Mechanics of nanoparticle adhesion — A continuum approach

32J. TomasFigure 8. Particle contact forces for titania powder (median particle diameter d 50,3 = 610 nm, specificsurface area A S,m = 12 m 2 /g, surface moisture X W = 0.4%, temperature = 20°C) according to thelinear model Eq. (72), non-linear model Eq. (79) for instantaneous consolidation t = 0 and the linearmodel for time consolidation t = 24 h (Eq. (73)). The powder surface moisture X W = 0.4% is accuratelyanalyzed with Karl–Fischer titration. This is equivalent to an idealized mono-molecular adsorptionlayer being in equilibrium with an ambient air temperature of 20°C and 50% humidity.ure of irreversible particle contact stiffness or softness. A shallow slope designatesa low adhesion level F H ≈ F H0 because of stiff particle contacts, but a largeslope means soft contacts, or consequently, a cohesive powder flow behavior [91,147, 149]. The contact flattening may be additionally dependent on time or displacementrate (Section 2.1.3). Thus, the contact reacts softer and, consequently,the adhesion level is higher than before. This new adhesion force slope κ vis ismodified by the viscoplastic contact repulsion coefficient κ p,t , which includes certainviscoplastic microflow at the contact (Table 2 and Fig. 8),κκ + κF = ⋅ F + ⋅FAt ,p p,tHtot ,κ −κ −κ H0κ −κ −κNAt , p pt , At , p pt ,( 1 κ )= + ⋅ F + κ ⋅Fvis H0 vis N(73)with the so-called total viscoplastic contact consolidation coefficient κ vis that includesthe elastic-plastic κ p and the viscoplastic contributions κ p,t of contact flattening,