Slip Phenomina in Micro-Fluidic Devices

Dr. Phil Ligrani:    p_ligrani@msn.com

Improvements in manufacturing technology and micro-fabrication have led to the miniaturization of devices and sensors such as heat exchangers, micro-sensors, micro-pumps, biological reactors, selective membranes, and other devices. The ability to predict the fluid motion in and around these devices is essential for design and optimization of small scale devices like micro-pumps. As the length scales of these devices decrease, effects such as viscous dissipation, slip flow, roughness effects, non-Newtonian fluid behavior, and variations of fluid properties become significant for liquid flows because of micro-scale dimensions.

Micro-fluid-mechanics of liquids is more complicated and much less characterized than that for gases. In particular, the mechanisms through which liquids transport mass, momentum and energy are different from those of gases. In dilute gases, intermolecular forces play no role as the molecules spend most of their time in free flight between brief collisions at which instances the molecules direction and speed abruptly change. Thus, random molecular motions are responsible for gaseous transport processes. In liquids, however, the molecules are closely packed although not fixed in one position and are in essence always in a collision state. Liquid molecules are much more closely packed than gases at normal pressures and temperatures, and the attractive or cohesive potential between the liquid molecules plays a dominant role if the characteristic length of the flow is sufficiently small. Water molecules are particularly complex, forming directional, short-range covalent bonds, which require more complex models to describe intermolecular interactions. The straining between liquid molecules causes some to separate from their original neighbors, bringing them into the force fields of new molecules. The incompressible Navier-Stokes equations describe liquid flows under many circumstances, but it is currently unknown at what point these continuum equations fail to adequately describe liquid flows. At very small scales or under extreme conditions, liquids whose behavior is dominated by the motions of discrete molecules are different from liquids which behave as a continuum. Of particular interest is how small a device must become before near-wall flow slippage is perceptible.

In many cases, wall slip for Newtonian fluids, which generally acts over distances of molecular size (and sometimes over distances on the order of a millimeter), has negligible effects on macroscopic behavior. However, in many other situations, slip is observed experimentally in liquid flows. Such slip phenomena in liquids is not a function of mean free path, as with gases, but is dependent on fluid properties, interactions between the fluid and the wall, and shear rate at the wall. For liquid flows, surface roughness also influences the magnitude of the slip flows. The relationship between surface roughness and surface slip is controversial but there are a number of methods for altering roughness and consequently slip conditions, for example, by employing hydrophobic needle structures on the solid surface, or “nanoturf”.

A spinning disk above a C-shaped channel provides the flow environment under investigation. The spinning of the disk induces fluid motion in the C-shaped channel by diffusion of momentum. Different flow rates are obtained by changing the disk rotational speed. This arrangement is unique and special because it gives lower magnitudes of experimental uncertainty for slip length in liquid flows with surface roughness compared to measurements of the same quantity in micro-passages and micro-channels, provided comparisons are made on the basis of similar flow passage hydraulic diameter. The present research examines effects of a variety of phenomena on slip due to roughness in Newtonian liquid flows, including the effects of changing either (in combination or individually), channel height, disk rotational speed, surface material, and level of disk surface roughness. Changes of these different parameters allow the effects of shear stress rate on slip to be quantified over a range of experimental conditions. Shear-rate dependence of slip flow in liquids is a characteristic of some non-Newtonian fluids, but may also be present at high shear rates, even in fluids that are generally considered to be Newtonian. Exact solutions to the Navier-Stokes equations with first-order slip flow boundary conditions are derived for these arrangements to show the effects of liquid slip flows on overall pressure rise and flow rate, and to account for surface roughness effects. The present experimental and analytical results are unique because they provide new information on the dependence of slip flows on a variety of different experimental flow conditions and parameters for a Newtonian liquid. An investigation is also underway to consider slip phenomena in non-Newtonian fluids.

Copyright Trademarks Ligrani Research Group 2009