A discussion of modeling passive scalar transport in turbulent flows is given. Several methods employed to close the scalar-flux term ⟨u′ϕ′⟩ that arises during Reynolds averaging are provided. Alternatives and improvements to the gradient diffusion hypotheses are addressed, most notably, the need for an alternative to the global constant turbulent Schmidt and Prandtl numbers. The reader is given a brief history covering methods used to predict turbulent Schmidt and Prandtl numbers, along with recommendations for future research, based partially on studies by Professor Stuart Churchill. More detailed formulations of turbulent Schmidt or Prandtl numbers will enable better approximations of the influence of turbulence in models of passive scalar flows using the gradient diffusion hypothesis.

Abstract. Oxidation flow reactors (OFRs) have been developed to achieve high degrees of oxidant exposures over relatively short space times (defined as the ratio of reactor volume to the volumetric flow rate). While, due to their increased use, attention has been paid to their ability to replicate realistic tropospheric reactions by modeling the chemistry inside the reactor, there is a desire to customize flow patterns. This work demonstrates the importance of decoupling tracer signal of the reactor from that of the tubing when experimentally obtaining these flow patterns. We modeled the residence time distributions (RTDs) inside the Washington University Potential Aerosol Mass (WU-PAM) reactor, an OFR, for a simple set of configurations by applying the tankin-series (TIS) model, a one-parameter model, to a deconvolution algorithm. The value of the parameter, N, is close to unity for every case except one having the highest space time. Combined, the results suggest that volumetric flow rate affects mixing patterns more than use of our internals. We selected results from the simplest case, at 78 s space time with one inlet and one outlet, absent of baffles and spargers, and compared the experimental F curve to that of a computational fluid dynamics (CFD) simulation. The F curves, which represent the cumulative time spent in the reactor by flowing material, match reasonably well. We value that the use of a small aspect ratio reactor such as the WU-PAM reduces wall interactions; however sudden apertures introduce disturbances in the flow, and suggest applying the methodology of tracer testing described in this work to investigate RTDs in OFRs to observe the effect of modified inlets, outlets and use of internals prior to application (e.g., field deployment vs. laboratory study).

24 25Oxidation flow reactors (OFRs) have been developed to achieve high degrees of oxidant exposures 26 over relatively short space times (defined as the ratio of reactor volume to the volumetric flowrate). 27While, due to their increased use, attention has been paid to their ability to replicate realistic 28 tropospheric reactions by modeling the chemistry inside the reactor, there is a desire to customize 29 flow patterns. This work demonstrates the importance of decoupling tracer signal of the reactor 30 from that of the tubing when experimentally obtaining these flow patterns. We modeled the 31 residence time distributions (RTDs) inside the Washington University Potential Aerosol Mass 32 (WU-PAM) reactor, an OFR, for a simple set of configurations by applying the tank-in-series (TIS) 33 model, a one parameter model, to a deconvolution algorithm. The value of the parameter, , is 34 close to unity for every case except one having the highest space time. Combined, the results 35 suggest that volumetric flowrate affects mixing patterns more than use of our internals. We 36 selected results from the simplest case, at 78s space time with one inlet and one outlet, absent of 37 baffles and spargers, and compared the experimental F-Curve to that of a computational fluid 38 dynamics (CFD) simulation. The F-Curves, which represents the cumulative time spent in the 39 reactor by flowing material, match reasonably well. We value that the use of a small aspect ratio 40 reactor such as the WU-PAM reduces wall interactions, and suggest applying the methodology of 41 tracer testing described in this work to investigate RTDs in OFRs and modify inlets, outlets, and 42 use of internals prior to applications (e.g., field deployment vs. laboratory study). 43 44 1 Introduction 45

This chapter reviews the art and science involved in understanding the multiscale multiphase phenomena that affect the performance of trickle bed reactors. Their application areas, the traditional approach to their design and scaleup, and some commonly encountered problems in practice are discussed. The foundations for rational scaleup are introduced. The recent attempts to develop a multiscale science‐based approach to scale up and design of these reactors is summarized at the end. The article contains sections titled: 1. Introduction 2. Design 2.1. Flow Regimes 2.2. Flow Distribution 2.3. Pressure Drop 2.4. Liquid Holdup 2.5. Catalyst Wetting and Liquid–Solid Contacting 2.6. Residence Time Distributions 2.7. Heat Transfer and Thermal Stability 3. Modeling and Analysis 3.1. Reactor Models 3.2. Hydrodynamic and Computational Fluid Dynamic Models 3.3. CFD Models of Trickle Beds 4. Trickle‐bed Reactor Scaleup 5. Reactor Troubleshooting 6. Acknowledgment References

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