ABSTRACT
The primary adhesion forces for a dry uncharged particle on a dry uncharged surface are the van der Waals and electrostatic forces. The van der Waals forces can increase due to particle and/or surface deformation that increases the particle contact area. Electrostatic forces, although they predominate for particles larger than 50 jim, play a significant role in bringing particles to surfaces. In humid environments, liquid can condense between the particle and substrate, giving rise to a very large capillary force, which increases the total force of adhesion. Zimon [7] concluded that when the relative humidity is above 70%, the capillary force dominates and should be the only adhesion force considered. The capillary force consists of two main components: the surface tension at the perimeter of the meniscus and the pressure difference between the liquid and vapor phases [18]. The effect of relative humidity on the removal force has also been studied by Bowden and Throssel [17]. They suggested that the force required to remove 98% of 50-micron glass particles from a glass substrate increases with increasing relative humidity. The study, however, did not provide the adhesion force as a function of humidity. Many studies have been conducted to investigate particle adhesion and removal. Very few studies, however, considered the effect of relative humidity. The overall objective of this study is to develop an understanding of the effects of the relative humidity on particle adhesion for different particle/ substrate systems. The specific objective of this study is to determine the effect of relative humidity on the adhesion force between the following
(2)
(3)
(4)
(5)
(7)
(8)
and the Saffman lift force that is given as [15]:
(9)
where d is the particle diameter, p is the fluid density, and v is the kinematic viscosity of the fluid. U* is the friction velocity. The friction velocity has the dimensions of velocity and is defined as:
(10)
where r0 is the shear stress. The centrifugal force in both flow regimes (laminar and turbulent)
depends on the mass of the particle as well as the speed of rotation and is given as [20]:
( i i )
where m is the mass of the particle, u is the rotational speed of the substrate, and R is the radial distance from the axis of rotation to the particle position on the substrate. The Reynolds number is calculated at any radial distances, R, from the center of the substrate. Equations (6) and (7) are used to calculate the drag and lift forces for laminar flow, and Eqs. (8) and (9) are used to calculate the drag and lift forces for turbulent flow. The centrifugal force is calculated using Eq. (11) and is vectorially added to the drag and lift forces to calculate the total removal force.
