M. J. Hernández

A time-dependent expression for thixotropic areas. Application to Aerosil 200 hydrogels

Experimental determination of the areas enclosed under the up curve, sigma = sigma(;gamma), corresponding to time zero, and the down curve, which would be obtained following complete rheodestruction of the system structure, is not an easy matter. In the present study a semi-empirical procedure for calculating the hypothetical values of these parameters is proposed. With these parameters it is possible to obtain a time-dependent expression for the thixotropic areas, S(T). This procedure has been applied to the study of the thixotropic behavior of Aerosil 200 hydrogels at different concentrations. The comparative analysis of these systems has been realized by studying the relative thixotropic areas and relative thixotropic rates that are obtained from S(T).

On the demonstration of the Young-Laplace equation in introductory physics courses

The Young-Laplace equation is usually introduced using mechanical rather than thermodynamic arguments when teaching surface phenomena at an elementary level. We discuss here three mechanical methods to deduce this equation, with the intention of avoiding certain misunderstandings that are found in these derivations, thus providing the correct demonstrations of the equation.

Rheological characterization of easy-to-disperse (ETD) Carbopol hydrogels

Experimental determinations of apparent viscosity were used to investigate the rheological behaviour of easy-to-disperse (ETD) Carbopol 2001, 2020 and 2050 hydrogels, involving different polymer concentrations, degrees of neutralization, agitation times and shear rates. Mathematical expressions were obtained, based on the power law, to allow calculation of the viscosity of each system, for the different variables studied. These equations proved valid within the 5.5-7.5 pH range, i.e., the pH interval of greatest interest in pharmaceutics and cosmetics. The rheological behaviours of the three types of ETD hydrogels were investigated comparatively and with respect to Carbopol 940, i.e., one of the most widely utilized hydrogels.

Viscous synergism in carrageenans (κ and λ) and locust bean gum mixtures : Influence of adding sodium carboxymethylcellulose

Synergistic interactions between locust bean gum (LBG) and two types of carrageenans (κ and λ) are studied. Viscous synergism index, I v as a function of concentration ratioz=ćLBG/ćcar, and shear rate were obtained for every mixture. In both binary systems the values of this index decrease with increasing shear rate. For the LBG + κ mixtures, I vpresented a maximum at a concentration ratio z≅60/40, which would be considered the optimum proportion of gums in the mixture. However, for the LBG + λ system, I v increased with z in the whole interval considered, i.e., the highest synergism corresponded to the lowest proportion of carrageenan. The addition of sodium carboxymethylcellulose (NaCMC) to the binary systems modified the above results. For LBG + κ + NaCMC mixtures, the maximum Ivvalues were similar to those corresponding to LBG + κ system, but the concentration ratio at which these maxima are produced shifted to a lesser proportion of locust bean gum (z ≅40/60). Moreover, the presence of NaCMC in the other ternary system totally eliminated the possible interaction between LBG and λ-carrageenan.

Influence of shear rate and concentration ratio on viscous synergism. Application to xanthan—Iocust bean gum— NaCMC mixtures Influencia de la velocidad de cizalla y la relación de concentraciones en la sinergia viscosa. Aplicación a mezclas de xantana-garrofín-CMCNa

A method is described that allows the development of an empirical approach to quantify synergistic interactions and their variations with shear rate. The approach is based on the definition of a viscous synergism index, I v. The method is applied to xanthan-locust bean gum gels, and an equation is developed for relating the synergism index to shear rate, γ, and the locust bean gum/xanthan gum concentration ratio, z. The value of at which that function has a maximum, I M V, is calculated. This value of z provided an estimation of the proportion of gums at which maximum synergism occurs. A decreasing exponential dependence of these I M V on γ is shown. The influence of the addition of a fixed proportion of a third gum (NaCMC) is also analyzed. The results obtained for the higher γ values are analogous to those of other authors.

A laboratory experiment on inferring Poiseuille's law for undergraduate students

In this paper a laboratory experiment is proposed to infer Poiseuilles law. A simple set-up based on two flasks joined by a detachable tube allows one to measure using tubes of different radii and different lengths. One of the flasks is connected to a vacuum pump to control the pressure differential between the tube extremes. The influence on the flow of different radii, lengths, pressures and viscosities can be studied in a didactic way by measuring the flow rate for each of these variables. The experiment can be performed getting together the students in groups, so that each group concentrates on the effect on the flow of a specific variable, leaving the rest fixed. After putting together all these results the law of Poiseuille can be obtained as a very good approach.

Thixotropic Behavior of Salad Dressings Stabilized with Modified Starch, Pectin, and Gellan Gum. Influence of Temperature

The thixotropy of low‐oil salad dressing has been analyzed at different temperatures (8–26°C). The usual formulation containing modified starch (4%) was compared with others in which part of the starch had been substituted by pectin (0.5%) or different concentrations of gellan (0.1 and 0.5%). Up and down flow curves were measured, showing in all cases shear thinning behavior and fitting the Herschel‐Bulkley model. Thixotropic areas enclosed by the up curve and the corresponding different down curves, STh, were obtained. With the aim of establishing comparative results, and since the viscosities were quite different, the parameter considered was relative thixotropic area, SR (%)=100 (STh/Sup). These areas increased with agitation time and depended on temperature. Their tendencies were reproduced by equations SR=SRmax {1‐exp [‐f(t)]}, with f(t)=βt0.5, where the maximum relative thixotropic area, SRmax , increases with increasing temperature while β decreases. The parameter β has different values for each formulation, and indicates the time dependence. The emulsion formulated with pectin was found to be the most stable with temperature and agitation time, while the greatest thixotropy corresponded to the emulsion formulated with starch only. The thixotropic behavior of the emulsions formulated with gellan gum was seen to be intermediate between the two above formulations—the emulsion formulated with the largest percentage of gellan gum being the least thixotropic of both.