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Go With the Flow: Pitt researchers receive NSF grant to better understand how liquids and solids interact

PITTSBURGH (September 16, 2013) … The interaction of a viscous liquid with a solid body is a common phenomenon in nature that impacts everyday life from arterial blood flow and animal locomotion to structural damage from flooding to the manufacturing of short-fiber composites. To address two fundamental aspects of this interaction - the motion of a rigid body with internal cavities that are completely filled with a viscous liquid, and the vibration-induced motion of a rigid body in a viscous liquid, the National Science Foundation (NSF) Division of Mathematical Sciences has awarded a $183,000 grant to two researchers at the University of Pittsburgh Swanson School of Engineering. 

The grant, "Analytical and Numerical Study of Two Problems Arising in solid-Liquid Interaction," is led by Principle Investigator  Giovanni P. Galdi, PhD , Leighton E. and Mary N. Orr Professor of Mechanical Engineering and Professor of Mathematics, and Co-PI  Paolo Zunino, PhD , Assistant Professor of Mechanical Engineering and Materials Science. Dr. Galdi is a world-renowned expert within the field of mathematical fluid mechanics and editor-in-chief of the Journal of Mathematical Fluid Mechanics, and this recent funding represents the sixth NSF grant that he has participated as PI for approximately 15 years.

"We're continuing our research to develop mathematical and numerical analysis to better understand and predict how liquids and solids interact at two critical levels," Dr. Galdi explains. "Mathematics investigates the reliability of the system of equations provided by the engineer to model a particular problem, while numerical simulation analyzes their outcome and compares it to the actual experiment. This would help to advance engineering, biological and medical studies at both macro and micro scales by better predicting outcomes in everything from large-scale infrastructure projects and space exploration to developing robots that can move through fluids without external propulsion."

The first problem will study how the spontaneous mechanical oscillations of a hollow body can be reduced or totally eliminated by filling the cavity with a viscous liquid, and how this effect is enhanced by an appropriate choice of the liquid characteristics (density, viscosity, physical properties). This research will address macro systems such as geological processes as well rocket propulsion and avionics. 

The second problem addresses small- to medium-scale robotics, and how to propel a hollow body in a viscous liquid by a time-periodic displacement of internal masses. This phenomenon is the basis for the design of mobile systems able to move without special propelling devices, which present several advantages over systems based on the conventional principles of motion. "When you want to design a robot that for example needs to move through a medium where a propeller or other external motor that would actually hamper its movement, simple is better," Dr. Galdi says. "You can conserve space by eliminating gear trains to transmit motion from the motor to the propellers, and their body can be sealed and smooth. Moreover, they can be driven to a prescribed position with high degree of accuracy, and thus be used in high-precision positioning systems in microscopes, as well as in micro- and nano-technological equipment. 

"This principle of motion is suitable for capsule-type microrobots designed for motion in a strongly restricted space, and in vulnerable media, like inside a human body. In theory you could deliver a drug directly to a cancer tumor or blood clot without having the treatment spread throughout the entire body."