In the manipulations of nanoparticles in different environments, the manipulation dynamics have to be modeled precisely and the critical force and time of manipulation have to be computed. A dynamic manipulation modeling can be performed two- or three-dimensionally; and a three-dimensional modeling process is obviously more exact and complicated. In order to precisely model, in three dimensions, the dynamics of a nano-manipulation is performed by an atomic force microscope, where the stiffness values of various atomic force microscope cantilevers need to be calculated and modeled correctly. The cantilevers of an atomic force microscope are classified into three general groups (rectangular, V-shaped, and dagger-shaped) and each of these types is used for the manipulation of nanoparticles with particular characteristics. Also, in addition to the important application of stiffness in the dynamic modeling of a manipulation process, this model is very much needed in computing the critical force and time of manipulation, which are the two key parameters in the first phase of a manipulation. Due to the importance of the three-dimensional stiffness modeling of atomic force microscope cantilevers, first, the three-dimensional stiffness values of rectangular, V-shaped, and dagger-shaped cantilevers have been determined. The extracted stiffness models have then been validated by means of the finite element method. The comparisons between the stiffness values along different directions for the three mentioned types of cantilevers indicate that the V-shaped cantilever has the highest lateral stiffness, the dagger-shaped cantilever has the least amount of normal stiffness, and the rectangular cantilever enjoys the highest torsional stiffness.
Three dimensional modeling of liquid droplet spreading on solid surface: An enriched finite element/level-set approach
