The Kruskal-Segur approach to selection theory in diffusion-limited or Laplacian growth is extended via combination with the Zauderer decomposition scheme. This way nonlinear bulk equations become tractable. To demonstrate the method, we apply it to two-dimensional crystal growth in a potential flow. We omit the simplifying approximations used in a preliminary calculation for the same system [Fischaleck, Kassner, Europhys. Lett. 81, 54004 (2008)], thus exhibiting the capability of the method to extend mathematical rigor to more complex problems than hitherto accessible.

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Commercially available flow sheet simulators cannot perform optimization runs with more than one criterion. To overcome this problem, the flow sheet simulator CHEMCAD is combined with an external optimization solver, and the Excel VBA client is used to arrange inter-process communications. The resulting tool for multi-criteria optimization in chemical process engineering is applied to two separation problems. First, a dividing-wall column is used as a theoretical example to test different starting points and different scalarization techniques. Second, a significant decrease in energy demand is achieved for a real continuous world-scale facility.

We use the method presented in M von Kurnatowski et al (2013 Phys. Rev. E 87 042405) to solve the nonlinear problem of free dendritic growth in an Oseen flow. The growth process is assumed to be limited by thermal transport via diffusion and convection. A singular perturbation expansion is treated to lowest nontrivial order in the framework of asymptotic decomposition. The resulting complex integro-differential equation is solved using an elaborate numerical method. The approximate scaling laws and for the growth velocity and the tip radius of curvature of the dendrite, respectively, are found as a function of the forced flow velocity. The results are compared to those by Pelcé and Bouissou, constituting the only other attempt so far to treat the problem analytically.

Many thermodynamic models used in practice are at least partially empirical and thus require the determination of certain parameters using experimental data. However, due to the complexity of the models involved as well as the inhomogeneity of available data, a straightforward application of basic methods often does not yield a satisfactory result. This work compares three different strategies for the numerical solution of parameter estimation problems, including errors both in the input and in the output variables. Additionally, the new idea to apply multi-criteria optimization techniques to parameter estimation problems is presented. Finally, strategies for the estimation and propagation of the model errors are discussed.