Interpretation of NO₃–N₂O₅ observation via steady state in high aerosol air mass: The impact of equilibrium coefficient in ambient conditions

Steady state approximation for interpreting NO3 and N2O5 has large uncertainty under complicated ambient conditions and could even produces incorrect results unconsciously. To provide an assessment and solution to the dilemma, we formulate data sets based on in-situ observations to reassess the applicability of the method. In most of steady state cases, we find a prominent discrepancy between Keq (equilibrium coefficient for reversible reactions of NO3 and N2O5) and correspondingly simulated [N2O5]/([NO2]×[NO3]), especially in wintertime high aerosol conditions. This gap reveals the accuracy of Keq has a critical impact on the steady state analysis in polluted region. In addition, the accuracy of γ(N2O5) derived by steady state fit depends closely on the reactivity of NO3 (kNO3) and N2O5 (kN2O5). Based on a complete set of simulations, air mass of kNO3 less than 0.01 s−1 with high aerosol and temperature higher than 10 °C is suggested to be the best suited for steady state analysis of NO3–N2O5 chemistry. Instead of confirming the validity of steady state by numerical modeling for every case, this work directly provides concentration ranges appropriate for accurate steady state approximation, with implications for choosing suited methods to interpret nighttime chemistry in high aerosol air mass.

The Double Phospho/Dephosphorylation Cycle as a Benchmark to Validate an Effective Taylor Series Method to Integrate Ordinary Differential Equations

The double phosphorylation/dephosphorylation cycle consists of a symmetric network of biochemical reactions of paramount importance in many intracellular mechanisms. From a network perspective, they consist of four enzymatic reactions interconnected in a specular way. The general approach to model enzymatic reactions in a deterministic fashion is by means of stiff Ordinary Differential Equations (ODEs) that are usually hard to integrate according to biologically meaningful parameter settings. Indeed, the quest for model simplification started more than one century ago with the seminal works by Michaelis and Menten, and their Quasi Steady-State Approximation methods are still matter of investigation nowadays. This work proposes an effective algorithm based on Taylor series methods that manages to overcome the problems arising in the integration of stiff ODEs, without settling for model approximations. The double phosphorylation/dephosphorylation cycle is exploited as a benchmark to validate the methodology from a numerical viewpoint.

Evaluation of a Quasi-steady state approximation of the cloud Droplet Growth Equation (QDGE) scheme for aerosol activation in global models using multiple aircraft data over both continental and marine environments

This research introduces a numerically efficient aerosol activation scheme and evaluates it by using stratus and stratocumulus cloud data sampled during multiple aircraft campaigns in Canada, Chile, Brazil, and China. The scheme employs a Quasi-steady state approximation of the cloud Droplet Growth Equation (QDGE) to efficiently simulate aerosol activation, the vertical profile of supersaturation, and the activated cloud droplet number concentration (CDNC) near the cloud base. We evaluate the QDGE scheme by specifying observed environmental thermodynamic variables and aerosol information from 31 cloud cases as input and comparing the simulated CDNC with cloud observations. The average of mean relative error of the simulated CDNC for cloud cases in each campaign ranges from 17.30 % in Brazil to 25.90 % in China, indicating that the QDGE scheme successfully reproduces observed variations in CDNC over a wide range of different meteorological conditions and aerosol regimes. Additionally, we carried out an error analysis by calculating the Maximum Information Coefficient (MIC) between the mean relative error (MRE) and input variables for the individual campaigns and all cloud cases. MIC values are then sorted by aerosol properties, pollution level, environmental humidity, and dynamic condition according to their relative importance to MRE . Based on the error analysis we found that the magnitude of MRE is more relevant to the specification of input aerosol pollution level in marine regions and aerosol hygroscopicity in continental regions than to other variables in the simulation.

Pressure Losses Generated by a Thixotropic Fluid When Subject to an Oscillating Flowrate

Rapid variations in the fluid velocity field influence pressure loss calculations. In this paper, we propose numerical methods for estimating pressure losses in a circular pipe when the flow rate oscillates. The method is described for Newtonian and two non-Newtonian rheological behaviors: the power law and the Quemada models. Also, as drilling fluids are usually thixotropic, i.e., their rheological behavior depends on the shear history, an expansion of the Quemada model is proposed to account for shear history effects. A laboratory flow-loop has been assembled and measurements conducted with a non-thixotropic aqueous solution of Carbopol and a thixotropic potassium chloride solution of xanthan gum. The measurements were analyzed and compared with estimates made with the proposed models. It is found that when applying a square wave oscillating flowrate to a non-thixotropic fluid, large surge and swab pressure spikes are generated. The same square wave signal does not produce pressure spikes when circulating a thixotropic fluid; on the contrary the acceleration and deceleration fronts are largely attenuated. When applying a triangular or sinusoidal wave form to the flowrate while circulating a non-thixotropic fluid, the peak-to-peak pressure gradient gets progressively larger when the oscillation amplitude increases or the signal period reduces, compared to the expected value when estimating the pressure losses with the steady state approximation. However, under the same conditions, when circulating a thixotropic fluid, the peak-to-peak pressure gradients are lower than those estimated with the steady state approximation.

Teaching and Learning Materials on the Quasi-Steady-State Approximation and the Partial-Equilibrium Approximation

Starting from simple examples of chemical schemes for which a concentration or an extent of reaction can be eliminated, we highlight the common features of the quasi-steady-state approximation and the partial-equilibrium approximation. General conditions to apply either of these adiabatic eliminations are mentioned.<br>

Teaching and Learning Materials on the Quasi-Steady-State Approximation and the Partial-Equilibrium Approximation

Starting from simple examples of chemical schemes for which a concentration or an extent of reaction can be eliminated, we highlight the common features of the quasi-steady-state approximation and the partial-equilibrium approximation. General conditions to apply either of these adiabatic eliminations are mentioned.<br>

Applying the quasi-steady-state approximation to the autocatalytic zymogen activation: A novel general methodology for scaling analysis

<p><br></p><table><tr><td>A zymogen is an inactive precursor of an enzyme that needs to go through a chemical change to become an active enzyme. The general intermolecular mechanism for the autocatalytic activation of zymogens is governed by the single-enzyme, single-substrate catalyzed reaction following the Michaelis-Menten mechanism of enzyme action, where the substrate is the zymogen and the product is the same enzyme that is catalyzing the reaction. In this article we investigate the nonlinear chemical dynamics of the intermolecular autocatalytic zymogen activation reaction mechanism. In so doing, we develop a general strategy for obtaining dimensionless parameters that, when sufficiently small, legitimize the application of the quasi-steady-state approximation. Our methodology combines energy methods and exploits the phase-plane geometry of the mathematical model, and we obtain sufficient conditions that support the validity of the standard, reverse and total quasi-steady-state approximations for the intermolecular autocatalytic zymogen activation reaction mechanism. The utility of the procedure we develop is that it circumnavigates the direct need for a priori timescale estimation, scaling, and non-dimensionalization. At the same time, a novel result emerges from our analysis: the discovery of a dynamic transcritical bifurcation that exists in the singular limit of the model equations. Moreover, associated with the dynamic transcritical bifurcation is an imperfect term. We prove that when the imperfect term vanishes and the singular vector field is perturbed, there exists a canard that follows a repulsive slow invariant manifold over timescales of <i>O</i>(1). This is the first report of such a solution for the intermolecular and autocatalytic zymogen activation reaction. By extension, our results illustrate that canards also exist in the classic single enzyme, single-substrate reversible Michaelis-Menten reaction mechanism.</td></tr></table>