APPLIED PHYSICS LETTERS 90, 034102 共2007兲

Shaping high-speed Marangoni flow in liquid films by microscale
perturbations in surface temperature
Amar S. Basua兲 and Yogesh B. Gianchandani
Department of Electrical Engineering and Computer Science, University of Michigan, 1301 Beal Avenue,Ann Arbor, Michigan 48109-2122

共Received 29 September 2006; accepted 7 December 2006; published online 18 January 2007兲
The authors show that a variety of controlled flow patterns, including toroidal cells and surface
doublets, can be generated in 80– 400 ␮m thick liquid films by placing scanning microscopy probeswith integrated heaters just above the surface 共⬍400 ␮m separation兲. The probes project sharp
temperature gradients on the liquid surface which drive Marangoni flow. Flow velocities
approaching 3000 ␮m / s are experimentally demonstrated on length scales of 20– 200 ␮m with
⬍20 mW input power. For liquids such as water and oil, in which the surface tension coefficient is⬇0.2 mN/ m K, flows ⬎1000 ␮m / s can be accomplished with surface temperature perturbations⬍1 ° C. This technique enables microfluidic manipulation on unpatterned substrates. © 2007
American Institute of Physics. 关DOI: 10.1063/1.2430777兴
Microfluidic actuation methods exploiting surface forces
共which scale favorably at small length scales兲 are being actively researched for use in miniaturized biochemical assays
and other applications. The actuation of microdroplets, forexample, typically utilizes interfacial forces generated byelectrowetting,1,2 substrate temperature gradients,3,4 chemicalgradients,5,6 and dielectrophoresis.7 Nevertheless, most actuation techniques utilize prefabricated 共and frequently complex兲 microchips that are typically assay specific. We showthat microfluidic actuation of films, droplets, and suspensions
can be achieved by the Marangoni effect, simply by creating
temperature perturbations on the free surface of the liquidsample using heated or cooled scanning microscopy probes
共Fig. 1兲. This letter focuses on toroidal flows and doublets
共Fig. 2兲, which are two of the most elementary flow patterns
that can be generated with a simple, pointlike heater geometry. Experiments show how these flow patterns can also beused for trapping and agglomerating particles and droplets.
In addition to providing a method of instrumentation, theseresults illuminate the dramatic impact of surface temperature
perturbations on microscale flow.
The microfabricated probes used in the majority of thefollowing experiments to create the thermal perturbations arethin film cantilevers similar to atomic force microscopy
probes, except that they contain an integrated joule heater
near the tip.8 The cantilever, with an orthogonal tip, extends
from the edge of an upturned silicon chip. It is made withthermally insulative polyimide; an embedded thin film ofgold, which covers the tip, also serves as a resistive heater. A
typical probe is 360 ␮m long, 120 ␮m wide, 3 ␮m thick,and has resistance ranging from 20 to 50 ⍀. The tip temperature can reach nearly 50 ° C with ⬍5 mW input power
because the low thermal conductivity of the polyimide suppresses conductive loss.
A probe tip placed within about 400 ␮m of the liquidcreates a localized increase in the surface temperature. The
consequent reduction in surface tension creates a shear stressthat is oriented radially outward, driving fluid flow awayfrom the hot spot on the surface. The continuity is maina兲

Electronic mail: basua@umich.edu and yogesh@umich.edu

tained by inward flux beneath the surface. Together, the surface and subsurface currents form a recirculating convection
cell which is axisymmetric about the heat source 关Fig. 2共a兲兴.
In a typical toroidal cell, the radial stress and resultant fluid
velocities are proportional to the surface temperature gradient, according to the surface stress condition boundary
condition9⌫r = ␮dVrd␴ dT=−,dndT dr共1兲

where ⌫r is the radial shear stress, ␮ is the fluid viscosity,
dVr / dn is the gradient of radial velocity perpendicular to thesurface, d␴ / dT is the temperature coefficient of surface tension, and dT / dr is the radial temperature gradient on thefluid surface. The speed and geometry of the flow can becontrolled by the gap between the sample and the probe andthe power supplied to it. For example, Fig. 3共a兲 shows measured flow velocities as a function of probe power obtainedFIG. 1. 共Color online兲 Controlling microfluidic flow with Marangoni convection. Thermal sources suspended above the surface of a thin liquid film
provide arbitrary, patterned heat fluxes to the liquid surface, resulting incontrolled surface tension gradients. Point heating sources causes flow awayfrom the heated surface, whereas point cooling sources cause inward flow.
Heat fluxes can be designed to produce complex flow patterns, as illustrated
here. Fast flow velocities 共⬎3 mm/ s兲 can be achieved with small increases
in surface temperature 共⬍3 ° C兲 when this technique is applied at small
length scales.

0003-6951/2007/90共3兲/034102/3/$23.00
90, 034102-1© 2007 American Institute of Physics
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A. S. Basu and Y. B. Gianchandani

Appl. Phys. Lett. 90, 034102 共2007兲

FIG. 2. 共Color online兲 Schematics of toroidal and doublet flows. 共a兲 Top
view of toroidal flow, which occurs when the probe is suspended above athin oil layer. Surface flows 共red arrows兲 are directed outward, and subsurface flows 共blue arrows兲 are directed inward. 共b兲 Top view of doublet flow,which generally occurs in water and is a two dimensional surface flow. The
positioning of the probe relative to the flow is shown.

on a 140 ␮m thick layer of mineral oil. This result is consistent with Eq. 共1兲. The radius of the convection cell depends
primarily on the thickness of the oil layer. In thin fluid layers
共⬍150 ␮m兲, the solid substrate below the liquid film absorbs
the heat, diminishing the lateral flow of heat. In addition, theincreased viscous drag impedes the opposing surface andsubsurface flows. As a result, the radial extent of the flow
diminishes. Simulations indicate that for fluids with a surface
tension coefficient ⬎0.2 mN/ m K, such as various oils, it ispossible to obtain fluid velocities ⬎1000 ␮m / s while thesurface temperature rise is ⬍1 ° C. The small temperature
increase required makes this technique a candidate for many
samples and assays. 共A cold probe, which actively cools a
localized region on the fluid surface, generates Marangoni
flows in the reverse direction.兲 These flow patterns offer control and usability that is not possible with self-organized cellular flow ensembles created by substrate heating.10,11
Aqueous samples exhibit high speed doublet flow patterns rather than toroids. Doublets are associated with linear
thermal gradients created by the polyimide probes. The silicon chip to which each probe is attached presents a heat sink,creating a surface temperature gradient. 共Simulations andother evidence12 suggest that evaporative cooling may additionally play a role in such cases.兲 Hence, the angle at which
the probe is held above the surface 共i.e., the attack angle兲 has
an impact on these flow patterns. For example, with a 15°attack angle above an aqueous film of 80 ␮m thickness, lin-FIG. 3. 共Color online兲 Experimental data. 共a兲 Toroidal flow velocities as afunction of input power to the probe. Power to the probe was ramped while
the probe-liquid separation was fixed at 60 and 90 ␮m. Flow velocities wererecorded with a charge coupled device camera. 共b兲 Doublet flow velocities
as a function of input power when the probe is held at an 80 ␮m separation.
共c兲 Fluorescent images of the doublet flow within a 1 mm droplet when aheated probe tip is held next to a droplet submerged in oil.

ear velocities of up to 3000 ␮m / s can be achieved in thecenter streamlines. Changing the attack angle can even reverse the flow. The fluid velocities can be controlled by adjusting the gap between the probe and liquid, or by adjusting
the power to the probe 关Fig. 3共b兲兴. Rotational velocities inthe doublet vortices approach 1300 rpm, indicating a potential for use in laminar mixing, which is often difficult toachieve at high speeds at the microscale.13,14
Marangoni flows could become a potentially useful toolin microdroplet-based chemical analysis sytems, wheresubmillimeter-sized droplets act as fluid compartments, andreactions can be initiated by merging the droplets. Since theheat sources do not make contact with the liquid, the chanceof sample loss or sample contamination is reduced. The recirculating nature of toroidal flows makes them suitable forcollecting and manipulating droplets. Doublet flows, on theother hand, could be used for mixing within individual droplets. Figure 3共c兲 shows the streamlines of high-speed vortices
generated within a 1 mm droplet.

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034102-3

We conclude that thermal perturbations on fluid surfaces
can control Marangoni flow at the microscale, and it caneffectively obtain fast velocities with relatively low power
and voltages. These perturbations could be extended to multiple line and point sources as well as arbitrary two dimensional arrays in order to produce geometrically complex flow
patterns in fluid films and pools.
Funding for this project was provided in part by the National Science Foundation, the University of Michigan, and aWhitaker Foundation Biomedical Engineering Fellowship to
one of the authors 共A.S.B.兲. The authors gratefully acknowledge Shamus McNamara for assistance in fabricating thethermal probes, and Seow Yuen Yee for laboratory assistance. Portions of this work have been published in conference abstract form in Refs. 15–17.
1Appl. Phys. Lett. 90, 034102 共2007兲

A. S. Basu and Y. B. Gianchandani

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