Time Invariants and Conservatively Perturbed Equilibrium (CPE) Gregory Yablonsky,1 Daniel Branco,2,* Guy B. Marin,3 and Denis Constales2 2Department of Mathematical Analysis 3Laboratory for Chemical Technology 1Department of Energy, Environmental and Chemical Engineering Washington University, Saint Louis MO 63130, USA Krijgslaan 281 S-8, B-9000 Ghent, Belgium Technologiepark 914, 9052 Ghent, Belgium https://www.ugent.be/ea/math-analysis https://eece.wustl.edu https://www.lct.ugent.be Introduction A k 1 + ⇄ k 1 − B k 2 + ⇄ k 2 − C New Ideas in planning kinetic experiments: Dual experiments: Symmetric initial conditions. Thermodynamic invariants Conservatively Perturbed Equilibrium (CPE) Mass balance: linear invariant Ao + Bo + Co = 1 Experiment # 1 (Ao, Bo, Co) = (1, 0, 0) Experiment # 2 (Ao, Bo, Co) = (0, 1, 0) Thermodynamic invariant from symmetric experiments The thermodynamic invariants are modified Onsager relationships, in terms of non-steady-state concentrations. Experimental evidence for water-gas shift, ferrocyanide-ferricyanide and estherification reactions is presented [1-3] Non-thermodynamic invariant from ratios of differences of SIC [4] Scaled Incremental Conversion SIC Differences of SIC Experiment # 3 (Ao, Bo, Co) = (Ceq, Beq, Aeq) Non-thermodynamic invariant from ratios of differences of SIC in CPE Conservatively Perturbed Equilibrium At balance conditions, some initial concentrations are equal to the equilibrium concentrations. The extreme time value depends exclusively on the kinetic coefficients. Ratios of differences of SIC in CPE yield invariants expressions. Substance B in CPE References: 1- Yablonsky G.S., Gorban A.N., Constales D., Galvita V.V., Marin G.B., EPL 93, 2011, 20004. 2- Hankins M.J., Yablonsky G.S., Kiss I.Z., PLOS ONE, 2017, 12(3): e0173786. 3- Peng B., Yablonsky G.S., Constales D., Marin G.B., Muhler M., Chem. Eng. Sci., 2018, submitted. 4- Branco D., Yablonsky G.S., Marin G.B., Constales D., Chem. Eng. Sci., 2018, 184, 25, ISCRE, Florence, 23/05/2018 E-mail: Daniel.BrancoPinto@UGent.be