Modeling of Hygro-Mechanical Behaviour through Raffia vinifera Fiber during the Water Diffusion Phenomenon

In an industrial context where the use of friendly materials is encouraged, natural fibers of vegetable origin become more solicited for the reinforcement of composite materials. This work deals with the modeling of the hygro-mechanical behavior through raffia vinifera fiber during the diffusion phenomenon. The modeling of water diffusion through the raffia vinifera fiber is described by Fick’s second law and taking into account the swelling phenomenon of the fiber. The equation obtained is solved numerically by the finite difference method, and the evolution of the fiber radius as a function of time is obtained. By applying the Leibniz integration rule, a mathematical expression to predict the evolution of this radius as a function of time is proposed. It is observed numerically and analytically an increase of the dimensionless fiber radius with time up to a critical value after what one observes the saturation. This model allowed us to propose a mathematical model describing the absorption kinetics of the raffia vinifera fiber through its absorption ratio. By comparing the results of this model with the experimental results from the literature, one observes a good agreement. Moreover, the induced stresses in the fiber during the water diffusion can also be estimated with the proposed mathematical model expression of fiber. These stresses increase with time and can reach between 5 and 7 GPa. The results of this work can be used to predict the behavior of the raffia vinifera fiber inside a composite material during its development.

MECHANICAL PROCESSES IN TRIBOTECHNICAL UNITS

The study examined the diffusion phenomenon caused by compressive forces in tribotechnical nodes adhering to each other under high contact pressure and the mechanism of rupture of surfaces during surface fatigue. As a result, for two metal surfaces, depending on the nature of the touch, the gravitational and repulsive forces generated during the interaction in any environment are determined based on the number of touches and an analytical expression is obtained to calculate them. Keywords: tribotechnical knot, mutual contact, diffusion phenomenon, surface attraction, molecular contact, mechanical contact.

A computational study of the Ludwig-Soret effect on the thermal-induced phase separation process in polymer solutions

Thermal-induced phase separation (TIPS) is one of the methods used to fabricate functional polymeric materials, i.e. PDLC films for electro-optical devices such flat-panel displays, switchable windows etc., and microporous synthetic membranes from polymer solutions. Since the characteristic thermal, mechanical, and optical properties of these materials are controlled by the morphological features, it it important to understand the phase separation mechanism that forms these materials. In this work, the effect of thermal diffusion, also known as the Ludwig-Soret effect, on the TIPS method of phase separation via the SD mechanism in polymer solutions under non-uniform temperature field has been investigated using the computational technique. The Ludwig-Soret effect occurs when a temperature gradient applied to a fluid mixture induces a net mass flow, which leads to the formation of a concentration gradient. A rigorous mathematical model for TIPS via the spinodal decomposition mechanism based on the nonlinear Cahn-Hilliard and Flory-Huggins theories combined with thermal diffusion phenomenon has been formulated for binary polymer solutions under non-uniform temperature field and solved numerically. Numerical simulation results revealed that the thermal diffusion phenomenon had very little or negligible effect on the phase separation mechanism under a non-uniform temperature field, which was reflected from the studies of the time evolution of structure factor and transition time from the early to the intermediate stages of SD.

A computational study of the Ludwig-Soret effect on the thermal-induced phase separation process in polymer solutions

Thermal-induced phase separation (TIPS) is one of the methods used to fabricate functional polymeric materials, i.e. PDLC films for electro-optical devices such flat-panel displays, switchable windows etc., and microporous synthetic membranes from polymer solutions. Since the characteristic thermal, mechanical, and optical properties of these materials are controlled by the morphological features, it it important to understand the phase separation mechanism that forms these materials. In this work, the effect of thermal diffusion, also known as the Ludwig-Soret effect, on the TIPS method of phase separation via the SD mechanism in polymer solutions under non-uniform temperature field has been investigated using the computational technique. The Ludwig-Soret effect occurs when a temperature gradient applied to a fluid mixture induces a net mass flow, which leads to the formation of a concentration gradient. A rigorous mathematical model for TIPS via the spinodal decomposition mechanism based on the nonlinear Cahn-Hilliard and Flory-Huggins theories combined with thermal diffusion phenomenon has been formulated for binary polymer solutions under non-uniform temperature field and solved numerically. Numerical simulation results revealed that the thermal diffusion phenomenon had very little or negligible effect on the phase separation mechanism under a non-uniform temperature field, which was reflected from the studies of the time evolution of structure factor and transition time from the early to the intermediate stages of SD.

Diffusion phenomenon for abstract linear wave equations with time decaying coefficients of propagation and dissipation

We show diffusion phenomenon for linear abstract dissipative wave equations with time dependant coefficients of propagation speed and dissipation. Coefficients are decaying in time but not assumed to be monotone.