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We show that the average length ⟨ L ⟩ of threadlike micelles in surfactant solutions predicted by fitting results of a mesoscopic simulation, the “pointer algorithm,” to experimental G′(ω), G″(ω) data, is longer than, and more accurate than, that from a scaling law that equates ⟨ L ⟩ / l e to the modulus ratio G 0 / G m i n ′ ′. Here, G0 is the plateau modulus, G m i n ′ ′ is obtained at the local minimum in G″, and l e is the entanglement length. The accuracy of the pointer algorithm is supported by the agreement of its predictions with results from a recent application of the slip-spring simulation method to threadlike micelles. Improved fits of the pointer algorithm to the slip-spring results are obtained for weakly entangled micelles (with an average number of entanglements of Z

We apply our recently developed mesoscopic simulation method for entangled wormlike micelle (WLM) solutions to extract multiple micellar characteristic lengths and time constants: i.e., average micelle length, breakage rate, and entanglement and persistence lengths, from linear rheological measurements on commercial surfactant solutions, one containing sodium lauryl one ether sulfate (SLE1S), and the other containing both SLE1S and cocamidopropyl betaine, as well as a perfume mixture, in both cases with a sample salt (NaCl) added. Measurements include both mechanical rheometry and diffusing wave spectroscopy, the latter providing the high-frequency data needed to determine micelle persistence length accurately. By fitting the experimental data ( G′ and G″) across the entire frequency range through our iteration procedure, the method is of practical use in predicting micellar parameters, which are difficult to obtain from other theoretical or experimental methods. The dependence of micellar parameters on a...

We present a fast “pointer” simulation method that extends the model of Cates and coworkers for the rheology of entangled wormlike micelles. Our method includes not only reptation, breakage/rejoining, contour length fluctuations, and Rouse modes, which were included in Cates' model, but also constraint release, bending modes, and a cross-over to the tight entanglement regime, which had not been previously considered. Our method also contains correlations in micelle length across multiple breakage/rejoining cycles, not included in previous approaches. Our method uses “pointers” that track the ends of unrelaxed regions along each micelle, thereby allowing efficient simulations of relaxation dynamics for ensembles containing thousands of micelles, to obtain accurate results without preaveraging or neglecting correlations. A modified genetic algorithm is applied to transform the simulation data from the time to the frequency domain. The method can span several regimes of behavior depending on the relative rat...

Thermal engineering related to industrial applications needs fast and accurate prediction for complex heat transfer problems. Proper orthogonal decomposition (POD) method can achieve this target. In this paper, the performances of POD interpolation and POD projection methods are compared for the purpose of method selection in those applications. The results show that under the same sampling condition, POD interpolation method can simulate the four-variable heat conduction problem quite accurately (maximum relative deviation is smaller than 1 × 10−8%) but losses accuracy for the six-variable heat conduction problem (maximum relative deviation is up to more than 50%); while POD projection method can obtain accurate results for both the problems (maximum relative deviations are only 0.187% and 1.83% respectively). Thus, POD projection method is more robust and adaptive than POD interpolation method for wider ranges of heat transfer problems. Moreover, the conclusion is also suitable for the guidance of applications in the fields of chemical engineering and fluid mechanics etc.

In general, proper orthogonal decomposition (POD) method is used to deal with single-parameter problems in engineering practice, and the linear interpolation is employed to establish the reduced model. Recently, this method is extended to solve the double-parameter problems with the amplitudes being achieved by cubic B-spline interpolation. In this paper, the accuracy of reduced models, which are established with linear interpolation and cubic B-spline interpolation, respectively, is verified via two typical examples. Both results of the two methods are satisfying, and the results of cubic B-spline interpolation are more accurate than those of linear interpolation. The results are meaningful for guiding the application of the POD interpolation to complex multiparameter problems.