Membranes Nonlinear isotherms

SSHG measurements have also been performed at ion-selective membrane electrodes (ISE) in presence of the cations Li", and Na dissolved in the aqueous phase and several ionophores like dibenzo-24-crown-8 in a poly(vinyl chloride) (PVC) membrane [49]. In these experiments, the nonlinear optical signal has been observed as a function of the analyte concentration in the aqueous phase and has been ascribed to the oriented cation-ionophore complexes at the aqueous phase/liquid membrane. Langmuir isotherms were built from the data and the results suggested that a saturation of the interface was achieved at high analyte concentration. 

Petrie and Ito (84) used numerical methods to analyze the dynamic deformation of axisymmetric cylindrical HDPE parisons and estimate final thickness. One of the early and important contributions to parison inflation simulation came from DeLorenzi et al. (85-89), who studied thermoforming and isothermal and nonisothermal parison inflation with both two- and three-dimensional formulation, using FEM with a hyperelastic, solidlike constitutive model. Hyperelastic constitutive models (i.e., models that account for the strains that go beyond the linear elastic into the nonlinear elastic region) were also used, among others, by Charrier (90) and by Marckmann et al. (91), who developed a three-dimensional dynamic FEM procedure using a nonlinear hyperelastic Mooney-Rivlin membrane, and who also used a viscoelastic model (92). However, as was pointed out by Laroche et al. (93), hyperelastic constitutive equations do not allow for time dependence and strain-rate dependence. Thus, their assumption of quasi-static equilibrium during parison inflation, and overpredicts stresses because they cannot account for stress relaxation furthermore, the solutions are prone to numerical instabilities. Hyperelastic models like viscoplastic models do allow for strain hardening, however, which is a very important element of the actual inflation process. 

Wankat and Koo (110) have shown that the efficient mass transfer achievable with small ( 10 micron diameter) monodisperse packing can provide excellent resolution on very short columns, even when adsorption isotherms are nonlinear. For high-throughput processes, the most efficient columns resemble squat disks or pancakes (109). The ultimate "column" geometry may well be a membrane or consolidated packing with mobile phase flow through monodisperse pores. 

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