Micro-Flow in a bundle of micro-pillars. A. Keißner, Ch. Brücker

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1 Micro-Flow in a bundle of micro-pillars A. Keißner, Ch. Brücker Institute of Mechanics and Fluid Dynamics, University of Freiberg, TU Freiberg, Germany, armin.keissner@imfd.tu-freiberg.de Abstract In this paper we investigate the flow in a fluid channel, which is generated by an oscillatory wall with a bundle of micro-pillars on it. The micro-pillars are arranged in a "V"-shape similar to the human outer hair cell cilia. One interesting active fluid-transport mechanism in the biological world at small scales is that of cilia. They are sometimes used in nature simultaneous as sensors and actuators. Such an example is the role of the inner (IHCs) and outer hair cells (OHCs) in the organ of Corti. The eye-catching V -shaped arrangement of the OHCs hints on an additional micro-pump -effect that may explain the high sensitivity and selectivity of human hearing in small frequency bands. The question rises whether such a V-shape-like arrangement of the cilia with an oscillatory wall motion at the base may leads to a net displacement flow. When a defined arrangement of flexible micro-pillars is rebuilt in a similar shape as the OHCs, such a structure may be useful for efficient flow control such as a valve-less flow transport in micro fluidics. For the measurements presented herein we used a Micro-PIV system. The flow field around such a bundle was first measured under steady flow conditions. Thereafter we measured the net displacement velocity field by oscillating the base plane of the bundle of micro-pillars. The results proof that the "V"-shape produces a specific flow field in the small channel with a net displacement flow in direction of the tip of the V, when the base of the pillar bundle is excited to vibrate normal to the base plane, which is also the case in the human cochlea. 1. Introduction Up to now, the fluid dynamical interaction with bundles of cilia (Fig. 1) such as in the inner ear is not fully understood. To achieve more information about the effect of a bundle of micro hairs in a viscose environment we carried out Micro-PIV measurements in a "V"-shaped (Fig. 2) arranged pillar-array. One question was whether the arrangement of the cilia in addition to the oscillatory motion of the basilar membrane acts like a valve-less micro pump. Such a concept may be reasonable because of an anisotropic resistance in oscillatory excited wall vibration (Goismann & Quacke 2004). In Fig. 3 such a principle is shown in use for a valve-less micro-pump. When the upper wall of the chamber is pulled out there will be fluid sucked in. The resistance of the flow through the nozzle is in this case larger than that in the diffuser. Thus more fluid is sucked in at the diffuser side. By pushing the wall in the fluid is pressed out of the chamber in the same direction as it was sucked in. So when the wall is oscillating a net transport of mass is achieved, without the need of valves. To analyze if similar anisotropic resistance effects may play a role in the case of the specific V - arrangement of the cilia in the inner ear, we carried out experiments with a bundle of micro-pillars (Brücker et al. 2007) which were placed in a micro channel with a flexible side-wall. The first step was the measurements of the development of the flow field around the "V"-shape bundle of pillars. For this a steady flow was realized in the micro channel. For the research of the pumping effect we mount the pillar array on a piston. The oscillation of the base surface of the pillars is driven by a lift - 1 -

magnet. Fig. 1 cilia of human inner / outer hair cells in the inner ear [1] Fig. 2 V-shaped bundle of pillars (double row) Fig.

The dimensions of the channel are 60mm length, 30 mm width and 0.8 mm high.

The pillars have a diameter of 50µm and a height of 500µm. A flow can be produced by two injection needles.

The channel is positioned under a microscope for investigation of the flow field by Micro-PIV.

2 magnet. Fig. 1 cilia of human inner / outer hair cells in the inner ear [1] Fig. 2 V-shaped bundle of pillars (double row) Fig. 3 concepts of valve-less micro pumps [2] 2. Experimental setup For the experiments a micro channel was constructed. The dimensions of the channel are 60mm length, 30 mm width and 0.8 mm high. The top wall is an object glass while the bottom wall is an elastic membrane with the bundle of micro-pillars mounted on. The pillars have a diameter of 50µm and a height of 500µm. A flow can be produced by two injection needles. One is mounted on a perfusion pump, the other one is used as a drain tank. As fluid we used a water glycerin mixture with a kinematic viscosity υ of 8 10e-6 m/s². The channel is positioned under a microscope for investigation of the flow field by Micro-PIV. The microscope has two light arms in which the laser can be coupled in and the high speed camera is mounted. A lift magnet is used to excite the base plane of the pillar bundle by moving the flexible base membrane up and down. The oscillatory motion is controlled by a frequency generator. As tracers we used fluorescently labeled microparticles with a diameter from 1 up to 20µm. The micro PIV measurements were done with an epifluorescent illumination. The measurement plane is defined by depth of focus of the microscope optics

Fig. 4 experimental setup Fig. 5 sketch of the optical setup 3. Results The first experiment is the measurement of the influence of the "V"-shaped bundle of micro pillars on a steady flow.

By the constriction caused by the pillars the flow partly is displaced around the structure such as if the bundle is a solid obstacle.

The flow field structure looks similar to the other flow direction. Fig. 6 micro PIV measurement under steady flow Re=1,13 related to the pillar length Fig.

3 Fig. 4 experimental setup Fig. 5 sketch of the optical setup 3. Results The first experiment is the measurement of the influence of the "V"-shaped bundle of micro pillars on a steady flow. The result is shown in Fig. 6. The flow field is symmetrical to the axis of the flow direction and the axis of the bundle. By the constriction caused by the pillars the flow partly is displaced around the structure such as if the bundle is a solid obstacle. Downstream, the arrangement of the pillars has the effect that the velocity vectors were focused to the middle of the "V"-shape. Fig. 7 displays the flow field when the flow direction is changed. The flow field structure looks similar to the other flow direction. Fig. 6 micro PIV measurement under steady flow Re=1,13 related to the pillar length Fig. 7 micro PIV measurement under steady flow Re=1,25 related to the pillar length For flow measurements with an oscillatory excitation of the base plane we removed the injection needles and drove the piston in a sinusoidal shape with different frequencies up to 20Hz at maximum amplitudes of 200µm. The micro PIV measurements were phase triggered. The results are shown in Fig. 8 and Fig

Fig. 8 pulse rate 3Hz, Reynolds number Re=8,75 10-5, Wormersley number Wo=0,77 Fig. 9 pulse rate 5Hz Reynolds number Re=3,1 10-3, Womersley number Wo=1 5.

Thus the near wall flow is locally accelerated around the "V"- shaped arrangement of pillars. When the base surface of the pillars oscillates a net flow rate in the tip direction is established.

the net mass transport. Because of the small Reynolds numbers the fluid has a pure viscous behavior balanced by the pressure distribution.

For the fluid ahead of the V -tip the resistance for passing the pillars outside is smaller as to move across the hairs in the bundle array (Fig. 10).

4 Fig. 8 pulse rate 3Hz, Reynolds number Re=8, , Wormersley number Wo=0,77 Fig. 9 pulse rate 5Hz Reynolds number Re=3,1 10-3, Womersley number Wo=1 5. Discussion When the bundle of pillars is exposed to a steady flow it can be shown that a focusing of the velocity vectors can be achieved. Thus the near wall flow is locally accelerated around the "V"- shaped arrangement of pillars. When the base surface of the pillars oscillates a net flow rate in the tip direction is established. Our assumption is that the asymmetry in the resistance of the V-bundle against the radially oriented displacement flow driven by the down- and upwards movement of the base surface is responsible for the net mass transport. Because of the small Reynolds numbers the fluid has a pure viscous behavior balanced by the pressure distribution. By the downward movement a sink occurs in the middle of the piston. The fluid in the plane parallel to the wall flows radially to the sink. For the fluid ahead of the V -tip the resistance for passing the pillars outside is smaller as to move across the hairs in the bundle array (Fig. 10). As the piston goes up the fluid is squeezed away from the piston. The fluid which flows toward the pillar array can't flow around the bundle again but it is forced to flow through the hairs of the bundle. An additional effect is the structural bending of the pillars itself in response to a downward or upward motion of the membrane, which leads to a shrinking and expanding motion of the hair bundle. Overall, the result is a net flow in direction of the tip of the bundle and a pair of vortices at the edges of the V. Fig. 10 radial inflow induced by the downward movement of the piston Fig. 11 radial outflow induced by the upward movement of the piston - 4 -

5 6. Conclusion A shown in the paper a "V"-shaped bundle of micro pillars in a fluid has an essential effect when the base plane is excited in the way of an oscillatory wall, i.e. it produces a net displacement flow field in the direction of the tip of the V. In a steady flow it reacts like a fluid dynamic lens. It vectorizes the flow field to middle of the V. By oscillating the base membrane a net mass transport can be achieved. The mechanism why this happens is related to the anisotropic resistance of the pillar bundle against different flow directions and a possible shrinking and expanding motion of the bundle. Further measurements are necessary to analyze the flow in different planes to determine the three dimensional motion. However, the experiments already give some new ideas about the specific configuration and arrangement of the cilia in the cochlea. The outer hair cells are used for amplifying the traveling waves in the corti organ and the so induced flow field may play an additional role. Further experiments with different excitation patterns are necessary to improve our understanding of the cochlea amplifier. The same experimental set-up can be used to study the active flow transport by beating cilia in metachronal waves, which is focus of future work. References [1] Karavitaki, Mountain (2003) Biophysics of the Cochlea: From Molecules to Models. A. W. Gummer, editor. World Scientific, Singapore [2] Goismann & Quacke (2004) A Microfluidic Rectifier: Anisotropic Flow Resistance at Low Reynolds Numbers, The American Physical Society [3] Brücker Ch., Bauer D., Chaves, H. (2007): Dynamic response of micro-pillar sensors measuring fluctuating wall-shear stress. Exp Fluids 42(5), p

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