5th Micro and Nano Flows Conference
Milan, Italy, 11-14 September 2016

Measurements of micro-mushroom patterns in a magnetic micromixer
F. Gökhan ERGİN 1,** Corresponding author: Tel.: +45 4457 8173; Fax: +45 4457 8001; Email: gokhan.ergin@dantecdynamics.com
1 Product Manager, Dantec Dynamics, Skovlunde, DK
Keywords: MicroPIV, Adaptive PIV, magnetic micromixer, local contrast normalization, difference of Gaussian filter, front detection

Fingers and mushroom patterns are common features atthe interface of surface instabilities. These can beobserved in different scales: large-scale examples are theremnants of supernova explosions, (Fig. 1a), nuclear
detonations (Fig. 1b), hot gas and ash produced byvolcanic eruptions (Fig. 1c). Smaller scale examples canbe produced at home using 2 liquids with differentdensities (Fig. 1d). These patterns are often described by
the Rayleigh-Taylor Instability (RTI), where a heavy fluid
is above a lighter fluid in the presence of a gravitational
field. Similar patterns can be produced with othermechanisms, as long as one fluid is forced to penetrate
into another across a flat interface. For example if
magneto-hydrodynamic forces are used the instability iscalled Magnetic Rayleigh-Taylor Instability (MaRTI).

(a)

(b)

(c)
(d)
Figure 1 Examples of finger and mushroom formations
observed in nature. (a) Crab nebula (b) Nuclear explosion(c) 1990 Redoubt volcano (d) Two liquids with different
densities in a glass container. Image credits: Wikipedia
commons
Recently, MaRTI has been the subject of several
experimental studies in micro scale, where a magnetic
fluid and water was forced to penetrate into each otherusing an electromagnet [1-5]. The first quantitative
velocity field was measured using MicroPIV incombination with image pre-processing functions, such as
contrast normalization and Gaussian difference filters [1].
A successful model was developed for the magnetic

microconvection problem [2] based on the experimentalresults. In order to understand the reasons behind theformation of these finger and mushroom patterns the flow
field information and the interface front is required
simultaneously [3]. Time-resolved information onvelocity and interface location revealed the well-known
finger and mushroom patterns typical to this instability inRef. 4 where an uncertainty analysis of the measurement
was also reported [4]. Modal analysis of the MaRTI
instability was performed using Proper Orthogonal
Decomposition (POD) and Oscillating Pattern
Decomposition (OPD) [5]. In this study we revisit thedata acquired in Ref. 4 and focus on an individual finger
turning into a mushroom.
MicroPIV technique has great potential in providing
multi-parameter information in microfluidics research on
mixing and the details of the experimental setup can befound in Ref. 4. Briefly, the Hele-Shaw cell wasconstructed using two cover glasses separated with a
127-µm-thick Parafilm. A magnetic fluid and deionised
water was brought into contact in the cell with a relatively
flat interface. Then the Hele-Shaw cell was placed in thecenter of the electro-magnet and the magnetic field wasapplied before pure solvent was mixed in the magnetic
fluid. The magnetic forces were produced using anelectromagnet, which produced a magnetic field strengthof 1.8 mT in the central part of the coil. Both phases wereseeded with 1µm Nile-red fluorescent particles with thesame seeding density. Experiments are performed using a
MicroPIV system consisting of an inverted fluorescencemicroscope, a high quantum efficiency PIV camera, apulsed LED illumination device, a synchronization box
and a system controller. Image recording, image
pre-processing, MicroPIV analysis, vector processing andgraphical display of results were performed using theDynamicStudio software.
In Ref. 4 both the velocity and the interface information
are extracted from a sequence of time-resolved particle
images. Planar velocity measurements are obtained using
an adaptive cross-correlation algorithm, where particle
image contrast was enhanced using image pre-processing.
The use of image pre-processing functions proved to be
essential: First, local contrast normalization anddifference of Gaussian filters are used to enhance theparticle image contrast [1]. Second, interface location isestimated using Prewitt edge detection filter together witha combination of standard image processing functions [3].

5th Micro and Nano Flows Conference
Milan, Italy, 11-14 September 2016

It was found that only some of the fingers turn intomushroom patterns in the presence of counter-rotating
vortex system [4]. The fingers oriented in the horizontal
plane (against the flow) tend to produce some mushroompatterns. On the other hand, the fingers located at the top
and bottom of the FoV oriented vertically (perpendicularto the flow direction) are simply convected towards left
under the influence of the main flow of the water phase.
In particular, one horizontal finger close to the middle of
the FoV in Fig. 8k to 8o in Ref. 4 gradually changes intoa mushroom shape (Fig. 2). The thickness of the finger in
Fig. 2a is approx 120µm, and this gradually turns into amushroom shape with a size of approx 195µm (Fig 2c).
The size of the transforming finger at each time step isshown next to each subfigure and the velocity vectors areplaced every 20µm in Fig. 2. To the authors knowledge
this is the smallest mushroom pattern measured as a resultof a RTI, where quantitative flow field and interface
information is available simultaneously. Motion of raw
particle images, time resolved velocity field, POD-filteredflow field and the interface are available in Ref. 6. Whenthe average flow velocity is subtracted, a counter-rotating
vortex system is observed with the center of the vortex
system coinciding with the centerline of the growing
finger. In fact, the observed counter-rotating vortex
system in the plane is the cross-sectional view of a
toroidal vortex in three dimensions.

REFERENCES[1] Ergin FG, Watz BB, Erglis K and Cebers A“Poor-contrast particle image processing in Microscale mixing” Proc. ASME ESDA 2010; 10th Biennial
Conference on Engineering Systems Design andAnalysis, Istanbul, Turkey (2010)[2] Erglis K, Tatulchenkov A, Kitenbergs G, Petrichenko
O, Ergin FG, Watz BB, and Cebers A, “Magnetic field
driven micro-convection in the Hele-Shaw cell”
J. Fluid Mech. 714 (2013) 612–633.
[3] Ergin FG, Watz BB, Erglis K and Cebers A“Planar velocity & concentration measurements in amagnetic micromixer with interface front detection”
Proc. PIV13; 10th International Symposium on
Particle Image Velocimetry, Delft, The Netherlands(2013)[4] Ergin FG, Watz BB, Erglis K and Cebers A“Time-resolved velocity measurements in a magnetic
micromixer” Exp. Therm. Fluid. Sci. 67 (2015) 6-13
[5] Ergin FG, Watz BB, Erglis K and Cebers A“Modal analysis of magnetic microconvection”
Magnetohydrodynamics 50 (2014) 339-352[6] Microfluidics application example – Modal analysisof magnetic microconvection:
http://www.dantecdynamics.com/microfluidics-category/modal-analysis-in-a-micromixer

120µm

(a)

175µm

(b)

195µm

(c)
Figure 2 Flow field around an individual finger turning
into a mushroom. (a) t=12.5 s (b) t=15 s (c) t=17.5 s