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          Resources/ServicesACMD Seminar: Resolving the Shock Layer in Fixed-Bed Adsorption with Boundary Layer Theory

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Robert DeJaco*Applied and Computational Mathematics Division, ITL, NIST*

Tuesday, March 30, 2021, 3:00 PM EDT (1:00 PM MDT)

**A video of this talk is available to NIST staff in the Math channel on NISTube, which is accessible from the NIST internal home page.**

**Abstract:** In adsorption separations, mixtures flow through a column packed with solid particles. The stronger adsorbing component moves more slowly, causing the exiting mixture to separate relative to the inlet. By exploiting differences in affinity for a solid material, rather than heating and cooling (e.g., conventional distillation), adsorption separations can be very energy efficient. Understanding the so-called “break-through curve” measurement – the outlet fluid concentrations as a function of time – is central to efficient industrial implementation. Mathematical modeling of the associated nonlinear PDE can provide a quantitative explanation of the physical and chemical features of the measurement. We apply boundary layer theory to study breakthrough curve measurements for isothermal single-solute adsorption with plug flow in the limit of fast adsorption compared to convection. Our perturbation theory connects two seemingly unrelated theories, one assuming infinitely fast mass transfer and the other an infinitely long column. The leading order “outer” form of the problem is a conservation law that yields shock waves via the method of characteristics. The discontinuity at the shock is resolved by a corresponding boundary layer that can be resolved by rescaling to a moving coordinate system. Analysis of the boundary layer reveals that the associated breakthrough curve has exactly one inflection point, is not necessarily symmetric, and only occurs when the relationship for solute partitioning adopts a certain convexity. Perturbation theory has the potential to improve the accuracy of base-case designs of adsorption processes and the screening of candidate materials which currently neglect the boundary layer associated with shock waves in the conservation law. A comparison to numerical simulations is presented to support the validity of the approach.

**Bio:** Dr. Robert DeJaco was educated at University of Kentucky (B.S., Chemical Engineering, 2014) and University of Minnesota (Ph.D., Chemical Engineering, 2019). His Ph.D. thesis involved molecular and process modeling of adsorption and membrane separations and their comparison to experiment. In his recent work in ACMD with Paul Patrone and Anthony Kearsley during the COVID pandemic, he has also developed an interest for the *ab*-sorption processes involved in viral detection by quantitative Polymerase Chain Reaction (RT-qPCR). During his time at NIST, Rob intends to use applied mathematics to enable chemical processes to be scaled-up more efficiently and enable RT-qPCR to be more accurate.

**Note:**This talk will be recorded to provide access to NIST staff and associates who could not be present to the time of the seminar. The recording will be made available in the Math channel on NISTube, which is accessible only on the NIST internal network. This recording could be released to the public through a Freedom of Information Act (FOIA) request. Do not discuss or visually present any sensitive (CUI/PII/BII) material. Ensure that no inappropriate material or any minors are contained within the background of any recording. (To facilitate this, we request that cameras of attendees are muted except when asking questions.)
  Mathematics and statistics

    
    Contacts
      
        

Robert Dejaco
    
      
  robert.dejaco@nist.gov

  Stephen Langer
    
      
  stephen.langer@nist.gov
  (301) 975-5423

Created March 2, 2021, Updated April 9, 2021
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