A Fractional-Order Model of Biopolyester Containing Naturally Occurring Compounds for Soil Stabilization

Abstract

Currently, the use of polymers and biopolymers as soil-stabilizer additives for control of the soil degradation, deterioration, and desertification and for improving the arid and semiarid soils has been expanded significantly in the agricultural sector. This research was conducted to determine the effect of naturally occurring compounds, such as quercetin (Q) and sodium montmorillonite (NaMMt) at different weight ratios, in biopolyester, such as polylactic acid (PLA), aiming to formulate ecosustainable materials to control the soil degradation and to protect the environment. As known, the use of sophisticated analytical tools to describe the material rheology and melting properties is nowadays very popular among physicists and material scientists. Certainly, several experimental tests conducted on polymeric- and biopolymeric-based materials, such as rubbers, foams, and hydro/aero gels, show that the relaxation time spectra are a continuous function, and as a consequence, multiple relaxation times are involved in the rheological description of the materials, yielding the need for nonconventional relaxation functions. Indeed, in this work, the considered fractional-order model could be considered a powerful tool to describe and to predict the melting properties of the complex polymer-based systems containing different additives.

A Review of the Application of Biopolymers on Geotechnical Engineering and the Strengthening Mechanisms between Typical Biopolymers and Soils

“…Guar gum accumulations are connected between guar gum and soil particles (i.e., poorly graded sand; Gs � 2.7) [55]. van der Waals forces as physical absorption generate the weakest bonds over a long range in the SEM (Figure 18) [78].…”

Fractional‐order poromechanics for a fully saturated biological tissue: Biomechanics of meniscus

“…The presence of biological tissues with a marked presence of hydrated collagen, as in meniscus tissue, makes, however, largely ineffective the elastic models of the material since a marked‐time dependent behavior of the representative volume element is observed also in absence of fluid‐filling material pores 13,16,27–34 . As a consequence a mathematical formulation that can be used to represent this mechanical behavior is the linear theory of material hereditariness that is nowadays described by the so‐called Fractional‐Order hereditariness (FOH).…”

“…and substituting Equation (34) into Equation (31), the constitutive equation for a isotropic viscoelastic porous medium becomes:…”

“…The presence of biological tissues with a marked presence of hydrated collagen, as in meniscus tissue, makes, however, largely ineffective the elastic models of the material since a marked-time dependent behavior of the representative volume element is observed also in absence of fluid-filling material pores. 13,16,[27][28][29][30][31][32][33][34] As a consequence a mathematical formulation that can be used to represent this mechanical behavior is the linear theory of material hereditariness that is nowadays described by the so-called Fractional-Order hereditariness (FOH). In this setting the formalism of fractional-calculus, lately used in several biomechanical contexts 18,21,25,26 allows to replace the well-known constitutive equations of classical linear elasticity with their-fractional-order counterparts, involving, as additional parameters the derivation order β 0, 1 ½ .…”