Modeling the dynamic adhesion of colloidal objects flowing over nanotextured heterogeneous surfaces
Selective dynamic adhesion of particles and objects from flow over heterogeneous surfaces is observed in natural systems as well as current technologies. Accurate modeling and prediction of the dynamics of particles interacting with such surfaces will facilitate their use in applications for sensing, separating, and sorting colloidal-scale objects. The current study is aimed at addressing the need for a theoretical model which could provide a comprehensive understanding of the physics of such systems at the length scale of the heterogeneities. The model could be used to investigate and interpret effects of systems parameters on particle dynamics and provide design guidelines for obtaining desired selectivity on artificially patterned surfaces.
In this study, the dynamic adhesion behavior of micrometer-scale particles is investigated numerically for a low Reynolds number shear flow over a flat collecting surface with randomly distributed electrostatic heterogeneity ("patches") at the 10-nanometer scale. These patches are realized in experiments as cationic polymers deposited from flowing solution and lie flat on the surface. A novel technique based on surface discretization is introduced to facilitate computation of the colloidal interactions between a spherical particle and the heterogeneous surface based on expressions for parallel plates. The colloidal interactions are combined with the hydrodynamic forces and torques on a spherical particle yield a computational model for particle motion in a solution flowing over a heterogeneous collector. Spatial fluctuations in the local surface density of the deposited patches, which are due to the random distribution of the charge heterogeneities, are shown responsible for the dynamic adhesion signatures observed experimentally, including particle capture on a net-repulsive surface and selectivity based on particle size or curvature. Particle deposition rates on these nanotextured surfaces are obtained by simulating particle trajectories over a large number of surfaces and analyzing the data using a probabilistic approach. The model is extended to account for particle motion after surface contact by including contact or frictional forces in the force and torque balances and yields a predictive and interpretative simulation tool for studying particle skipping, rolling, and arrest on the heterogeneously charged surface. The influence of the patch density on the surface, particle size, Debye length, and shear rate is quantified through the construction of adhesion regime diagrams, which delineate the regions in parameter space that give rise to different dynamic adhesion signatures and suggest ways to control particle-surface interactions. The simulation data is analyzed to determine the threshold density of patches and the binding energy per patch at the adhesion sites.
The predicted adhesion signatures, adhesion thresholds, particle deposition rates, and selectivity are in strong agreement with experimental results and are reminiscent of motion signatures observed in cell adhesion under flowing conditions, although for the synthetic system long range, non-specific colloidal interactions take the place of specific physical bonds between the cells and functionalized surface.