A three-dimensional Hellinger-Reissner Virtual Element Method for linear elasticity problems

We present a Virtual Element Method for the 3D linear elasticity problems, based on Hellinger-Reissner variational principle. In the framework of the small strain theory, we propose a low-order scheme with a-priori symmetric stresses and continuous tractions across element interfaces. A convergence and stability analysis is developed and we confirm the theoretical predictions via some numerical tests.Comment: submitted to CMAM

Solvent-free microwave extraction of essential oil from aromatic herbs: From laboratory to pilot and industrial scale

Solvent-free microwave extraction (SFME) has been proposed as a green method for the extraction of essential oil from aromatic herbs that are extensively used in the food industry. This technique is a combination of microwave heating and dry distillation performed at atmospheric pressure without any added solvent or water. The isolation and concentration of volatile compounds is performed in a single stage. In this work, SFME and a conventional technique, hydro-distillation HD (Clevenger apparatus), are used for the extraction of essential oil from rosemary (Rosmarinus officinalis L.) and are compared. This preliminary laboratory study shows that essential oils extracted by SFME in 30 min were quantitatively (yield and kinetics profile) and qualitatively (aromatic profile) similar to those obtained using conventional hydro-distillation in 2 h. Experiments performed in a 75 L pilot microwave reactor prove the feasibility of SFME up scaling and potential industrial applications

Some Virtual Element Methods for Infinitesimal Elasticity Problems

The chapter presents Virtual Element Methods for linear elasticity. In particular, displacement based methods stemming from the principle of virtual works for 2D problems, and mixed methods based on the Hellinger-Reissner variational principle for 2D and 3D problems are discussed and detailed. A series of numerical examples for each set of methods are given in order to show the characteristic features of the newly developed methods and to assess their accuracy and convergence properties

Histo-cytochemistry and scanning electron microscopy of lavender glandular trichomes following conventional and microwave-assisted hydrodistillation of essential oils: a comparative study

The conventional hydrodistillation method (HD) has been compared with three different variants of the microwave-assisted hydrodistillation technique (MADH), on Lavandula anguslifolia flowers, both in terms of oil yield and effects on the glandular trichome morpho-structure. The amount and composition of essential oil extracted in 4 h by HD was similar to that obtained in only 20 min by MADH and even lower than that extracted with a steam variant (MASD) of MADH itself. Histo-cytochemical investigations and scanning electron microscopy showed that glandular trichome, after 4 h of HD, appeared swollen, with a deeply wrinkled surface and empty of essential oil, however maintaining the integrity of their cuticle. Many oil droplets were stuck to the outside of the trichome cuticle, sometimes arranged in large aggregates. After 20 min of MADH or MASD, trichomes appeared empty as well, but also particularly disrupted, or at least with holes in their head cuticle. Oil droplets were present outside the glands and in the inter-rib regions of the flower calyx, except in the case of MASD. After this extraction method, neither oil droplets nor other lipid staining were present in the samples, confirming the effectiveness of this particular MADH technique. These investigations suggest that the rapidity of MADH and MASD in extracting essential oil is mainly due to the collapse of trichome structure and the consequent direct release of its content, without which it has to slowly permeate through membranes and cuticle, as in the case of HD. Copyrigh