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Interface Components: Nanoparticles, Colloids, Emulsions, Surfactants, Proteins, Polymers
Self-transport and manipulation of aqueous droplets on oil-submerged diverging groove Suresh Dhiman, K.S. Jayaprakash, Rameez Iqbal, and Ashis K. Sen Langmuir, Just Accepted Manuscript • DOI: 10.1021/acs.langmuir.8b01889 • Publication Date (Web): 18 Sep 2018 Downloaded from http://pubs.acs.org on September 20, 2018
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Self-transport and manipulation of aqueous droplets on oil-submerged diverging groove
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S. Dhiman , K. S. Jayaprakash , R. Iqbal , A. K. Sen*
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† Department
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ABSTRACT
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†
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of Mechanical Engineering, Indian Institute of Technology Madras, Chennai-600036, India * Email:
[email protected] The first three co-authors have equally contributed to the work.
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We report experimental study of self-transport of aqueous droplets along an oil-submerged diverging groove structure. The migration phenomenon is illustrated and the effect of various parameters such as droplet size , oil layer thickness ℎ, groove angle and groove thickness on the droplet transport behaviour (i.e. migration velocity and length) is investigated. Our study reveals that complete engulfment of aqueous droplets in the oil layer, that is attributed to a positive spreading parameter ( > 0), is a prerequisite for the droplet transport. The results show that only droplets of diameter larger than the oil layer thickness (i.e. ≥ ℎ) get transported owing to a differential Laplace pressure between the leading and trailing faces of a droplet due to the diverging groove. Using experimental data, the variation of droplet migration velocity with distance along the diverging groove is correlated as ( ) = . , where = . . ℎ. . . The submerged groove structure was used to demonstrate simultaneous and sequential coalescence and transport of multiple droplets. Finally, the submerged groove structure was employed for extraction of aqueous droplets from oil. The proposed technique opens up a new avenue for evaporation and contamination free transport and coalescence of droplets for chemical and biological applications.
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INTRODUCTION
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Self-transport of droplets at micro and nano scales have been investigated extensively due to its numerous applications in the development of lab-on-a-chip and point-of-care microfluidic devices1,2. The advantages of this technology involves use of minimal quantity of the reagent and sample volume required for the assay, smaller size of the device, lower fabrication cost, and faster reaction time3. Various passive and active techniques have been studied for the manipulation of micron size droplets4. The active techniques require external fields and user controller mechanism but offer faster movement of droplets, quick response and better control on the droplet motion4. In active techniques, droplet manipulation can be achieved using external forces such as magnetic force5, electric force6 or acoustic force7. On the other hand, passive techniques involve use of surface tension8–10, deformability of a droplet11,12 or surface wettability13,14 for droplet transport. In spite of significant promises, both the passive and active techniques reported in the literature have inherent limitations. For instance, magnetic actuation of droplets require labeling which may lead to the contamination of droplets due to the magnetic particles15. In case of acoustic technique, the surface acoustic force is not localized and hence the control may not be precise4. Similarly, the use of electrical techniques requires a complex electronic system for its functioning6. In addition, active techniques demand expensive equipments and may have issues in terms of reusability of the devices. On the other hand, surface tension mediated manipulation requires temperature gradient9 or concentration gradient8 across a droplet for its transport. So there is a need of a more efficient technique that is simple, cost effective and inherits fewer limitations to find wider applications.
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Among the various passive techniques, directional motion owing to the curvature or solid surface energy gradient has been studied extensively. Recently, a strategically patterned wedge shaped track was used as a self-driven surface micromixer that operated by harnessing the wettability contrast and geometry of the patterns through a combination of coalescence and the differential Laplace pressure16. Directional and long-range transportation of droplets were achieved by leveraging a gradient in the wettability of the substrate over a range from superhydrophobic to hydrophilic17,18. The tendency of liquid drops to exist at the leaf apex as opposed to the flat leaves in order to minimize the free energy of the system is reported by Shahnan19. Recently, it has been studied that droplets trapped in V-shaped grooves with adjustable wettability can be utilized as a tool for the droplet manipulation12. Manipulation of liquid plugs and interfaces using elastocapillary flow in microchannels have been reported20. Dynamics of a water droplet over a sessile oil droplet has been studied in the recent
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past, wherein a water droplet above a critical size (for a fixed volume of oil droplet), if dispensed at an off-centered position, migrates towards the axisymmetric position in order to minimize the total free energy of the system21.
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Droplet manipulation due to the curvature difference across two opposite faces of a droplet has received tremendous attention in recent years11,13,22–29. Nature inspired directional transport of the droplet has long been investigated30–34, which provides further insight into the underlying mechanism responsible for the movement of droplets. For example, the Syntrichia caninervis plants found in the deserts have tiny hairs in the form of cones at the end of the leaves which collect water from humid atmosphere in the form of tiny droplets and transport it to the leaves30. The movement of the water droplets on tiny hair is due to the curvature difference formed across the two faces of the droplets that creates an unbalanced Laplace pressure to drive the droplets. Similar behaviour is also observed in the case of various cactus species31. The spontaneous self-directed motion of droplet on a chemically patterned wedge-shaped surface was investigated where the droplet travelled on a horizontal wedge-shaped gradient at a speed of 0.4 mm/s due to the combined effect of surface wettability and curvature gradient.
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Recently, transport of water droplet on a wedge-shaped superhydrophobic copper surface combining with a poly- dimethyl oil layer on it has been demonstrated26. Droplets of ferrofluid on a wedge-shaped gradient surface were observed to move spontaneously without and with a magnetic field parallel to flow direction. The droplet motion was stopped or arrested with a moderate magnetic field perpendicular to the flow direction, which can be used as a switch or valve to direct the motion28. ‘Curvi-propulsion’ of nanoscale droplets on tapered substrate with velocity of the order of 100 m/s were recently reported as an ultrahigh velocity motion of droplets using molecular dynamics simulations25. Most of the studies reported in the literature on the passive manipulation of droplets were either using a gradient in the surface wettability or a combination of wettability and the curvature gradient.
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None of the works in literature discuss about exclusively curvature induced manipulation of droplets. Besides, droplets on open surface suffer from the inherent limitations in terms of faster evaporation, contact line pinning and substrate contamination. Furthermore, on a wettability gradient surface, the droplet loses its shape while moving from the hydrophobic to hydrophilic region due to the enhanced pinning and wettability. Manipulation of droplets submerged inside an oil layer proves to be advantageous over that on an open surface in terms of lower evaporation rate and absence of contact line pinning and non-contamination due to non-contact with the substrate.
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Here, we report the phenomenon of self-transport and manipulation of aqueous droplets along an oil-submerged diverging groove. The mechanism of droplet transport is illustrated and the effect of various influencing parameters on the transport is investigated. A simple theoretical model shows that the droplet transport is governed by the balance between the differential Laplace pressure and the drag force. Similarly, the total length travelled by the droplet along the groove is dependent on the droplet volume, thickness of the oil layer and the divergence angle of the groove. Finally, using the oilsubmerged diverging groove setup, coalescence of aqueous droplets and separation of water droplets from oil is demonstrated.
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MECHANISM OF DROPLET TRANSPORT AND THEORETICAL MODEL
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A schematic of the setup comprising the diverging groove (of rectangular cross-section) submerged in oil is shown in Fig. 1a. The diverging groove is specified in terms of the groove angle (2) and groove thickness (). The groove is submerged in oil so that there is an oil layer of thickness ℎ formed on top of the groove. When an aqueous droplet of volume and diameter is dispensed on the converging end of the rectangular groove, the interfacial properties (as discussed later in section 4) facilitates the droplet to enter completely into the oil phase (Fig. 1b). Thus aqueous droplets of diameter larger than the thickness of the oil-layer ℎ get deformed into a spheroid while droplets of diameter smaller than the thickness of the oil layer remain undeformed (spherical). Due to the presence of the groove, the droplets tend to enter into the groove in order to minimize surface energy. However, since the groove is diverging, the radius of curvature of the droplet at its leading and trailing edges are different (i.e. droplet is no longer a spheroid as the top view projection the droplet does not have a round shape any more) (Fig. 1c). The radius of curvature at the leading face of the droplet is higher as compared to that at its trailing face. The resulting Laplace pressure due to the difference in the radii of curvatures directs the droplet to get transported along the groove at velocity . The motion of the droplet continues until a point (at a distance from the corner of the groove) where the radius of curvature on both leading and trailing faces becomes equal (i.e. droplet attains a spherical shape) thus there is no Laplace pressure difference (Fig. 1d).
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Figure 1. (a) Schematic of the setup comprising the diverging groove (of rectangular cross-section) submerged in oil. (b) Top and side views of the droplet immediately after dispense. (c) Top and side views of the droplet immediately during migration. (d) Top and side views of the droplet after it has migrated and come to rest position.
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During droplet transport (Fig. 1c), the difference in the Laplace pressure22,35 jump at the leading and trailing faces of the droplet is given by the equation below,
∆ =
! = "#$ %
! &
! ' &!
(1)
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where, Δ) and Δ) are the Laplace pressures jumps at the leading and trailing faces of the droplet, respectively, *+, is the interfacial tension of water-oil interface, - and - are the radii of curvature at the leading and trailing faces of the droplet, respectively, as shown in Fig.1c. Here, the radii of curvatures of the droplet parallel to the plane of the groove is considered since the radii of curvatures perpendicular to the plane of the groove are equal.
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As a result, the net force experienced by the droplet can be scaled as,
./ ~ ∆ 1 ~ 2 3
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where 4 is the projected area of the droplet normal to the direction of motion. As the droplet moves, it experiences an opposing drag force26,36 which can be scaled as,
.3 ~ 5673
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(2)
(3)
where is the velocity of the droplet, 8 is the dynamic viscosity, is the undeformed droplet diameter and 9 is a constant that depends on the shape of the deformed droplet.
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By equating both the forces, the velocity of the droplet can be written as,
7 =
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"#$ 3 ! % :6 &
! ' &!
where ; is a scaling constant. So, the droplet migration velocity is proportional to the droplet size , water-oil interfacial tension *+, and the difference of the reciprocal of the radii of curvatures at the trailing and leading edges of the droplets
=?
@ and inversely proportional to the oil viscosity 8. It is to be noted that the radii of curvatures - and - are
functions of location in the direction of motion (see Fig. 1c) thus the droplet velocity (A) is also a function of location as
7(B) = %
"#$ 3 ' &(B) :6
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At a location =L, ( = ) = 0, and in that case is the droplet migration distance.
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EXPERIMENTS
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(4)
(5)
A schematic of the experimental setup is depicted in Fig. 2. The diverging groove was submerged in silicone oil and mineral oil (Sigma Aldrich, India). De-ionized water (18.2 MΩ.cm resistivity; Elga Lab Water, UK) was used as the droplet phase (aqueous) in the experiments. The density of water, silicone oil, mineral oil and olive oil are 998 kg/m , 995 kg/m , 857 kg/m , and 898 kg/m , respectively at 20 °C. The surface tension of DI water, silicone oil, mineral oil, olive oil and the interfacial tension between oil and water was measured at 25° C using Du Nouy ring method using tensiometer (Sigma 702 Tensiometer, Biolin Scientific). The surface tension values obtained were: 72.51 ± 0.39 mN/m, 23.05 ± 0.32 mN/m, 28.8 ± 0.2 mN/m, 26.1± 0.1 mN/m, respectively. The interfacial tension values obtained were: 20.12 ± 0.21 mN/m for silicone oil-DI water and 45.6 ± 0.5 mN/m for mineral oil-DI water and 20 ± 0.22 mN/m for olive oil-DI water. The diverging groove structure used for droplet transport and manipulation was fabricated using polydimethylsiloxane (PDMS) using soft lithography technique. A leak-proof chamber made of glass was fabricated in order to submerge the groove into oil as shown in Fig. 2. The groove structure was then placed inside a leak proof chamber and silicone oil was gently poured into it in order to submerge the structure. Before the start of the experiments the surface and chamber were cleaned using isopropyl alcohol (IPA) followed by drying with compressed N2. The thickness of the oil layer above the groove structure is maintained to be always less than the diameter of the water droplet. A micropipette (Eppendorf) was used to dispense the micron size DI water droplets. In all experiments, the droplet was dispensed manually at an off-set distance of = 5.0 mm from the corner of the groove to eliminate the effect of sharp corners on the droplet dynamics. The behavior of aqueous droplets on the diverging groove was captured using two digital microscopes (AM7515MZT and AM7115MZT, Dinolite, Taiwan) connected to a PC. In the droplet coalescence experiments, in order to clearly distinguish the oil-water interface, a blue color dye (Hi-Tecpoint Ink, Luxor, Japan, 0.1% concentration (wt/wt)) was used with the aqueous phase. The effect of the addition of dye on the variation of the surface and interfacial properties of the water droplet is found to be
