Third-order Relation Research Articles

The Porosity-dependence of Bulk Modulus of Dry Porous Materials

By semi-analytical modifications to Mackenzie’s equation, a new third-order relation between bulk modulus and porosity is developed for porous materials. Compared with Mackenzie’s equation, the proposed equation takes into consideration critical porosity and real geometry represented by the assembly of hollow spheres. It has been shown that the proposed equation is in better agreement with 10 sets of published data than Mackenzie’s equation and that has an advantage in predicting the matrix bulk modulus even lack of the data of dense porous specimens. In addition, the proposed equation can describe the bulk modulus of porous materials with critical porosity well. However, Mackenzie’s equation cannot work.

Maxwell’s second- and third-order equations of transfer for non-Maxwellian gases

Condensed algebraic forms for Maxwell’s second- and third-order equations of transfer are developed for the case of molecules described by either elastic hard spheres, inverse-power potentials, or by Bird’s variable hard-sphere model. These highly reduced, yet exact, equations provide a new point of origin, when using the moment method, in seeking approximate solutions in the kinetic theory of gases for molecular models that are physically more realistic than that provided by the Maxwell model. An important by-product of the analysis, when using these second- and third-order relations is that a clear mathematical connection develops between Bird’s variable hard-sphere model and that for the inverse-power potential.

Aggregation of methyl orange in aqueous acidic solutions below room temperature

The absorptivity decrease observed for aqueous acidic methyl orange as a function of time, caused by aggregation of the dye, occurs in two steps clearly discernible at lower temperatures. An immediate substantial decrease, the rate of which strongly depends on both temperature and initial dye concentration, is followed by a slower one. In between both steps an actual equilibrium is observed, at which the degree of aggregation is evaluated (using the methods of D. Pugh and M. Hida). Varying the temperature does not markedly influence the nature of the aggregated species but varying the surface–volume ratio of the solution does.For the first reaction step a third-order relation with respect to the dye concentration is found at all temperatures.