whereas previous models, Rumpf model [6] and the

Relative humidity is another practical parameter encountered in fine powder (approx. less than 100 pcm) handling, and the resultant capillary forces contribute significantly to the adhesion force between the particles. A systematic investigation was conducted at the PERC to evaluate the role of humidity in adhesion between surfaces with nano-scale roughness. The simplified geometry of liquid bridges between an ideal smooth solid sphere and flat substrate for varying humidity conditions is shown in Fig. 2. At any given circumstance, depending on the relative humidity, only one of the two radii would exist and the bridge would be symmetric. This geometry was the basis for the theoretical framework developed to predict the onset and magnitude of capillary and dry adhesion forces in the presence of nanoscale roughness [19]. The force of adhesion (F) of a particle of radius R to a flat surface as a function of separation distance, H, at a given relative humidity was expressed as:

where y is the surface tension of the liquid and 6 is the contact angle of the liquid on the particle surface. RMS is the root mean square roughness of the surface

(2)

and r is the equilibrium radius of the liquid bridge at the given relative humidity as calculated by the Kelvin equation [20]. This basic framework was validated with direct measurement of surface forces using the A F M . Capillary adhesion was substantially lower in the presence of nanoscale roughness as shown in Fig 3. The points in the figure represent the experimental data and the solid black line is the theoretical estimate using equation (2). The values of RMS roughness shown in Fig. 3 were used as fitting parameters for equation (2) and these values were in good agreement with directly measured values of roughness of the substrates. In addition to the lowering in the magnitude of the adhesion force, the critical relative humidity, where capillary forces are first observed, increased with the nanoscale roughness. Although higher scales (micrometer level) of roughness may be present on real surfaces, it is suggested that the smallest scale (nanoscale) roughness contributes primarily to the reduction in adhesion between the surfaces [19]. The reduction in adhesion in the dry state is due to decrease in contact area and increase in the separation distance between the bulk surfaces. This phenomenon is of significant practical relevance when de-dusting or detachment of fine particles from surfaces is required, or where powder caking might occur.