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We develop a forensic-like framework for network structural characterization based on an analysis of their nonlinear response to mechanical deformation. For model networks, this methodology provides information about the strand degree of polymerization between cross-links, the effective cross-link functionality, the contribution of loops and entanglements to network elasticity, as well as the fraction of stress-supporting strands. For networks with trapped entanglements, we identify a transition from cross-link-controlled to entanglement-controlled network elasticity with increasing degree of polymerization of network strands between cross-links and show how specific features of this transition are manifested in changes of entanglement and structural shear moduli characterizing different modes of network deformation. In particular, this cross-link-to-entanglement transition results in saturation of the network shear modulus at small deformations and renormalization of the degree of polymerization of the effective network strands determining nonlinear elastic response in the strongly entangled networks. The developed approach enables the classification of networks according to their topology and effectiveness of stress distribution between network strands. 

Flow-based manipulation of particles is an essential tool for studying soft materials, but prior work has nearly exclusively relied on using two-dimensional (2D) flows generated in planar microfluidic geometries. In this work, we demonstrate 3D trapping and manipulation of freely suspended particles, droplets, and giant unilamellar vesicles in 3D flow fields using automated flow control. Three-dimensional flow fields including uniaxial extension and biaxial extension are generated in 3D-printed fluidic devices combined with active feedback control for particle manipulation in 3D. Flow fields are characterized using particle tracking velocimetry complemented by finite-element simulations for all flow geometries. Single colloidal particles (3.4 μm diameter) are confined in low viscosity solvent (1.0 mPa s) near the stagnation points of uniaxial and biaxial extensional flow for long times (≥10 min) using active feedback control. Trap stiffness is experimentally determined by analyzing the power spectral density of particle position fluctuations. We further demonstrate precise manipulation of colloidal particles along user-defined trajectories in three dimensions using automated flow control. Newtonian liquid droplets and GUVs are trapped and deformed in precisely controlled uniaxial and biaxial extensional flows, which is a new demonstration for 3D flow fields. Overall, this work extends flow-based manipulation of particles and droplets to three dimensions, thereby enabling quantitative analysis of colloids and soft materials in complex nonequilibrium flows.