We measure the deformation of particles made of several slender arms in a two-dimensional (2D) linear shear and a three-dimensional (3D) turbulent flow. We show how these measurements of arm deformations along with the rotation rate of the particle allow us to extract the velocity gradient tensor of the flow. The particles used in the experiments have three symmetric arms in a plane (triads) and are fabricated using 3D printing of a flexible polymeric material. Deformation measurements of a particle free to rotate about a fixed axis in a 2D simple shear flow are used to validate our model relating particle deformations to the fluid strain. We then examine deformable particles in a 3D turbulent flow created by a jet array in a vertical water tunnel. Particle orientations and deformations are measured with high precision using four high speed cameras and have an uncertainty on the order of 10 −4 radians. Measured deformations in 3D turbulence are small and only slightly larger than our orientation measurement uncertainty. Simulation results for triads in turbulence show deformations similar to the experimental observations. Deformable particles offer a promising method for measuring the full local velocity gradient tensor from measurements of a single particle where traditionally a high concentration of tracer particles would be required.
The behavior of deformable structures in fluid flows is a standard problem, but normally involves the interaction between a complex flow and a complex structure. Fibers are an example such an interaction: the curvature of a fiber in a fluid flow will correspond to the derivative of the velocity gradient tensor. In simpler flows however, where the velocity gradient tensor remains constant over time, fibers exhibit no deformation, making them no more useful than non-deformable structures. [1] We have identified a new opportunity for deformable structures by using deformable ramified particles. These particles interactions with linear velocity fields (i.e. flows with constant velocity gradient tensors) are simple enough that we can extract the full velocity gradient from a single deformable particle. Normally, numerous non-deformable particles would be required to extract the same information. This is of particular value when studying turbulent flows. Turbulent flows exhibit linear behavior at the kolmogorov length, but because this length is often exceedingly small, the seed density (density of tracer particles) needed to re-assemble the full velocity gradient tensor is prohibitively high. Using deformable ramified particles, which extract far more information on a per particle basis, we can make the same measurements while maintaining a low seed density.The use of ramified deformable particles represents a novel development in the field of fluid dynamics. As a proof of concept, we set out to test them in a simple, well understood fluid flow with well known fluid structure interactions.
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