Oscillating Flow

Understanding the physics of oscillating (or transient) flows of complex fluids in small channels is of fundamental interest for many biological and industrial processes. E.g. the quasi-periodic blood flow in the cardiovascular system can be described by the frequency components of the pressure and flowrate pulses, and many vascular diseases are associated with disturbences of the local flow conditions in the blood vessels. In many technical applications like inkjet-printing a rapid switching between “flow” and “no flow” of a non-Newtonian fluid is required, and often very small channel geometries are involved. Especially the usually low-Reynolds numbers in such flows and the fact, that the dimensions of the channels and macromolecules in the fluid can be on the same order of magnitude, can lead to effects unseen in macroscopic systems.

We aim to shed light on bulk phenomena as well as on the behaviour of single molecules in constricted oscillatory flows. With oscillating the fluid, we can study both frequency-dependent effects and “long-time” effects that would require nonpractically long channels to be observed in steady flow.

Topics we investigate:  

 

  • Pressure and flow propagation in viscoelastic deformable channels
  • Secondary flow structures in oscillatory flows (steady streaming)
  • „Long time“ effects in high shear rate flows  

Setup:

A speaker is coupled to a reservoir with an elastic membrane and driven by a function generator. This generates oscillatory pressures in the reservoir which is connected to our standard microfluidic setup. 

 

 

Fig 1: While in bulk fluids a pressure oscillation is spreading with the speed of sound vc, in small channels with dimensions d << λ = vc/f the transmittance of flows is coupled to the properties of the channel walls. If the channel is “soft” and is deformed by the pressure, pressure pulses travel along the channel with speeds way lower than vc and disperse on their way through the channel. The same effect (shown here for a viscoelastic PDMS microfluidic channel) occurs in blood circulation: The distinct sharp pressure and flow pulses in the big arteries become more and more uniform while travelling further downstream into the smaller vessels. Reaching the smallest capillaries, the pulses are transformed into an almost steady flow.

 

Flash ist Pflicht!

Fig. 2: (click on the movie)

In small channels, the ratio between inertial and viscous forces (given by the Reynolds number Re) Wikipedia Link?  becomes quite small, so that inertia can usually be neglected in microfluidics. The centrifugal forces occurring at curved streamlines always point outward, regardless of the flow direction. Therefore, the (in steady flows neglectable) effects of the centrifugal forces accumulate in oscillatory flows and can give rise to a secondary, steady streaming flow. The movie shows a microfluidic contraction flow oscillating at 40 Hz. Fluorescent tracer beads of 1µm diameter are illuminated over approx 4 oscillation periods for each frame and therefore appear as stripes. The stripes show the direction of the underlying oscillating flow, the two vortices are the resulting steady streaming motion. 

Fig. 3:  Near the channel walls, DNA molecules in shear flow exhibit a lift force pointing away from the wall due to hydrodynamic interaction. The picture shows how fluorescently labelled DNA molecules are migrating away from the walls. The oscillation frequency is 0.5 Hz, each picture is a time average over several oscillation periods.