Numerical modeling of centrifugal microfluidic flow in rectangular channels for Lab-on-a-CD platform applications

Viorel IONESCUa

aDepartment of Physics and Electronics, Ovidius University, Constanta, Romania

1. Abstract A rectangular radial microchannel model having the same geometric

dimensions as one type of microchannel placed on a PC-controlled

centrifugal Disk: length l = 2.1 cm, height h = 65 µm and width Δy =

320 µm (AR = 4.9) was considered here from an experimental work

reported in the literature. Fluid flow transport through this

standard channel was numerically developed with the Finite

Element Method (FEM) based Comsol Multiphysics software,

simulation performed at rotating speeds ω between 25 and 300 rad/s.

Other three rotating microchannel models with different aspect

ratios AR have been simulated after by increasing the channel height

from 65 µm to 160 µm, 200 µm and 240 µm and by maintaining the

same width of 320 µm. From the simulations of rotating channel

with AR = 4.9 resulted that even at 300 rad/s, transverse Coriolis

force was only close to half of centrifugal force (β = 0.44), no

secondary flow being induced in this case and a diffusion-based

mixing is developed for this particular channel geometry.

4. Conclusions

Simulation study regarding the effect of AR reduction on the fluid flow transport showed that

when the channel height h increased from 65 µm to 160 µm for the same channel width Δy = 320

µm, a secondary flow start to arise under the Coriolis force based mixing regime (1 < β < 2).

A further increase of h at 240 µm generated a concave shape of velocity distribution near the

channel right wall (at outlet) for the channel model with the lowest hydraulic resistance R and the

highest average wall shear stress .

Simulations performed at ω = 300 rad/s for the microchannels with different AR values showed

that Coriolis force is manifesting with higher intensity along with an increasing channel distance

(starting from inlet) when AR decreased from 2 to 1.3 and Dh increased from 213.3 to 273.3 µm,

with a distortion of the convex pressure profile in the channel inlet direction.

2. Introduction. Model set-up In recent years, the areas of chemical analysis and biomedical

diagnostics have been boosted by the centrifugally operated

microfluidic devices [1,2]. These devices are based on an array of

microchannels placed on a circular substrate under rotation at a

specific frequency, an arrangement known as a lab-on-a-CD

platform (LabCD) [3]. When the rotation speed of a LabCD

platform is low, centrifugal force fω will dominate the flow in

microchannels. At higher rotation frequency, the dominant force will

be Coriolis force fc and a secondary flow will be developed,

perpendicular to the primary flow velocity. So, the enhanced fluid

mixing at such small scales appears by generating this secondary

flow caused by inertial forces [4].

One of the main advantages offered by the centrifugal techniques

is the simple motor actuation mechanism witch reduce the necessity

of an external pumping system, so this type of mixing system can be

ideal for low-cost applications.

A better understanding on the mixing effect produced by the

Coriolis force inside the channels of a CD-based platform after the

initiation of secondary flow can lead to an improved design

efficiency of the rotating microchannels through a proper selection

of their cross-section dimensions.

Fig. 3. Velocity field distribution pattern at different downstream positions close

to channel inlet for the first channel model with AR = 4.9 at ω = 300 rad/s

Fig. 4. Normalized axial velocity profiles along y-axis at Z-mid-plane at the channel outlet

with AR = 4.9 and (b) pressure drop along the radial direction for different rotational speeds

Fig. 5. Contour velocity profiles at the outlet of the rotating

microchannel models having: a) AR = 4.9, b) AR = 2, c) AR

= 1.6 and d) AR = 1.3, simulated at ω = 300 rad/s.

3. Results

References [1] Shamloo, A., Selahi, A. A., and Madadelahi, M., J. Micromech. Microeng. 26, 035017-035026 (2016). [2] Kong, L. X., Perebikovsky, A., Moebius, J., Kulinsky, L. and Madou, M., Journal of Laboratory Automation 21(3), 323–355 (2016). [3] Silva, G., Semiao, V., and Reis, N., “Flow Measurement and Instrumentation 67, 153–165 (2019). [4] Sengupta, S., Ghosh, S., Saha, S., Chakraborty, D., Physics of Fluids 31, 054101 (2019). [5] S. Haeberle, T. Brenner, H.-P. Schlosser, R. Zengerle, L. Ducree, Centrifugal Micromixer, Chem. Eng. Technol. 2005, 28(5), 613 – 617.

Fig.1. Geometry and forces for a mixing microchannel placed

on a microfluidic disk [5]

Fig. 2. Closer view of mesh discretization network (extra fine mesh) for

microchannel model under validation (l = 10 mm, Δy = h = 200 μm),

along with complete mesh statistics

2

0

D

yt

DMixing time: , y0 – diffusion distance

Average residence time of water molecules in the channel tres = ratio between

the channel volume (m3) and volumetric flow rate (m3/s)

tres ≥ tD at the end of the channel => complete diffusion of the fluids.

Fig. 6. (a) Pressure drop profile and

b) transversal velocity profile along the

channels center direction formed by

the intersection of Y and Z mid-planes

a = 22/7 and b = 65/3.