Mechanics of nanoparticle adhesion â A continuum approach

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2J. Tomasfeeding and dosing, as well as undesired effects such as widely spread residencetime distribution, time consolidation or caking, chemical conversions and deteriorationof bioparticles. Finally, insufficient apparatus and system reliability ofpowder processing plants are also related to these flow problems. The rapid increasingproduction of cohesive to very cohesive nanopowders, e.g., very adheringpigment particles, micro-carriers in biotechnology or medicine, auxiliary materialsin catalysis, chromatography or silicon wafer polishing, make theseproblems much serious. Taking into account this list of technical problems andhazards, it is essential to deal with the fundamentals of particle adhesion, powderconsolidation and flow, i.e. to develop a reasonable combination of particle andcontinuum mechanics.The well-known failure hypotheses of Tresca, Coulomb and Mohr and Druckerand Prager (in Refs. [1, 2]), the yield locus concept of Jenike [3, 4] and Schwedes[5], the Warren–Spring equations [6–10], and the approach by Tüzün [12], etc.,were supplemented by Molerus [13–16] to describe the cohesive, steady-stateflow criterion. Nedderman [17, 18], Jenkins [19] and others discussed the rapidand collisional flow of non-adhering particles, as well as Tardos [20] discussedthe frictional flow for compressible powders without any cohesion from the fluidmechanics point of view. Additionally, the simulation of particle dynamics of freeflowing granular media is increasingly used, see, e.g., Cundall [21], Campbell[22], Walton [23, 24], Herrmann [25] and Thornton [26].Additionally, particle adhesion effects are related to undesired powder blockingat conveyer transfer chutes or in pneumatic pipe bends [27] in powder handlingand transportation, to desired particle cake formation on filter media [28, 29], towear effects of adhering solid surfaces [30, 31], fouling in membrane filtration,fine particle deposition in lungs, formulation of particulate products [32–35] or tosurface cleaning of silicon wafers [36–40, 133], etc.The force–displacement behaviors of elastic, elastic–adhesion, plastic–adhesion, elastic–plastic, elastic–dissipative, plastic–dissipative and viscoplastic–adhesion contacts are shown. Based on these individual theories, a general approachfor the time and deformation rate dependent and combined viscoelastic,plastic, viscoplastic, adhesion and dissipative behaviors of a spherical particlecontact is derived and explained.2. PARTICLE CONTACT CONSTITUTIVE MODELSIn terms of particle technology, powder processing and handling, Molerus [13,14] explained the consolidation and non-rapid flow of dry, fine and cohesivepowders (particle diameter d < 10 µm) in terms of the adhesion forces at particlecontacts. In principle, there are four essential mechanical deformation effects inparticle–surface contacts and their force–response (stress-strain) behavior can beexplained as follows (Table 1):
Mechanics of nanoparticle adhesion — A continuum approach 3(1) elastic contact deformation (Hertz [41], Huber [42], Derjaguin [43], Bradley[44, 45], Cattaneo [46], Mindlin [47], Sperling [48], Krupp [49], Greenwood[50], Johnson [51], Dahneke [52], Thornton [53, 54], Sadd [55]), which is reversible,independent of deformation rate and consolidation time effects andvalid for all particulate solids;(2) plastic contact deformation with adhesion (Derjaguin [43], Krupp [56], Schubert[57], Molerus [13, 14], Maugis [58], Walton [59] and Thornton [60]),which is irreversible, deformation rate and consolidation time independent,e.g. mineral powders;(3) viscoelastic contact deformation (Yang [61], Krupp [49], Rumpf et al. [62]and Sadd [55]), which is reversible and dependent on deformation rate andconsolidation time, e.g., bio-particles;(4) viscoplastic contact deformation (Rumpf et al. [62]), which is irreversible anddependent on deformation rate and consolidation time, e.g., nanoparticles fusion.This paper is intended to focus on a characteristic, soft contact of two isotropic,stiff, linear elastic, smooth, mono-disperse spherical particles. Thus, this soft orcompliant contact displacement is assumed to be small (h K /d
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Mechanics of nanoparticle adhesion â A continuum approach