In this article, we analyze, through mathematical modeling, the drying of a spherical drop of a colloidal suspension. The originality of our modeling lies in considering the transport phenomena in both the colloidal drop and the surrounding gas, allowing to describe and understand the problem comprehensively. We present a general model taking into account the diffusive and convective transports in the non-isothermal gas phase, and the unsteady diffusion of the particles within the drop. This general model involves a collective diffusion coefficient depending on the particle concentration to take into account the interactions between the particles, considered as hard spheres. This leads us to introduce a new expression of the Péclet number, Pe, comparing a characteristic time of the diffusion of the particles within the drop and a characteristic time of the evaporation of the drop. In particular, Pe appears to be independent of the drop size. The variation of Pe with the parameters of the system is analyzed and its influence on the dynamics of the colloidal particles is discussed. Furthermore, a new equation to evaluate the Darcy's stress arising in the drop during its drying is derived. In particular, it reveals that this mechanical stress continuously increases overtime until it diverges. Two simplified versions of the model are also presented. The comparison of the results obtained from the three versions of the model enables discussing what level of complexity of the modeling should be used for the quantification of several of its properties, depending on the system parameters.
The fully developed laminar flow of a viscous non-Newtonian fluid in a rough-walled pipe is considered. The fluid rheology is described by the power–law model (covering shear thinning, Newtonian, and shear thickening fluids). The rough surface of the pipe is considered to be fractal, and the surface roughness is measured using surface fractal dimensions. The main focus of this study lies in the theoretical investigation of the influence of the pipe surface roughness on the velocity profile and the Darcy friction factor of an incompressible non-Newtonian fluid. The plotted results demonstrate that shear thinning fluids are the most sensitive to the surface roughness compared with Newtonian and shear thickening fluids. For a particular value of the surface fractal dimension, there exists an intersection point where shear thinning, Newtonian, and shear thickening fluids behave the same way regarding the amplitude of the velocity profile and the friction factor. This approach has a variety of potential applications, for instance fluid dynamics in hydrology, blood flow in the cardiovascular system, and many industrial applications.
The presence of a sudden expansion generates a variation of the static pressure commonly called Pressure Recovery (PR). In this paper, we made firstly an extensive literature survey to list existing gas-liquid two-phase flow pressure recovery models and to collect an experimental database. Thus, a total of 305 data was collected from 6 recent works and 18 predictive models was identified. An analysis of the different existing models was carried out firstly. Then, the predictive capability of nine existing models was assessed using the collected database. It was reported that none of the models can predict the experimental results for a large range of experimental conditions. This finding highlighted the necessity to propose a new model. The proposed predictive model was developed using the two-phase multiplier and mass quality. These two parameters were correlated using 157 data points from the collected database, while the other data was used to validate it. It was found that the proposed model gives better predictions compared to existing ones in the range of conditions and parameters of the experimental database used in this analysis.
In this paper, the study of the fully developed flow of a self-similar (fractal) power-law fluid is presented. The rheological way of behaving of the fluid is modeled utilizing the Ostwald–de Waele relationship (covering shear-thinning, Newtonian and shear-thickening fluids). A self-similar (fractal) fluid is depicted as a continuum in a noninteger dimensional space. Involving vector calculus for the instance of a noninteger dimensional space, we determine an analytical solution of the Cauchy equation for the instance of a non-Newtonian self-similar fluid flow in a cylindrical pipe. The plot of the velocity profile obtained shows that the rheological behavior of a non-Newtonian power-law fluid is essentially impacted by its self-similar structure. A self-similar shear thinning fluid and a self-similar Newtonian fluid take on a shear-thickening way of behaving, and a self-similar shear-thickening fluid becomes more shear thickening. This approach has many useful applications in industry, for the investigation of blood flow and fractal fluid hydrology.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.