variation in the surface tension which is imposed as a boundary condition that described in the next section.
(1)
T
(4)
·( U ) = 0
( U) / t +
3.2. Boundary condition As we discussed in Section 3.1., there are external forces in the both equations of energy and Navier-Stocks that were not incorporated in these equations and are imposed as a boundary conditions in this paper. We assume a flat, non-deformable liquid interface at the top of our computational domain. From this, we can compute the liquid velocity gradient at the top of domain by Eq. (6):
)
will have two different signs T > 0, T < 0 which completely change the flow (thermally induced circulation flow) inside the fluid. By considering the mineral oil properties and also according to the literatures we chose the negative sign for gradient of surface tension during the whole simulation process. Also, in order to compute the particles velocity inside the minerial oil we can use the following equation:
2 a (2 + 3 )(2 + k )
(3)
3.1.2. Fluid flow In this section we considered the continuity and momentum equations (Narvier-Stocks equations):
where is the temperature derivative of the surface tension (Nm is the dynamic viscosity (kgm 1s 1), u is the velocity vector (ms 1), and T is the temperature (K ). Eq. (1) states that the shear stress on a surface is proportional to = T where is the surface tension. The
Uth =
·(k T ) + ST
where is the fluid density, U is the velocity vector, t is the time, Cp is the specific heat constant, T is the temperature, and k is the thermal conductivity. In Eq. (3), ST are the external forces such as the heat in flux from the laser and heat out flux at the surface which are imposed as a boundary condition that will be discussed in the next section.
1K 1),
(
·( UCp T ) =
u = y
T x
(6)
where is the temperature derivative of the surface tension (Nm is the dynamicviscosity (kgm 1s 1), u is the velocity vector (ms 1), and T is the temperature (K ). Eq. (6) states the shear stress on a surface is / T that is the surface tension. Depending on proportional to = the properties of mineral oil, the is constant and negative. The thermal boundary condition at the top surface equates the heat conduction flux in the mineral oil medium to the sum of incoming laser heat flux and heat loss flux from the top surface to the surroundings due to radiation and convection. The heat flux into the material is completely determined by the laser. The laser heat flux is assumed to have an ideal radial Gaussian distribution: 1K 1),
(2)
is the gradient of the interfacial where a is the droplet radius, T tension ( ) with the local temperature (T ), and and k are the ratios of viscosity and thermal conductivity, respectively, between the internal and surrounding fluid. The thermocapillary migration speed is proportional to droplet size (R ). By considering the droplet size, this force either traps the droplet or makes it circulate with the flow pattern continuously that we will elaborate on this at the discussion section. 3. Theoretical model for Marangoni convection in the mineral oil
Qlaser = qmax exp( 2r 2 /rq2 )
3.1. Governing equation
(7)
where rq is the laser beam waist radius and qmax is the peak intensity of laser beam. The total heat flux out of the material is composed of two different mechanisms: free convection, energy radiation.
In order to simulate the behavior of suspended droplet inside the mineral oil, the fluid flow inside the mineral oil at the presence of Gaussian laser beam was considered. Due to the small size of the
2
Optics and Laser Technology 120 (2019) 105749
Z. Saeedian Tareie, et al.
Fig. 1. (a and b) Simulation of the velocity field and temperature distribution in a 1 mm thick layer of the mineral oil for negative Marangoni boundary condition (a) Velocity field and circulation effect generated by a static heat source at x = 0 mm after 2 s, (b) temperature distribution generated by a static heat source at x = 0 mm after 2 s.
The convective heat loss can be calculated as following:
Qconvection = hc (Tsurface
T1)
capacity = 1670 Jkg 1K 1. To model the heat source, a Gaussian profile was used. As shown in Fig. 1(a), velocity field inside of the oil fluid is toward the center of the heat source which causes the suspended droplet inside the oil to begin to migrate toward the center of the heat source.
(8)
where hc is the convection heat transfer coefficient expressing the heat exchange between the material surface and the environment. The energy radiation is given by the Stefan-Boltzmann law:
Qradiation =
(T 4 surface
T14)
4. Experimental setup
(9)
Fig. 2 shows a schematic diagram of the droplet control system. A CW fiber laser operating at 1064 nm was used to exert the radiation force and produce temperature gradient. The light was locally focused by a 4 cm focal length lens. The laser power used in this work was 1.5 W . A 200 frame per second CMOS camera was employed for recording while a yellow LED was used as the light source. Mineral oil were purchased from CinnaGen. The refractive indices of water droplet and oil are 1.333 and 1.463, respectively. The droplets suspended in mineral oil were located on a glass substrate that was coated by PDMS. Different sizes of water droplets were suspended in an oil environment. ImageJ software was used to determine the sizes of the droplets.
In this formula is the Stefan-Boltzmann constant and is the emissivity and the absorption of the material. We assume that these parameters are temperature independent. Finally the total heat out flux is:
Qheat , out = Qconvection + Qradiation
(10)
Finally, a 2D infinite-element modeling was modeled by coupling the Navier-Stokes equations, the Heat transfer equation, and the Marangoni effect at a liquid/air or liquid/liquid interface. We used comsol multiphysics software to perform this simulation. Fig. 1. Shows the simulation of convection in a 1mm layer of oil. The properties of the oil are: density = 838 kgm 3 , absolute viscosity = 231.9 centipoise at and heat 20°, thermal conductivity = 0.136 Wm 1K 1,
5. Results and discussion As we observed experimentally, at an appropriate wavelength, and 1.5 W power of the laser, Marangoni and flow convections generated. In Fig. 3, the displacement of droplet in z direction is shown. As shown in Fig. 3, due to the droplet movement in z direction, it is focused and defocused in each frames of movie. The change in the focuse of the droplets during movement is clearly evident (Fig. 3) that indicates its displacement in the z direction. With regard to the experimental measurement and simulation results due to the small movement of the droplet in z diredction (13–17 μm), we examined the oscillatory behavior of the droplet on the x y plane. We analysed the recorded video to determine the x and y coordinates of the droplets in each frame (see movie in supplementary material). Fig. 4 shows the trajectories of one of the droplets when it moves away from the hot region (a–d) and when it moves toward the hot region (e–h). In Fig. 4, the oscillatory motion of one of the droplets is observed in x y plane.
Fig. 2. Schematic diagram of the experimental setup. Red arrow shows the direction of laser irradiation. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Optics and Laser Technology 120 (2019) 105749
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Movie 1.
Due to the light absorption of mineral oil at 1064 nm, a temperature gradient is generated in the focal volume which in turn causes a thermocapillary (or Marangoni) convection. The droplets are trapped in the convection flow and travel with thermocapillary convection flow (depending on the droplet sizes) along the streamline with high speed. As shown in Fig. 4(a–d), the droplets go to the hot region and as
shown in Fig. 4(e–h), move away from the hot region. Point ( x 0 , y0 ) is the origin based on which all of the measurements were calculated and shows the location of the focused laser beam. The velocity field and temperature contribution in oil are shown in Fig. 1, theoritically. As shown in Fig. 1(a), velocity field inside of the oil fluid is toward
Fig. 3. Optical microscope images of the focused and defocused of the movement of a water droplet (25.5 μm in diameter) in mineral oil versus time produced by thermal convection. The droplet shows by the red circule and the droplet motion path is shown: in down row the droplets move toward the location of laser irradiation and in top row they move away from it. (Scale bar 25 μm). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. Optical microscope images of the movement of a water droplet (25.5 μm in diameter) in mineral oil versus time produced by a CW fiber laser operating at 1064 nm. The blue cross shows the initial location of the droplet and the droplet shows by the red circule. The red arrow shows the direction of the laser irradiation and the green cross shows the laser focusec location, respectively: in (a–d) the droplets move toward the location of laser irradiation and in (e–h) they move away from it. (Scale bar 25 μm). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Optics and Laser Technology 120 (2019) 105749
Z. Saeedian Tareie, et al.
Fig. 5. Droplet trajectory over time (for one of the droplets) is shown in parts (a) and (b). The red dash line in part (a) is the origin (x 0 , y0 ) based on which all of the measurements were calculated and shows the location of the focused laser beam. (b) Enlarged section of the spectrum in part a. Points D1 and P1 show one of the dips and peaks of the spectrum where the droplet move in z direction. (c) the time derivative of the curve r (t ) . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
the center of the heat source which causes the suspended droplet inside the oil to begin to migrate toward the center of the heat source and move away. By using a Matlab code, we were able to trace the trajectory of the droplets over time. The location of the droplet in each moment in time was calculated based on point ( x 0 , y0 ). In Fig. 5a the red dash line shows the location of the focused laser beam (point ( x 0 , y0 )). Fig. 5a shows that the droplets never reach the mentioned point due to the presence of large restoring forces at this point. For a better understanding of the droplet behavior, we magnified a part of Fig. 5a shown in Fig. 5b. Fig. 5c obtains by computing and analyzing the time derivative of the curve r (t ) in Fig. 5b. From Fig. 5c, it is clear that that when the droplet goes away from the hot region, the slope of the graph (0–0.85 s) is greater than that when it moves toward the hot region (0.85–2.42 s) as we expected. This phenomenon is exactly what we got in simulation section (Fig. 1). This means that the velocity of the droplet when it moves away from the hot region is almost twice as much as when it moves toward the hot region. Furthermore, the velocity of the droplet is zero in the dips and peaks of Fig. 5b which means that the droplet moves small distance (13–17 μm) in the z direction that we discard. Note that the dips of the spectrum (e.g. point D1) in Fig. 4b are sharper than the peaks (e.g. point
Fig. 6. The spectrum of droplet oscillation amplitude versus oscillation frequency.
5
Optics and Laser Technology 120 (2019) 105749
Z. Saeedian Tareie, et al.
Fig. 7. (a) The droplet oscillation amplitude versus diameter and (b) The droplet oscillation frequency versus diameter.
P1) of the spectrum. This means that the droplets spend more time in the peaks than in the dips. For different droplet diameters, we calculated the oscillation frequency as shown in Fig. 6. As shown in Fig. 7a, by increasing the droplet diameter, the frequency of oscillation is increased linearly which means that there is a direct relationship between velocity and droplet diameter which is in agreement with Eq. (2). Fig. 7b illustrates the size-dependent migration displacements of the droplets (oscillation amplitude) from the hot region based on their diameters. This result clearly shows that by increasing the droplet diameter, oscillation amplitude increases. This phenomenon can be described as follows: for the same temperature gradient, a larger temperature difference is generated at both ends of a larger droplet, resulting in a stronger driving force by the Marangoni convection exerted on the droplet.[31]
References [1] A. Ashkin, J.M. Dziedzic, T. Yamane, Optical trapping and manipulation of single cells using infrared laser beams, Nature 330 (6150) (1987) 769–771. [2] S. Sato, H. Inaba, Optical trapping and manipulation of microscopic particles and biological cells by laser beams, Opt. Quant. Electron. 28 (1) (1996) 1–16. [3] W.H. Wright, G.J. Sonek, Y. Tadir, M.W. Berns, Laser trapping in cell biology, IEEE J. Quantum Electron. 26 (12) (1990) 2148–2157. [4] M. Ozkan, M. Wang, C. Ozkan, R. Flynn, S. Esener, Optical manipulation of objects and biological cells in microfluidic devices, Biomed. Microdevices 5 (1) (2003) 61–67. [5] S.A.I. Seidel, et al., Microscale thermophoresis quantifies biomolecular interactions under previously challenging conditions, Methods 59 (3) (2013) 301–315. [6] C.N. Baroud, J.-P. Delville, F. Gallaire, R. Wunenburger, Thermocapillary valve for droplet production and sorting, Phys. Rev. E 75 (4) (2007) 046302. [7] C.J. Wienken, P. Baaske, U. Rothbauer, D. Braun, S. Duhr, Protein-binding assays in biological liquids using microscale thermophoresis, Nat Commun 1 (100) (2010), https://doi.org/10.1038/ncomms1093. [8] K. Zillner, M. Jerabek-Willemsen, S. Duhr, D. Braun, G. Langst, P. Baaske, Microscale thermophoresis as a sensitive method to quantify protein: nucleic acid interactions in solution, Methods Mol. Biol. (Clifton, N.J.) vol. 815, (2012) 241–252. [9] P. Sajeesh, A.K. Sen, Particle separation and sorting in microfluidic devices: a review, Microfluids Nanofluids 17 (1) (2014.) 1–52. [10] J. Schnelle, R. Meissner, P. Rose, C. Alpmann, M. Esseling, C. Denz, Integrated optofluidics: optical control of particles and droplets in fluidic environments in 2016, Progress in Electromagnetic Research Symposium (PIERS), 2016, pp. 995–996. [11] M. Motosuke, J. Shimakawa, D. Akutsu, S. Honami, Noncontact manipulation of microflow by photothermal control of viscous force, Int. J. Heat Fluid Flow 31 (6) (2010) 1005–1011. [12] Y. Kang, D. Li, Electrokinetic motion of particles and cells in microchannels, Microfluids Nanofluids 6 (4) (2009) 431–460. [13] B. Roda, et al., Field-flow fractionation in bioanalysis: a review of recent trends, Anal. Chim. Acta 635 (2) (2009) 132–143. [14] D.R. Gossett, et al., Label-free cell separation and sorting in microfluidic systems, Anal. Bioanal. Chem. 397 (8) (2010) 3249–3267. [15] P.Y. Chiou, S.-Y. Park, M.C. Wu, Continuous optoelectrowetting for picoliter droplet manipulation, Appl. Phys. Lett. 93 (22) (2008) 221110. [16] Z. Wang, J. Zhe, Recent advances in particle and droplet manipulation for lab-on-achip devices based on surface acoustic waves, Lab Chip 11 (7) (2011) 1280–1285, https://doi.org/10.1039/C0LC00527D. [17] P. Beránek, R. Flittner, V. Hrobař, P. Ethgen, M. Přibyl, Oscillatory motion of water droplets in kerosene above co-planar electrodes in microfluidic chips, AIP Adv. 4 (6) (2014) 067103. [18] H. Yun, K. Kim, W.G. Lee, Cell manipulation in microfluidics, Biofabrication 5 (2) (2013) 022001. [19] A. Jonáš, P. Zemánek, Light at work: The use of optical forces for particle manipulation, sorting, and analysis, Electrophoresis 29 (24) (2008) 4813–4851. [20] A. Ashkin, J.M. Dziedzic, J.E. Bjorkholm, S. Chu, Observation of a single-beam gradient force optical trap for dielectric particles, Opt. Lett. 11 (5) (1986) 288–290. [21] E. Vela, C. Pacoret, S. Bouchigny, S. Regnier, K. Rink, A. Bergander, Non-contact mesoscale manipulation using laser induced convection flows in 2008, IEEE/RSJ International Conference on Intelligent Robots and Systems, 2008, pp. 913–918. [22] M. Gugliotti, M.S. Baptista, M.J. Politi, Laser-induced marangoni convection in the presence of surfactant monolayers, Langmuir 18 (25) (2002) 9792–9798.
6. Conclusion In this paper, we investigated the oscillatory behavior of droplets with different sizes. By using a localized focused laser beam, the water droplets suspended in mineral oil were oscillated. The oscillatory motion was produced by Marangoni convection flow in oil medium. The Marangoni force caused the droplet to move toward and back away the hot region. Experimentally, we observed the velocity of the droplet when it moved away from the hot region was almost twice as much as that when it moved toward the hot region. We studied the behavior of the droplet theoretically and experimentally and found out that the relationship between the oscillation frequency and droplet diameter is linear in x y plane. This means that a droplet with a larger diameter oscillates faster than a droplet with a smaller diameter. Furthermore, we found that the oscillation amplitude is linearly related to droplet diameter. Finally, we found out that the initial location of the droplet with respect to the laser spot and the diameter of the droplet are crucial for investigating the oscillatory behavior of droplet. Acknowledgement Thanks are due to O.R. Ranjbar, Dr S. Nader, S. Reihani and Dr S. Feiz for valuable discussions. 6
Optics and Laser Technology 120 (2019) 105749
Z. Saeedian Tareie, et al. [23] M.F. Schatz, G.P. Neitzel, Experiments on thermocapillary instabilities, Annu. Rev. Fluid Mech. 33 (1) (2001) 93–127. [24] S.C. Hardy, The motion of bubbles in a vertical temperature gradient, J. Colloid Interface Sci. 69 (1) (1979) 157–162. [25] H.J. Keh, L.S. Chen, Droplet interactions in thermocapillary migration, Chem. Eng. Sci. 48 (20) (1993) 3565–3582. [26] A.S. Basu, Y.B. Gianchandani, Virtual microfluidic traps, filters, channels and pumps using Marangoni flows, J. Micromech. Microeng. 18 (11) (2008) 115031. [27] B. Selva, V. Miralles, I. Cantat, M.-C. Jullien, Thermocapillary actuation by optimized resistor pattern: bubbles and droplets displacing, switching and trapping, Lab
Chip 10 (14) (2010) 1835–1840, https://doi.org/10.1039/C001900C. [28] A.A. Darhuber, J.P. Valentino, J.M. Davis, S.M. Troian, S. Wagner, Microfluidic actuation by modulation of surface stresses, Appl. Phys. Lett. 82 (4) (2003) 657–659. [29] F.J. Higuera, Steady thermocapillary-buoyant flow in an unbounded liquid layer heated nonuniformly from above, Phys. Fluids 12 (9) (2000) 2186–2197. [30] H.J. Keh, S.H. Chen, The axisymmetric thermocapillary motion of two fluid droplets, Int. J. Multiph. Flow 16 (3) (1990) 515–527. [31] M. Muto, M. Yamamoto, M. Motosuke, A noncontact picolitor droplet handling by photothermal control of interfacial flow, Anal. Sci. 32 (1) (2016) 49–55.
7
Contents lists available at ScienceDirect
Optics and Laser Technology journal homepage: www.elsevier.com/locate/optlastec
Full length article
Observation of water droplets oscillation due to laser induced Marangoni convection
T
Zahra Saeedian Tareiea, Hamid Latifia,b, , Saeid Parcheganib, Kobra Soltanloub ⁎
a b
Laser and Plasma Research Institute, Shahid Beheshti University, Evin, Tehran 1983969411, Iran Department of Physics, Shahid Beheshti University, Evin, Tehran 1983969411, Iran
HIGHLIGHTS
the first time, the oscillatory behaviour of water droplets by Marangoni force was observed. • For velocity and oscillation frequency of the droplets were measured. • The relationship between droplet diameter versus oscillation frequency and amplitude are observed. • Linear • This method is suitable for separation according to the size and refractive index. ARTICLE INFO
ABSTRACT
Keywords: Fiber laser Manipulation Temperature gradient Convection Thermocapillary Marangoni force Oscillation frequency
In this paper, using experimental characterizations, we explore the motion of water droplets suspended in mineral oil under exposure of a focused continuous wave (CW) fiber laser beam. The laser beam exposure heats the surrounding oil medium as well. The temperature gradient generates thermocapillary (or Marangoni) convection flows. This approach uses infrared laser-induced thermocapillary-driven flow for manipulation of droplets in the range of 10 to 30 µm in diameter. The droplets are trapped in the convection flow and travel with thermocapillary convection flow (depending on the droplet sizes) along the streamline with high speed. This motion is observed at a certain critical power of the laser. The behavior of a droplet in response to thermally induced convection can be consider. we also examined the oscillatory behavior of the droplet on the x y plane. As expected, oscillation frequency/amplitude are linearly correlated to the droplet size.
1. Introduction The micro-object manipulation (e.g. particle and droplet manipulation) is an important technique required for many chemical, biological and medical applications [1–6]. Many methods have been utilized to manipulate particles and droplets in an aqueous solution, using electric, magnetic, acoustic, Marangoni, thermophoresis and optical forces[7–18] .Among different techniques mensioned above, the need for a technique capable of manipulating larger objects (above 10 μm) is critical. Optical manipulation can be carried out either through optical forces exerted upon micro-objects or through the temperature gradient induced nearby the objects [19,20]. The optical manipulation is noncontact and contamination-free as well as having higher precision in the manipulation process but the energy required to displace the objects larger than 10 μm is much higher than radiation pressure can achieve (a few pN ). The laser induced convection flows (Marangoni) is an intresting ⁎
method to achieve better manipulation of micro objects (1–200 μm) in a liquid medium [21]. Over the past few years, some studies on laser induced complex convection in liquids have been reported [22]. By local strong heating of a free surface between either liquid and air or two liquids by high-power lasers, Marangoni (or thermocapillary) convection in liquids can be generated [23]. Marangoni force is an external force applied on the droplets causing them to move [24,25]. The important factors in the interaction between the Marangoni force and objects are size, wavelength and power of the laser beam as described by different models [26]. In this study, we explored the motion of droplets in presence of Marangoni (thermophoresis) force induced by a localized focused infrared laser beam. While the infrared laser exposure resulted in exertion of a temperature gradient in the oil medium. The induced temperature gradient changed the surface tension nearby the localized heated point and thus, the Marangoni convection was resulted as well. As we observed experimentally, at an appropriate wavelength, and adequate
Corresponding author. E-mail address: [email protected] (H. Latifi).
https://doi.org/10.1016/j.optlastec.2019.105749 Received 6 April 2019; Received in revised form 14 July 2019; Accepted 1 August 2019 Available online 21 August 2019 0030-3992/ © 2019 Elsevier Ltd. All rights reserved.
Optics and Laser Technology 120 (2019) 105749
Z. Saeedian Tareie, et al.
power of the laser, existence of Marangoni and flow convections, resulted in droplets exhibiting oscillatory motions. With regard to the experimental and simulation results and the small movement of the droplet in z diredction (13–17 μm), we examined the oscillatory behavior of the droplet on the x y plane. Analysis of experimental data revealed that the characteristics of this oscillatory motion (e.g. frequency and amplitude) were linearly correlated to the droplet size as well as its location relative to the laser spot. The findings of this paper may shed new lights on our understanding of droplet manipulation that is for instance very essential to new biological technologies in microfluidics.
droplets, we assumed that the movement of droplets were in the same direction as the vortices that were created by the Marangoni effect in the mineral oil and therefore we did not introduce the droplet in the simulation process. The effect of droplets interactions on thermocapillary motion in general is weak, unless the droplets are nearly touching [30], the intractions between droplets are not taken into account in our simulation. In this paper, the fluid flow is modeled using the continuum equation off mass, momentum and energy conservation that in the following section, the details of them are provided. 3.1.1. Energy equation In this section, we assumed that the fluid is incompressible which provide the energy conservation equation:
2. Theory The presence of a temperature gradient at a liquid/air or liquid/ liquid interface creates a net force in the fluid called Marangoni force that can be exploited for manipulating the droplet. Conventional thermocapillary devices typically use micro-fabricated electrical resistors to generate temperature gradient for transporting and trapping the droplets and sorting them on the trajectories of pre-patterned structures [27,28]. Another way for producing the temperature gradient is to use localized laser heating such as a Gaussian laser beam profile shaping at the droplet interface. This increased local temperature produces a surface tension gradient at the heated site. This gradient gives rise to the Marangoni force which is balanced by the viscous force of the fluid. From this we can compute the liquid velocity gradient at the weld pool surface. The Marangoni force can be described by investigating the velocity field among the liquid layers induced by the thermal Marangoni effect as [29]:
u = y
T x
( Cp T )/ t +
/ t +
T
·( UU ) =
P +
·(µ U ) + SU
(5)
where is the fluid density, U is the velocity vector, P is the pressure, µ is the dynamic viscosity and SU is the external forces from spatial variation in the surface tension which is imposed as a boundary condition that described in the next section.
(1)
T
(4)
·( U ) = 0
( U) / t +
3.2. Boundary condition As we discussed in Section 3.1., there are external forces in the both equations of energy and Navier-Stocks that were not incorporated in these equations and are imposed as a boundary conditions in this paper. We assume a flat, non-deformable liquid interface at the top of our computational domain. From this, we can compute the liquid velocity gradient at the top of domain by Eq. (6):
)
will have two different signs T > 0, T < 0 which completely change the flow (thermally induced circulation flow) inside the fluid. By considering the mineral oil properties and also according to the literatures we chose the negative sign for gradient of surface tension during the whole simulation process. Also, in order to compute the particles velocity inside the minerial oil we can use the following equation:
2 a (2 + 3 )(2 + k )
(3)
3.1.2. Fluid flow In this section we considered the continuity and momentum equations (Narvier-Stocks equations):
where is the temperature derivative of the surface tension (Nm is the dynamic viscosity (kgm 1s 1), u is the velocity vector (ms 1), and T is the temperature (K ). Eq. (1) states that the shear stress on a surface is proportional to = T where is the surface tension. The
Uth =
·(k T ) + ST
where is the fluid density, U is the velocity vector, t is the time, Cp is the specific heat constant, T is the temperature, and k is the thermal conductivity. In Eq. (3), ST are the external forces such as the heat in flux from the laser and heat out flux at the surface which are imposed as a boundary condition that will be discussed in the next section.
1K 1),
(
·( UCp T ) =
u = y
T x
(6)
where is the temperature derivative of the surface tension (Nm is the dynamicviscosity (kgm 1s 1), u is the velocity vector (ms 1), and T is the temperature (K ). Eq. (6) states the shear stress on a surface is / T that is the surface tension. Depending on proportional to = the properties of mineral oil, the is constant and negative. The thermal boundary condition at the top surface equates the heat conduction flux in the mineral oil medium to the sum of incoming laser heat flux and heat loss flux from the top surface to the surroundings due to radiation and convection. The heat flux into the material is completely determined by the laser. The laser heat flux is assumed to have an ideal radial Gaussian distribution: 1K 1),
(2)
is the gradient of the interfacial where a is the droplet radius, T tension ( ) with the local temperature (T ), and and k are the ratios of viscosity and thermal conductivity, respectively, between the internal and surrounding fluid. The thermocapillary migration speed is proportional to droplet size (R ). By considering the droplet size, this force either traps the droplet or makes it circulate with the flow pattern continuously that we will elaborate on this at the discussion section. 3. Theoretical model for Marangoni convection in the mineral oil
Qlaser = qmax exp( 2r 2 /rq2 )
3.1. Governing equation
(7)
where rq is the laser beam waist radius and qmax is the peak intensity of laser beam. The total heat flux out of the material is composed of two different mechanisms: free convection, energy radiation.
In order to simulate the behavior of suspended droplet inside the mineral oil, the fluid flow inside the mineral oil at the presence of Gaussian laser beam was considered. Due to the small size of the
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Fig. 1. (a and b) Simulation of the velocity field and temperature distribution in a 1 mm thick layer of the mineral oil for negative Marangoni boundary condition (a) Velocity field and circulation effect generated by a static heat source at x = 0 mm after 2 s, (b) temperature distribution generated by a static heat source at x = 0 mm after 2 s.
The convective heat loss can be calculated as following:
Qconvection = hc (Tsurface
T1)
capacity = 1670 Jkg 1K 1. To model the heat source, a Gaussian profile was used. As shown in Fig. 1(a), velocity field inside of the oil fluid is toward the center of the heat source which causes the suspended droplet inside the oil to begin to migrate toward the center of the heat source.
(8)
where hc is the convection heat transfer coefficient expressing the heat exchange between the material surface and the environment. The energy radiation is given by the Stefan-Boltzmann law:
Qradiation =
(T 4 surface
T14)
4. Experimental setup
(9)
Fig. 2 shows a schematic diagram of the droplet control system. A CW fiber laser operating at 1064 nm was used to exert the radiation force and produce temperature gradient. The light was locally focused by a 4 cm focal length lens. The laser power used in this work was 1.5 W . A 200 frame per second CMOS camera was employed for recording while a yellow LED was used as the light source. Mineral oil were purchased from CinnaGen. The refractive indices of water droplet and oil are 1.333 and 1.463, respectively. The droplets suspended in mineral oil were located on a glass substrate that was coated by PDMS. Different sizes of water droplets were suspended in an oil environment. ImageJ software was used to determine the sizes of the droplets.
In this formula is the Stefan-Boltzmann constant and is the emissivity and the absorption of the material. We assume that these parameters are temperature independent. Finally the total heat out flux is:
Qheat , out = Qconvection + Qradiation
(10)
Finally, a 2D infinite-element modeling was modeled by coupling the Navier-Stokes equations, the Heat transfer equation, and the Marangoni effect at a liquid/air or liquid/liquid interface. We used comsol multiphysics software to perform this simulation. Fig. 1. Shows the simulation of convection in a 1mm layer of oil. The properties of the oil are: density = 838 kgm 3 , absolute viscosity = 231.9 centipoise at and heat 20°, thermal conductivity = 0.136 Wm 1K 1,
5. Results and discussion As we observed experimentally, at an appropriate wavelength, and 1.5 W power of the laser, Marangoni and flow convections generated. In Fig. 3, the displacement of droplet in z direction is shown. As shown in Fig. 3, due to the droplet movement in z direction, it is focused and defocused in each frames of movie. The change in the focuse of the droplets during movement is clearly evident (Fig. 3) that indicates its displacement in the z direction. With regard to the experimental measurement and simulation results due to the small movement of the droplet in z diredction (13–17 μm), we examined the oscillatory behavior of the droplet on the x y plane. We analysed the recorded video to determine the x and y coordinates of the droplets in each frame (see movie in supplementary material). Fig. 4 shows the trajectories of one of the droplets when it moves away from the hot region (a–d) and when it moves toward the hot region (e–h). In Fig. 4, the oscillatory motion of one of the droplets is observed in x y plane.
Fig. 2. Schematic diagram of the experimental setup. Red arrow shows the direction of laser irradiation. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Movie 1.
Due to the light absorption of mineral oil at 1064 nm, a temperature gradient is generated in the focal volume which in turn causes a thermocapillary (or Marangoni) convection. The droplets are trapped in the convection flow and travel with thermocapillary convection flow (depending on the droplet sizes) along the streamline with high speed. As shown in Fig. 4(a–d), the droplets go to the hot region and as
shown in Fig. 4(e–h), move away from the hot region. Point ( x 0 , y0 ) is the origin based on which all of the measurements were calculated and shows the location of the focused laser beam. The velocity field and temperature contribution in oil are shown in Fig. 1, theoritically. As shown in Fig. 1(a), velocity field inside of the oil fluid is toward
Fig. 3. Optical microscope images of the focused and defocused of the movement of a water droplet (25.5 μm in diameter) in mineral oil versus time produced by thermal convection. The droplet shows by the red circule and the droplet motion path is shown: in down row the droplets move toward the location of laser irradiation and in top row they move away from it. (Scale bar 25 μm). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
Fig. 4. Optical microscope images of the movement of a water droplet (25.5 μm in diameter) in mineral oil versus time produced by a CW fiber laser operating at 1064 nm. The blue cross shows the initial location of the droplet and the droplet shows by the red circule. The red arrow shows the direction of the laser irradiation and the green cross shows the laser focusec location, respectively: in (a–d) the droplets move toward the location of laser irradiation and in (e–h) they move away from it. (Scale bar 25 μm). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
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Fig. 5. Droplet trajectory over time (for one of the droplets) is shown in parts (a) and (b). The red dash line in part (a) is the origin (x 0 , y0 ) based on which all of the measurements were calculated and shows the location of the focused laser beam. (b) Enlarged section of the spectrum in part a. Points D1 and P1 show one of the dips and peaks of the spectrum where the droplet move in z direction. (c) the time derivative of the curve r (t ) . (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)
the center of the heat source which causes the suspended droplet inside the oil to begin to migrate toward the center of the heat source and move away. By using a Matlab code, we were able to trace the trajectory of the droplets over time. The location of the droplet in each moment in time was calculated based on point ( x 0 , y0 ). In Fig. 5a the red dash line shows the location of the focused laser beam (point ( x 0 , y0 )). Fig. 5a shows that the droplets never reach the mentioned point due to the presence of large restoring forces at this point. For a better understanding of the droplet behavior, we magnified a part of Fig. 5a shown in Fig. 5b. Fig. 5c obtains by computing and analyzing the time derivative of the curve r (t ) in Fig. 5b. From Fig. 5c, it is clear that that when the droplet goes away from the hot region, the slope of the graph (0–0.85 s) is greater than that when it moves toward the hot region (0.85–2.42 s) as we expected. This phenomenon is exactly what we got in simulation section (Fig. 1). This means that the velocity of the droplet when it moves away from the hot region is almost twice as much as when it moves toward the hot region. Furthermore, the velocity of the droplet is zero in the dips and peaks of Fig. 5b which means that the droplet moves small distance (13–17 μm) in the z direction that we discard. Note that the dips of the spectrum (e.g. point D1) in Fig. 4b are sharper than the peaks (e.g. point
Fig. 6. The spectrum of droplet oscillation amplitude versus oscillation frequency.
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Fig. 7. (a) The droplet oscillation amplitude versus diameter and (b) The droplet oscillation frequency versus diameter.
P1) of the spectrum. This means that the droplets spend more time in the peaks than in the dips. For different droplet diameters, we calculated the oscillation frequency as shown in Fig. 6. As shown in Fig. 7a, by increasing the droplet diameter, the frequency of oscillation is increased linearly which means that there is a direct relationship between velocity and droplet diameter which is in agreement with Eq. (2). Fig. 7b illustrates the size-dependent migration displacements of the droplets (oscillation amplitude) from the hot region based on their diameters. This result clearly shows that by increasing the droplet diameter, oscillation amplitude increases. This phenomenon can be described as follows: for the same temperature gradient, a larger temperature difference is generated at both ends of a larger droplet, resulting in a stronger driving force by the Marangoni convection exerted on the droplet.[31]
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6. Conclusion In this paper, we investigated the oscillatory behavior of droplets with different sizes. By using a localized focused laser beam, the water droplets suspended in mineral oil were oscillated. The oscillatory motion was produced by Marangoni convection flow in oil medium. The Marangoni force caused the droplet to move toward and back away the hot region. Experimentally, we observed the velocity of the droplet when it moved away from the hot region was almost twice as much as that when it moved toward the hot region. We studied the behavior of the droplet theoretically and experimentally and found out that the relationship between the oscillation frequency and droplet diameter is linear in x y plane. This means that a droplet with a larger diameter oscillates faster than a droplet with a smaller diameter. Furthermore, we found that the oscillation amplitude is linearly related to droplet diameter. Finally, we found out that the initial location of the droplet with respect to the laser spot and the diameter of the droplet are crucial for investigating the oscillatory behavior of droplet. Acknowledgement Thanks are due to O.R. Ranjbar, Dr S. Nader, S. Reihani and Dr S. Feiz for valuable discussions. 6
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