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We present a numerical study of the dynamics of an elastic fibre in a shear flow at low Reynolds number, and seek to understand several aspects of the fibre's motion using the equations for slender-body theory coupled to the elastica. The numerical simulations are performed in the bead-spring framework including hydrodynamic interactions in two theoretical schemes: the generalized Rotne–Prager–Yamakawa model and a multipole expansion corrected for lubrication forces. In general, the two schemes yield similar results, including for the dominant scaling features of the shape that we identify. In particular, we focus on the evolution of an initially straight fibre oriented in the flow direction and show that the time scales of fibre bending, curling and rotation, which depend on its length and stiffness, determine the overall motion and evolution of the shapes. We document several characteristic time scales and curvatures representative of the shape that vary as power laws of the bending stiffness and fibre length. The numerical results are further supported by an interpretation using an elastica model. 

The dynamics of the wrapping of a charged flexible microfiber around an oppositely charged curved particle immersed in a viscous fluid is investigated. We observe that the wrapping behavior varies with the radius and Young's modulus of the fiber, the radius of the particle, and the ionic strength of the surrounding solution. We find that wrapping is primarily a function of the favorable interaction energy due to electrostatics and the unfavorable deformation energy needed to conform the fiber to the curvature of the particle. We perform an energy balance to predict the critical particle radius for wrapping, finding reasonably good agreement with experimental observations. In addition, we use mathematical modeling and observations of the deflected shape of the free end of the fiber during wrapping to extract a measurement of the Young's modulus of the fiber. We evaluate the accuracy and potential limitations of this in situ measurement when compared to independent mechanical tests. 

Pulsed-UV light in the continuous flow of a photo-crosslinkable liquid can result in gelation and is a useful method to produce soft microfibers with uniform sizes. With modeling and experiments, we characterize some aspects of this fiber fabrication process. We model the spatial concentration profiles of radical species and molecular oxygen in the flow direction during light exposure, and predict the critical conditions for the onset of fiber formation and compare these predictions with experimental observations. We also characterize the different regimes of microfiber production (no polymerization, non-uniform fibers, and uniform microfibers), qualitatively characterize the rigidity of the fibers, and demonstrate that we can predictably control the length of the produced microfibers for a range of process parameters. 

We report an experimental investigation of pressure-driven flow of a viscous liquid across thin polydimethylsiloxane (PDMS) membranes. Our experiments revealed a nonlinear relation between the flow rate $$Q$$ and the applied pressure drop $$\unicode[STIX]{x0394}p$$ , in apparent disagreement with Darcy’s law, which dictates a linear relationship between flow rate, or average velocity, and pressure drop. These observations suggest that the effective permeability of the membrane decreases with pressure due to deformation of the nanochannels in the PDMS polymeric network. We propose a model that incorporates the effects of pressure-induced deformation of the hyperelastic porous membrane at three distinct scales: the membrane surface area, which increases with pressure, the membrane thickness, which decreases with pressure, and the structure of the porous material, which is deformed at the nanoscale. With this model, we are able to rationalize the deviation between Darcy’s law and the data. Our result represents a novel case in which macroscopic deformations can impact the microstructure and transport properties of soft materials. 

A microfluidic technique recently proposed in the literature to measure the interfacial tension between a liquid droplet and an immiscible suspending liquid [Hudson et al. , Appl. Phys. Lett. , 2005, 87 , 081905], [Cabral and Hudson, Lab Chip , 2006, 6 , 427] is suitably adapted to the characterization of the elastic modulus of soft particles in a continuous-flow process. A microfluidic device consisting of a cylindrical pipe with a reduction in cross-section is designed, and the deformation and velocity of incompressible elastic particles suspended in a Newtonian liquid are tracked as they move along the centerline through the constriction. Kinematic and shape information is exploited to calculate the particle's elastic modulus by means of the theory of elastic particle deformation in extensional flow. The approach is validated for different orders of magnitude of the elastic capillary number through experiments and numerical simulations.