VIRTUAL COMPONENTS FOR DROPLET CONTROL USING MARANGONI FLOWS:SIZE-SELECTIVE FILTERS, TRAPS, CHANNELS, AND PUMPS
Amar S. Basu *, Seow Yuen Yee, and Yogesh B. Gianchandani
Department of Electrical Engineering and Computer Science
University of Michigan, Ann Arbor, USAABSTRACTThis paper describes several microfluidic components,
including channels, filters, traps, and pumps, formanipulating aqueous droplets suspended in a film of oil onblank, unpatterned substrates. These “virtual” devices haveno physical structure; they accomplish their function entirelyby localized Marangoni flows created in a non-contact
manner by heat sources suspended just above the liquidsurface. Various flow patterns can be engineered throughthe geometric design of the heat sources on size scales
ranging from 10-1,000 µm. Channels and circular traps,
emulated by linear and annular heat fluxes respectively,
demonstrate nearly 100% selectivity for droplets ranging
from 300-1,000 µm. A pump, emulated by a triangular heat
flux with a 10° taper, translates droplets of about the samerange at speeds up to 200 µm/s.
Keywords: Marangoni effect, droplet, filter, channel, pump,microfluidics, thermal probe

I. INTRODUCTIONIn droplet-based microfluidic systems, droplet motion isgenerally guided by microfabricated channels or byinteractions with specialized or patterned surfaces.
Examples of the latter include electrowetting [1] anddielectrophoresis [2] (both require patterned electrodes),chemical gradients defined during deposition [3], andoptoelectronic surfaces [4]. Approaches which do not
require specialized substrates include optical tweezers [5].
However, their use in water-in-oil microdroplet systems ismade difficult because lasers tend to repel droplets rather
than trap them.
This research seeks to eliminate microfabricatedfeatures on fluidic substrates. In addition to the evident
manufacturing advantages, this can potentially eliminate
droplet contact with solid surfaces, reducing the likelihoodof sample adsorption to channel walls or other surfaces.
The present approach makes use of the Marangoni
effect, i.e. the flow on a liquid surface driven by surface
tension gradients. Due to the inverse relation between
surface tension and temperature, the presence of atemperature gradient on a liquid surface causes Marangoni
flow directed from high to low temperature [6]. The small
temperature perturbations required to drive Marangoni flow
are created by submillimeter-scale heat sources placed justabove the surface. The shape of the heat source can beengineered to produce a diversity of flows which can*Fig 1: Concept illustration for a microfluidic system driven bysuspended heat sources. Various “virtual” fluidic components fordroplet manipulation, including channels, filters, traps, anddroplet mixers, are all created in a non-contact manner by small
temperature perturbations on the liquid surface. On the fluidic
substrate, the red lines represent virtual walls formed by
Marangoni flows. Only the right-sized droplets are allowed into
these virtual structures. Temperature perturbations are created bya separate structure suspended above the substrate.

emulate integral microfluidic components such as channels,traps, and pumps. Together, these virtual components arebuilding blocks toward a microsystem for droplet-based
assays (Fig. 1). In addition to reducing the complexity of thesubstrate, another advantage of this approach is that it does
not require the actuators to contact the liquid; thus, theactuators can be reused without contamination concerns.
Initial simulations also suggest that Marangoni actuation canachieve >1 mm/s flow velocities with changes in surface
temperature on the order of 1°C or even less.
Our past work [7-8] focused on the most basic heatsource geometry: a point source. This pattern generates anaxisymmetric toroidal flow cell directed outward on thesurface, and inward below the surface. Flow velocities up to1.7 mm/s were achieved in several mineral oils with <20mW power, and the recirculating flows were used to hold,Address: 1301 Beal Avenue, Ann Arbor MI 48109-2122, USA; Tel: (734) 647-2040; Fax: (734) 647-1781; Email: basua@umich.edu

merge, and pre-concentrate aqueous droplets suspended inthe oil. This effort reports more complex droplet operations
that can be achieved by further engineering the geometry of
the heat flux, and by taking advantage of Marangoni flows at
both surface and subsurface levels. Size-selective droplet
channels, droplet traps, and pumping are systematicallydesigned and demonstrated. Each component is discussed inturn.

II. SIZE-SELECTIVE VIRTUAL CHANNELS
AND TRAPS
Size-selective channels collect droplets within a specificrange and confine them within its boundaries (Fig. 2). They
are formed by parallel heat sources separated by a spacing s.
When placed above a layer of oil, the sources project twolinear heat fluxes on the liquid surface which define thevirtual walls of the channel (Fig. 2a). The range of droplets
captured within the channel is a function of the spacing s.
Target-sized droplets are pulled into the channel; others arepushed out.
The parallel heat sources create two local peaks insurface temperature. The resulting Marangoni flow iscomprised of two recirculating cells on opposite sides of theheat sources, and a relatively still region between them (Fig.
2b). Surface flows are directed away from the channel, andsubsurface flows are directed toward it. Droplets ofappropriate size are pushed into the channel by thesubsurface flows, which apply a lateral force to the center ofmass of the droplet. The surface flows, which apply only atangential force on the top side of the droplet, do not cause
lateral movement.
They do, however, affect smaller
droplets, whose center of mass is closer to the surface.
These droplets become trapped in the recirculating flows andare therefore excluded from the channel. The distinction
between ‘large’ and ‘small’ droplets is a function of s.
A second, equally viable way to create a virtual channel(not illustrated) is with a single line heat source instead oftwo parallel sources. In this case, the channel size and thedroplet size-selectivity are defined by the width of the heatsource (w) rather than the spacing s. The double line heatFig 2: Virtual droplet channels. (a) Virtual channel projected by
two heated wires with separation s held parallel to the liquidsurface. Target-sized droplets are pulled into the channel; others
are excluded. (b) Cross section schematic illustrating principle ofoperation. Recirculating flows occurring as a result of theMarangoni effect are shown with arrows. The large droplet istrapped in the virtual channel region.

source offers some flexibility in that virtual channel region
be easily made much wider than the single line channel.
Both techniques can be simulated using a computational
fluid dynamics (CFD) solver (FLUENT 6.0, Fluent Corp).
The appropriate surface heat flux is placed as a boundary
condition on a 3-dimensional fluid layer, the bottom ofwhich is held at ambient temperature. The simulator
calculates the Marangoni flows using an iterative procedure
which includes the following steps: 1) calculating thesurface temperature profile gradient using a heat conduction
simulation, 2) equating the surface temperature gradient tosurface shear stresses, and 3) solving the constituent fluid
flow equations with the shear stress as a boundary condition.
Fig 3: CFD simulations of virtual
droplet channels. (a,b) Surface andcross section temperature profiles
resulting from (a) 2 parallel linear heatsources with a spacing s=900 µm, and(b) a single line heat source with width
w=350 µm. (c,d) Flow vectors
resulting from (c) the parallel heatsources, and (d) the single line heatsource.
In each case, surface
temperature profiles are drawn above
the flow vectors. Simulations assume
a 200 µm-thick mineral oil layer witha surface tension coefficient -0.16
mN/m-K. Heat flux amplitudes are
6,000 W/m2. u MAX is the maximum
flow velocity, and T MAX is the max
surface temperature change.

Simulation results (Fig. 3) illustrate the differences inflow patterns of the double and single line heat sources.
Recirculating flows are present inside the double line
channel but do not appear in the single line version.
Experimentally, these internal flows do not appear to affectthe trapping capability of the channel. It is notable that inboth cases, up to 4 mm/s surface velocities can be obtainedwith <6°C change in surface temperature. This illustrates
the favorable scaling of Marangoni flows: surface effects
tend to dominate in thin fluid layers, which allows
Marangoni flows to be an efficient micro-scale actuation
technique. The subsurface flows are only about 1/3rd thevelocity of the surface flows, but they are sufficient to pullin selected droplets.
The functionality and size-selectivity of droplet
channels were experimentally verified by placing twoparallel, cylindrical metal structures above a thin layer ofphenylmethyl polysiloxane oil (PMPS, Dow Corning 550Fluid). This particular oil was chosen for its high density(specific gravity=1.07), which causes the aqueous droplets tofloat on the oil surface. Droplets with diameters ranging
from 20-2,000 µm were pipetted into the oil. Larger
droplets tended to adopt a pancake shape rather than aperfect sphere due to the buoyant force against the oilsurface. The metal structures were heated to approximately
110°C with an attached soldering iron and placed 200 µm
above the oil surface. Droplets within a specific size range
move into the channel, and smaller droplets are actively
removed from the channel by the Marangoni flows (Fig. 4a).
Very large droplets are unaffected by the flows, andtherefore are not actively recruited into the channel.
The ability to tailor the size selectivity of the channels isquantitatively shown in Fig. 4b. A histogram of droplet

Fig 4: Droplet filtration capability of virtual channels. (a)Micrographs showing two ø=500 µm droplets (circle) entering thechannel while a smaller one (square) is rejected. (b) Histogram
showing the size selectivity of two droplet channels with 600 µm
and 970 µm spacing. Droplet statistics were compiled over video
clips spanning 40 minutes. Bins are in 100 µm increments.

capture vs. droplet size is shown for two channels withdifferent spacings (s). When s=600 µm, the minimum
diameter for entry into the channel is 250 µm, and whens=970 µm, the minimum diameter is 350 µm. A sharptransition can be seen in both cases, and nearly 100%exclusion of off-sized droplets is shown. Therefore, thesechannels inherently provide an effective size-based filtration
capability.
The single droplet trap is implemented using a ringshaped annular heat source (Fig. 5). The primary difference
between this component and the channel is that the droplet isconfined in both lateral dimensions. The trap is useful as areservoir for holding single droplets, and for manipulating
droplets if the heat source is translated laterally. The
simulated flow vectors along a cross section of the ring areidentical to those shown in Fig. 3c; however, when viewed
from above, the flow pattern is axially-symmetric about theheat source. The subsurface flows (Fig. 5b), composed of
two distinct regions, are responsible for droplet trapping.
Flows along the perimeter of the ring, oriented inward, push

Fig 5: Single droplet trapping with an annular heat flux. (a)Schematic illustrating a trapped droplet and the exclusion of larger
or smaller droplets. (b) CFD Simulation. The shaded contours
represent the surface temperature gradient. White arrows represent
the subsurface flow (140 µm depth). The two regions of flow aremarked with dashed lines. (c) Micrographs showing affinity of adroplet to the annular heat source (T120°C). Gap is 200 µm.

the droplet to the center. Within the boundaries of the ring,
the flow vectors are oriented outward, but these flows do notaffect the trapped droplet because the body forces they
impart on the droplet are symmetric and therefore cancel
each other. The surface flows (not shown), which arealways oriented opposite the subsurface flows, reject smaller
droplets from the trap. Therefore, the size exclusion
capability applies to this geometry as well.
Figure 5c shows experimental results. A rectangularring-shaped metal pin (T120°C, s=600 µm) is suspended
200 µm above a PMPS oil layer to approximate an annularheat flux. Figure 5 shows that a ø=700 µm droplet isactively pulled into the trap, driven by the subsurface flows
directed into the channel. If the trap boundary is moved (bythe translation of the substrate or heat source), the droplet
follows it. Droplet velocities are 200 µm/s.

III. GUIDEWIRE PUMP
Pumping or actuation of droplets can be accomplishedby two methods. The first is simply a consequence of thetrapping: the heat source projecting a channel or a trap canbe translated physically with respect to the substrate, and thetrapped droplets follow it. However, droplet actuation canbe also accomplished by steady-state, motionless heating
provided by a tapered shape and angled spacing (Fig. 6).
This geometry provides a triangular heat flux on the fluid
surface, and a temperature gradient oriented in the directionof increasing width. The resulting subsurface flows (Fig.
6b) are biased in the direction of increasing taper, and canpush appropriately sized droplets along the length of theguidewire. The surface flows (not shown) are biased in theopposite direction, and they reject small droplets from theguidewire similar to the previous components.
Figure 6c shows a guidewire pump projected by a steel
needle (T130°C) with 10° lateral taper, and a 5° taper invertical spacing. The ø=523 µm droplet is pulled from left
to right by virtue of the Marangoni flows. The droplet
achieves a maximum velocity of 196 µm/sec.

Fig 6: Guidewire pump. (a) A triangular heat flux projected on thefluid surface pulls droplets in and along its longitudinal axis. (b)CFD Simulation.
Shaded contours represent the surface
temperature gradient, and white arrows represent the subsurface
flow (140 µm depth) which pushes a droplet from left to right. (c)Micrographs illustrating movement of droplet at 196 µm/s caused
by a suspended heat source (T130°C) with 10° lateral taper and a5° taper in vertical spacing. Gap is 200 µm.

REFERENCES[1]

CONCLUSIONS
Several components for droplet manipulation werepresented, all of which operate without physical structures
solely by localized Marangoni flows. The distinguishingaspects of this approach are that 1) it is a non-contact
method of actuation, 2) droplets do not make contact withsolid surfaces, 3) it does not require patterned substrates, and
4) a size-filtration capability is inherent to each component.
The favorable scaling of surface forces also makes
Marangoni actuation a promising approach to microfluidics.
Future work will be directed at combining the various
components to create a functional system for microdropletbased assays.

[2]

[3]
[4]
[5]
[6]

[7]

ACKNOWLEDGEMENTS
Partial support for this effort was provided by the NSF,
NIH, the University of Michigan, and a Whitaker
Foundation Fellowship (AB).

[8]

S.K. Cho, H. Moon, C.-J. Kim, “Creating, transporting,cutting, and merging liquid droplets by electrowetting-based
actuationfor
digitalmicrofluidic
circuits,”
J.
Microelectromech. Sys., vol. 12, pp. 70-80, Feb. 2003.
T.B. Jones, M. Gunji, M. Washizu, M.J. Feldman,“Dielectrophoretic liquid actuation and nanodropletformation,” J. Appl. Phys., vol. 89, pp. 1441–1448, Jan.
2001.
M.K. Chaudhury, G.M. Whitesides, “How to make waterrun uphill,” Science, vol. 256, pp. 1539–1541, June 1992.
P.Y. Chiou, Z. Chang, M. Wu, “Light Actuated Microfluidic
Devices,” Proc. MEMS, 2003, pp. 355-358
A. Ashkin, “Application of radiation pressure,” Science, vol.
210, pp. 1081-1087, Dec. 1980.
F.J. Higuera, “Steady thermocapillary-buoyant flow in an
unbounded liquid layer heated nonuniformly from above”,
Phys. Fluids, vol. 12, pp. 2186-2197, Sept. 2000.
A.S. Basu, Y.B. Gianchandani, “Trapping and Manipulationof Particles and Droplets Using Micro-Toroidal Convection
Currents,” Proc. Transducers, 2005, pp. 85-88.
A.S. Basu, Y.B. Gianchandani, “Microthermal Techniquesfor Mixing, Concentration, and Harvesting DNA and Other
Microdroplet Suspensions,” Proc. TAS, 2005, pp. 131-134.