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In this paper, the auxiliary principle technique is extended to study a system of generalized nonlinear mixed variational-like inequalities problem for set-valued mappings without compact values in Banach spaces with p-uniformly convex bidual spaces. First, the existence of the solutions of the related auxiliary problem is proved. Then, a new iterative algorithm based on the system of auxiliary variational inequalities is constructed. Finally, both the existence of the solutions of the original problem and the convergence of the iterative sequences generated by the algorithm are proved. And we also present a numerical example to demonstrate the result. Our results improve and extend some known results. [ABSTRACT FROM AUTHOR]

Abstract Microparticle adhesion and resuspension are critical in studies of surface contamination, non-contact sampling, environmental and occupational health assessments, and surface cleaning. Direct adhesion measurement methods that evaluate the pull-out force are often limited to a range of operational conditions. The established analytical models need additional terms to account for roughness, morphology, and environmental conditions. The proposed aerodynamic method offers a non-contact evaluation of particle-surface adhesion force. In this work, aerodynamic detachment of silica microspheres in the 12–26 µm range from a smooth glass surface is studied experimentally. Computational fluid dynamics (CFD) calculates the drag and lift forces acting on the particles. The adhesion force is derived from the moment balance required to initiate the rolling motion of the particle. The aerodynamic forces acting on the particle, calculated by the CFD, agree with the theoretical values for a spherical particle in the shear flow in the Stokes regime (Re <1). The aerodynamic force calculations are extended to Re = 1–1000. The aerodynamic method shows a monotonically increasing dependency of the adhesion force with particle diameter; the results are consistent with the theoretical models and the published experimental data. The approach can be extended to more complex systems, including the effects of roughness, particle morphology and aging, and a range of environmental conditions. Highlights • The aerodynamic method for determining the particle adhesion force provides consistent results with the DMT and JKR models. • The drag force computed numerically is consistent with the modified Stokes flow theory for Re<1. For Re>1. • Relationship between the drag coefficient and particle is developed for 1 < Re < 10 3. • The lift force is consistently at least at an order of magnitude less than the drag force and several orders of magnitude less than the adhesion force. The lift can be neglected in the adhesion calculations of spherical particle. Graphical abstract fx1 [ABSTRACT FROM AUTHOR]