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Liquids

Liquids is an international, peer-reviewed, open access journal on all aspects of liquid material research published quarterly online by MDPI.

All Articles (150)

It has been shown for the first time that in the case of a pressure flow of a Newtonian fluid in a circular pipeline, the influence of forces of rheological origin, ion electrostatic and Van der Waals nature on the radius of the undeformed flow core is described by a third-degree polynomial with respect to the thickness of the layer, where the suspension structure is destroyed and its shear flow occurs. In this polynomial, the contributions of rheological forces and the influence of the hydraulic size of the solid-phase particles in the suspension enter as linear terms; ionic electrostatic and Van der Waals forces enter as quadratic and constant terms, respectively. For conditions typical of water–coal fuel, we demonstrate that the hydraulic (size) term is several orders of magnitude smaller than the leading terms and may be neglected, and that the quadratic term is negligible compared with the constant (free) term, so that the limiting value of the undeformed core radius is obtained as the real root of a cubic equation containing cubic, linear and constant terms. At DLVO equilibrium, the constant term vanishes, and the limiting relative core radius reduces to the rheological–hydraulic expression; away from equilibrium, the constant term becomes positive or negative, thereby altering the admissible interval of the relative core radius. Using Cardan’s method, we show analytically that (i) when the cubic discriminant is positive, a single real root exists and physically admissible solutions occur only for a negative constant term; (ii) when the discriminant is negative, three real roots exist and the maximum relative radius at which the suspension structure is preserved shifts above or below the rheological-only radius depending on the sign of the constant term. Numerical evaluation of the proposed lyophobicity model for proportionality coefficients k1 in the range 1–10 yields a lyophobicity function varying approximately from 0.67 to 1.06, confirming the modest but non-negligible role of interparticle interaction energy in modifying the undeformed core size under water–coal fuel conditions. These results quantify the competing roles of rheology and interparticle forces in determining the stability and extent of the undeformed core in pipeline transport of structured suspensions.

24 December 2025

Dependence of the lyophobicity function E on the proportionality coefficient k (k > 1).

Arid zones, such as the MENA regions and the Sahara countries, are experiencing significant water stress. To address this global challenge, desalination technologies provide a crucial solution, particularly the reverse osmosis (RO) technique, which is widely used to treat Seawater or Brackish water. Mauritania is among the countries facing a scarcity of potable water resources and relies on desalination technologies to meet its water demand. In this work, a numerical and experimental study was carried out on the functional and productive parameters of the Nouadhibou desalination plant in Mauritania using MATLAB/Simulink (R2016a). The study considered two operating scenarios: with and without the energy recovery unit. The objective of this paper is to perform an analytical study of the operating procedures of the Nouadhibou RO desalination plant by varying several parameters, such as the pressure exchanger, and the feed water mixing ratio in the pressure exchanger unit, etc., in order to determine the system’s optimal operating point. This paper analyzes the system’s performance under different conditions, including recovery rate, feed water temperature, and PEX splitter ratio. In Case No. 1 (without a pressure recovery unit), and with a recovery rate of 20%, doubling the plant’s productivity from 400 to 800 m3/d requires 400 kW of power. In contrast, in Case No. 2 (with a pressure recovery unit), achieving the same productivity requires only 100 kW, with a 75% of energy saving. When the desalination plant operates at a productivity of 400 m3/d@40%, the SPC decreases from 6 kWh/m3 (Case No. 1) to 2.7 kWh/m3 (Case No. 2), resulting in a 55% specific power consumption saving. The results also indicate that power consumption increases with both feed water temperature and PEX splitter ratio, while variations in these parameters have a negligible effect on permeate salinity.

24 December 2025

Different membrane types pore-size, sizes of solutes and particles [12].

Over the past two decades, terahertz (THz) spectroscopy has demonstrated remarkable potential for the investigation of liquids, including studies of living organisms and biological components in their natural, aqueous environments. The main advantages of THz radiation lie in its ability to interact with collective and low-energy vibrational modes of macromolecules and microorganisms, while being non-harmful due to the low photon energy involved. These characteristics make THz spectroscopy particularly valuable for research in liquids compared to other well-established techniques such as Raman and infrared spectroscopy. In this study, we offer a concise overview and comparison of two case studies from our earlier publications, highlighting how Ultrabroadband THz spectroscopy and Intense THz Spectroscopy serve as complementary methods for advancing research in liquids. Ultrabroadband THz spectroscopy enables simultaneous probing of both intermolecular and intramolecular interactions in a single experiment. On the other hand, intense THz spectroscopy greatly simplifies the determination of the optical constants of liquid solutions, eliminating the need for additional assumptions or prior knowledge. Moreover, it offers high sensitivity, allowing the detection of dilute solutions and subtle spectral variations. Currently, these two techniques typically rely on different THz sources, as achieving both broadband coverage and high intensity in a single setup remains challenging. In fact, the experimental results reviewed here were obtained at two different times and within two distinct scientific collaborations. In particular, the intense source was accessed through a collaboration with Prof. Novelli at Ruhr University in Bochum. Integrating both capabilities into a single apparatus would be highly desirable. Therefore, we also present a theoretical investigation of a novel experimental approach that could enable combined ultrabroadband and intense THz spectroscopy, merging the strengths of both methods.

23 December 2025

State of the art of THz sources for Time Domain Spectroscopy. The gray lines represent the scale of the average power. The numbers near the points indicate the references of the corresponding works [21,22,23,24,25,26,27,28,29,30,31,32,33].

In this article, we discuss the relationship and transition between self- and Fick diffusion coefficients in continuous implicit solvents across different particle densities. By applying the established expressions for self-diffusion and Fick diffusion coefficients in binary solutions, we analyze how the local environment influences diffusion through thermodynamic factors, which can be readily evaluated within the framework of Kirkwood–Buff (KB) theory. These thermodynamic factors, originally defined as derivatives of thermodynamic activity, vary with changes in local particle densities, particularly in the presence of aggregation effects. Consequently, the transition from self- to Fick diffusion coefficients can be understood as a reflection of variations in these thermodynamic factors. Langevin Dynamics simulations at low number densities show excellent agreement with the analytical expressions derived. Overall, our findings provide deeper insight into how local structural environments shape particle dynamics, clarifying the connection between KB theory and the transition from self- to Fick diffusion coefficients.

10 December 2025

Center-of-mass radial distribution functions 
  
    
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 for different densities of spherical particles.

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Liquids - ISSN 2673-8015