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CNA Seminar/Colloquium/Joint Pitt-CNA Colloquium
Colloquium
Roberto Camassa
University of North Carolina
Title: Tailoring the tails in Taylor dispersion

Abstract: The interplay between fluid flow and diffusion of a solute in the fluid is a primary mechanism for transport and mixing of substances, and one of the most ubiquitous phenomena in nature. Since the seminal investigation by G.I. Taylor in 1953, it has also been the focus of much mathematical efforts to model it. Taylor's counterintuitive result -- that at long times the effective diffusivity determined by the flow scales like the inverse of the tracer's molecular diffusivity -- is a classical illustration of mathematical analysis' predictive power and arguably one of the most remarkable effects demonstrated in this context. This talk will report results that focus on the interaction of advection and diffusion with fluid boundaries, such as pipes or ducts, at early and intermediate time scales in the transport process. This can have direct applications to microfluidics. Many microfluidic systemsincluding chemical reaction, sample analysis, separation, chemotaxis, and drug development and injectionrequire precision and control of solute transport. Although concentration levels are easily specified at injection, pressure-driven transport through channels is known to spread the initial distribution, resulting in reduced concentrations downstream. By monitoring the skewness (centered, normalized third moment) of the tracer distribution in laminar, pressure driven flows an unexpected phenomenon can be revealed: The channel's cross-sectional aspect ratio alone can control the shape of the concentration profile along the channel length. Thin channels (aspect ratio << 1) deliver solutes arriving with sharp fronts and tapering tails, whereas thick channels (aspect ratio ~ 1) produce the opposite effect. Thus, it is possible to deliver solute with prescribed distributions, ranging from gradual buildup to sudden delivery, based only on the channel dimensions.

Recording: http://mm.math.cmu.edu/recordings/cna/roberto_camassa_small.mp4
Date: Thursday, April 5, 2018
Time: 4:30 pm
Location: Wean Hall 7218
Submitted by:  Ian Tice