Micromixing Effects on Autocatalytic Reactions in a Stirred Tank:  The Random Replacement IEM Model

Abstract

The random replacement interaction-by-exchange-with-the-mean (IEM) model, which was proposed previously as a numerically more preferable IEM scheme, had been employed for investigating the micromixing effects on the steady-state multiplicity and the relative stability of the oscillatory and stationary state of the Gray-Scott model (Gray, P.; Scott, S. K. Chem. Eng. Sci. 1983, 38, 29). In the bistable region, incomplete micromixing tends to largely reduce the attraction basin for the thermodynamic branch, while in the region where the stable limit cycle exists, it tends to weaken the relative stability of the oscillatory states. Owing to the random replacement nature of the present micromixing model, a stochastic response behavior is observed for the resulting limit cycle attractor and the attraction basin boundary on the parameter space.

Micromixing and Macromixing Effects in Unsteady Chemical Reaction System

“…Poor micromixing favors a flow-branch steady state; the next preferred state is the oscillatory state, and the least favorable state is the thermal-branch steady state. The observation of enhancing the flow-branch steady state in a poorer micromixing environment correlates with previous findings for the Gray−Scott model . However, for the first time, this study identifies the bifurcation sequence from thermal-branch steady state → oscillatory state → flow-branch steady state as micromixing gets worse (even at the perfect macromixing limit).…”

“…Chang et al . refined the original IEM model 2 by improving its capability of taking care of stiff chemical kinetics, such as the Oregonator model (discussed later). The so-called “random replacement IEM model” adopted a molecular dynamics-like scheme that could be applied in investigating the effects of imperfect micromixing …”

Micromixing efficiency in static mixer

“…Segregation index cannot be directly used. Fournier et al (1996b) employed an incorporation model for estimating the micromixing time, t m , which is an essential parameter for many micromixing models (Chang, Mou, & Lee, 1996Lee, Chang, & Mou, 1997). Fournier et al assumed a simple dilution-reaction scheme as stated in the following:…”

“…Mixing can quantitatively or even qualitatively alter the complex system dynamics when the mixing time is comparable to the reaction characteristic time (Villermaux, 1991;Lee, Chang, & Mou, 1997). Ottino (1994) thoroughly reviewed pertinent literature before 1994.…”

Skeleton kinetic model of acetaldehyde oxidation from comprehensive models

“…For instance, with skeleton models for oscillatory reactions, the effects of nonideal mixing in the flow reactor were demonstrated (Hsu et al, 1994, Chang et al, 1996, 1999. The manner in dispute is whether the skeleton model can represent the real system of comprehensive scheme (Lee et al, 1997;Sirdeshpande et al, 2001;Banerjee and Ierapetritou, 2003). The link between skeleton model and comprehensive chemical model remains unclear to most complex chemical system.…”