Celebrating singularities: Mathematics and chemical engineering

Abstract

in Wiley Online Library (wileyonlinelibrary.com)The authors review and project their group's work in reaction engineering, electrokinetics, thin-film lubrication/wetting, biosensing, mass spectrometry, etc., that share one common mathematical underpinning: singularities. These can be geometric singularities of actual surfaces or objects, where focused electrical, acoustic, optical and shear-stress fields produce anomalous physical phenomena that have been explored mathematically with a spectral theory or exploited for specific applications. They are also singularities of mathematical manifolds, such as solution branches and Riemann manifolds, defined by abstract mathematical formulations, so that they can be used to design optical sensors, and understand nonlinear dynamical behavior that is relevant to system control and surface characterization. The common mathematical framework for these diverse topics underscores how mathematics can reveal, organize and inspire real and industrially relevant problems in chemical engineering.The DC Taylor theory is based on the dominant mode from the spectral analysis of the Laplace operator with induced charge (displacement) boundary conditions. The AC theory is based on a variational analysis of space charge Columbic repulsion. Note the different dependence on b, (c) the charge state of the apomyoglobin mass spectrum at different frequencies of the AC spray and for DC spray, and (d) mass spectra at different frequencies, showing the shift to higher charge states at high frequencies.

On skirted drops in an immiscible liquid

“…Zeleny, 1917;Taylor, 1934Taylor, , 1964 but have recently acquired greater relevance due to the wide diffusion of electrospray mass spectrometry (see e.g. Fenn et al, 1989;Abonnenc et al, 2010;Wang et al, 2013) and the production of micro-drops in co-flowing fluid systems (Basaran, 2002;Suryo and Basaran, 2006;Barrero and Loscertales, 2007;Marin et al, 2009;Castro-Hernandez et al, 2012).…”

How can potential engineers seek and discover their genuine vocations?

“…Ramkrishna and Amundson (2004) provided an overview of mathematics in chemical engineering during the second half of the past century (Ramkrisna and Amundson, 2004). Wang et al (2013) observed a common mathematical feature of geometric and parametric singularities observed in their research in chemical engineering (Wang et al, 2013). Finlayson et al (2015) comprehensively covered mathematical topics useful for chemical engineering (Finlayson et al, 2015).…”

Seeking Genuine Vocations through Sustainability in Chemical Engineering

“…Ramkrishna and Amundson (2004) provided an overview of mathematics in chemical engineering during the second half of the past century and concluded that mathematics is the principal instrument not only for chemical engineering processes but also for interceding about materials and products [74]. Wang et al (2013) observed a common mathematical feature of geometric and parametric singularities in their chemical engineering research [75]. Finlayson et al (2015) comprehensively covered mathematical topics useful for chemical engineering [76].…”