There are a number of reasonably well understood forces that cause particles to adhere to a surface. While not necessarily, or even usually, the dominant force, van der Waals forces are universal they are always present. These van der Waals forces alone can be quite large. For example, the Hamaker expression for the van der Waals force between a spherical particle and a planar surface [Ref 1] is:
Fadh = A132 dp/12 Z02 (1) where:
- A132 is the Hamaker constant based on the composition of the three materials making up the system: particle (1), surface (2) and medium (3),
- dp is the diameter of the spherical particle, and
- Z0 is the atomic separation distance between the sphere and the plane.
Assuming the particle is a 1-micron glass sphere and the plane a bare silicon wafer, the magnitude of the van der Waals adhesion force calculated by inserting the appropriate values in eq. 1 is about 2.5 mdynes [Ref 2]. If the contact area between the sphere and the plane is 1 percent of the spherical diameter, the pressure resulting from this van der Waals force is predicted to be:
Interfacial pressure = Fadh/contact area = 10 x 10 -3 dynes/ π10 -12 cm2 or about 3.2 x 109 dynes/cm2.
The force required to remove surface particles is expected to be of the same order of magnitude as Fadh, varying somewhat with the mechanism by which the removal force is applied (centrifugal, hydrodynamic or aerodynamic drag, ultrasonics/megasonics, or other).
Researchers writing on particle adhesion estimate that particles of submicron diameter can be dislodged from a surface only by the application of forces corresponding to huge “g” forces [Ref 1]. Yet the common observation is that an ordinary flick of the finger against tubing feeding the input of a particle counter invariably causes a cascade of counts to be registered by the particle counter. How can these adhesion forces be as large as claimed and yet allow particles to be so easily re-entrained by such modest forces?
Part of the answer may lie with a particle deposit typically consisting of more than a monolayer. Another part may be due to the cohesion among the multiple particle layers stacked upon the surface of the tubing walls. This cohesion may be the controlling factor rather than the calculated van der Waals forces between the particle and the tube wall.
I've been startled by the highly visible layers of dust particles collected on the walls of the ducts I've used to measure the particle removal efficiencies of various particle control devices. In such measurements, a challenge particle stream of known, controlled properties, including concentration, enters the upstream side of the control device. The upstream and the downstream aerosol particle concentrations are then compared in calculating a particle removal efficiency of the device.
With efficient particle control devices, the downstream aerosol particle concentrations are quite small. Yet highly visible dust layers will coat the duct walls that are downstream of such a control device that has been under test over a period of time. This accumulation of particle layer shows that the aerodynamic forces of the airflow through the duct during the test series are insufficient to cause re-entrainment of all the wall particles.
Particle deposition and adhesion to the duct walls or the previously deposited particle layers exceeds or at the least matches the particle re-entrainment from the wall in a delicate balance. However, a simple finger flick can upset the delicate balance between aerodynamic drag and adhesion/cohesion, resulting in the large, temporary shower of downstream aerosol particles noted. Strange, unpredictable behavior, these particles.
Robert P. Donovan is a process engineer assigned to the Sandia National Laboratories as a contract employee by L & M Technologies, Inc., Albuquerque, NM.
1. Ranade, M. B., “Adhesion and Removal of Fine Particles on Surfaces”, Aerosol Sci. Technol. 7(2), 1987, p 161.
2. Menon, V. B., “Particle Adhesion to Surfaces: Theory of Cleaning”, Chap 21 in Particle Control for Semiconductor Manufacturing, R. P. Donovan, Editor, Marcel Dekker, Inc., NY, NY, 1990.