Boundary layers: small regions, huge impact
07/01/2002
by Robert P. Donovan
The transition region between different materials in intimate contact can have profound effects. Consider the p-n junction, the metal-semiconductor contact, the oxide-silicon interface and thermocouples-all examples of solid-solid interfaces.
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People and equipment in a cleanroom introduce boundary layers that upset the idealized vertical laminar flow characteristic initially hypothesized for clean airflow between ceiling entry filters and floor exit vents.
The transition regions to be discussed in this column, however, are the various boundary layers that exist between a fluid (liquid or gas phase) and a solid surface. Such transition regions have important consequences in the design and operation of liquid baths and rinse tanks, in R/O operations, in gas flow-through pipes, in airflow through cleanrooms and in virtually all fluid dynamic phenomena.
The aerodynamic/hydrodynamic boundary layer
The aerodynamic/hy dro dynamic boundary lay er describes the transition region be tween fluid flow at a solid surface and the free stream fluid flow in the region re mote from that surface and independent of it.
This most common of boundary layers assumes a no-slip condition at the surface. In a no-slip condition, fluid flow at a surface is zero, regardless of the free stream flow velocity remote from that surface. The boundary layer is the region between the surface at which fluid velocity equals zero and the closest point having the constant free stream fluid velocity.
In a simple, two-dimensional laminar flow boundary layer, the fluid velocity increases with the square of the distance from the surface, giving a parabolic shape to a plot of fluid velocity across the boundary layer. In turbulent flow, the boundary layer still represents the transition region between the surface and the free stream region, but the fluid velocity in the boundary layer is disordered and unsteady.
People and equipment in a cleanroom introduce boundary layers that upset the idealized vertical laminar flow characteristic initially hypothesized for clean airflow between ceiling entry filters and floor exit vents in cleanrooms.
The concentration/diffusion boundary layer
Similar to the velocity of fluid streamlines remote to a surface, the concentration of particles and other contaminants in a well-mixed fluid are independent of remote surfaces.
With the assumption that particle/contaminant contact with a surface implies capture, their concentration becomes zero at the surface, analogous to the zero fluid velocity of the aerodynamic/hydrodynamic boundary layer. Between the boundary defining the start of the remote region of constant, non-zero concentration and the zero concentration at the surface is the transition region in which particle/contaminant concentration decreases.
Diffusion is the primary mechanism by which particle/contaminants traverse this concentration/diffusion boundary layer, and the concentration profile across this boundary layer is that characteristic of diffusion processes, such as the complementary error function.
The width of a concentration/diffusion boundary layer is typically less than that of the aerodynamic/hydrodynamic boundary layer. Its existence, however, is one of the major factors determining contaminant deposition on surfaces exposed to contaminated fluid flows.
Concentration polarization
Concentration polarization describes the accumulation of contaminants adjacent to the membrane of a cross-flow filter such as an R/O element.
Liquid flow on the contaminated side of the membrane has a component perpendicular to the membrane surface. Species rejected by the membrane accumulate in the hydrodynamic boundary layer adjacent to the contaminated fluid side of the membrane and obstruct the flow of subsequent contaminated fluid to the membrane surface, reducing the permeate flow.
In addition, this buildup of contaminants on the dirty side of the membrane increases the osmotic pressure across the membrane, further reducing the permeate flow. The width of the concentration polarization region is less than that of the hydrodynamic boundary layer.
Other boundary layers
Other types of boundary layers can also be important. For example, an electrostatic boundary adjacent to solid surfaces immersed in liquids can play a dominating role in particle deposition on wafers in a liquid bath. [1]
The electrostatic potential at the shear plane between an immersed particle and a flowing fluid-the zeta potential-interacts with the electrostatic potential of the wafer to create either a repulsive or an attractive electrical force. Repulsive electrical forces can prevent particle/wafer contact and thus prevent particle deposition. The width of such electrostatic boundary layers is considerably smaller than either the hydrodynamic or diffusion boundary layers.
Boundary layers between different phases, like transition regions between different materials, are small volumes that can have big effects in cleanrooms and on the performance of cleanroom products.
However, different types of boundary layers arise from different properties and have different consequences. In order to avoid unnecessary confusion, the term boundary layer should be preceded by an explicit, qualifying adjective.
Robert P. Donovan is a process engineer assigned to the Sandia National Laboratories.
Reference
- Riley, D. J., "Particulate Deposition in Liquid Systems," Chapter 6 in Contamination-Free Manufacturing for Semiconductors and Other Precision Products, Robert P. Donovan, Editor, Marcel Dekker Inc. (2001)