A brand new approach to establish stresses in advanced fluids

Fluid dynamics researchers use many strategies to review turbulent flows like ocean currents, or the swirling environment of different planets. Arezoo Adrekani’s crew has found {that a} mathematical assemble utilized in these fields offers precious details about stress in advanced movement geometries.

Ardekani, a Purdue College professor of mechanical engineering, research advanced flows: from the transport processes associated to biopharmaceuticals, to the conduct of microorganisms round an oil spill. “Newtonian fluids like water are easy to know, as a result of they don’t have any microstructure,” she mentioned. “However advanced fluids have macromolecules that stretch and calm down, and that adjustments many properties of the fluid, resulting in very thrilling fluid dynamics.”

Viscoelastic flows happen often in nature, in biomedical settings, and in industrial functions—resembling options utilized in groundwater remediation. “When groundwater turns into contaminated, remediators use sure polymer-based options to disperse chemical compounds designed to interrupt down the contaminants,” Ardekani mentioned. “However what sort of polymer ought to they use, how a lot, and the place ought to they inject it? The one approach to reply these questions is by understanding the conduct of those flows, which comes all the way down to measuring stresses.”

Presently, the one approach to quantify the stresses of polymeric fluids is a way known as birefringence, which measure particular optical properties of the fluid. But it surely’s very troublesome to carry out, usually inaccurate, and would not apply to all varieties of macromolecules.

Ardekani’s crew has found a brand new method. The researchers created a mathematical framework that takes enter from movement velocity, obtained from particle picture velocimetry (a typical method in fluid dynamics), and outputs stress and stretching discipline topologies for advanced fluids. Their analysis has been featured in Proceedings of the Nationwide Academy of Sciences (PNAS).

In particle picture velocimetry (PIV), tracer particles are injected right into a fluid. Through the use of the motion of these particles, researchers can extrapolate details about the general movement kinematics. Whereas this may be readily used to judge stress in Newtonian fluids, Ardekani’s crew has found a mathematical correlation between these measurements and the stresses in viscoelastic flows.

All of it connects via one thing known as Lagrangian coherent constructions (LCSs). “Lagrangian coherent constructions are mathematical constructs used to foretell the dynamics of fluid flows,” Ardekani mentioned. “They’re utilized by oceanographers to foretell how currents will transfer; biologists who’re monitoring microorganisms; and even astrophysicists, who’re observing the turbulent clouds on locations like Jupiter.”

Whereas LCSs are sometimes utilized by turbulence researchers, they’ve by no means been utilized to polymeric stress till now. “We’ve got united two disparate branches of continuum mechanics,” Ardekani mentioned. “Utilizing Lagrangian stretching, and making use of it to Eulerian stress fields. And this is applicable to a variety of scales, from the mesoscale all the best way as much as trade scale measurements.”

The paper is a collaboration between Ardekani, her Ph.D. scholar Manish Kumar and Jeffrey Guasto, Affiliate Professor of Mechanical Engineering at Tufts College. They offered their findings in November on the seventy fifth Annual Assembly of the APS (American Bodily Society) Division of Fluid Dynamics in Indianapolis, which Ardekani co-organized.

Whereas the analysis is basically mathematical, Ardekani is worked up to see how experimentalists will use the method within the lab and in the true world. “Let’s use our groundwater remediation instance once more,” Ardekani mentioned. “Researchers sometimes use tracer evaluation on the injected fluids to measure the speed discipline. However now, they will additionally establish the stress fields, to allow them to extra precisely predict the transport of that fluid.”