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This article is focused on the derivation of constitutive equations for magnetic liquids. The results can be used for both ferromagnetic and magnetorheological fluids after the introduced simplifications. The formulation of constitutive equations is based on two approaches. The intuitive approach is based on experimental experience of non-Newtonian fluids, which exhibit a generally non-linear dependence of mechanical stress on shear rate; this is consistent with experimental experience with magnetic liquids. In these general equations, it is necessary to determine the viscosity of a liquid as a function of magnetic induction; however, these equations only apply to the symmetric stress tensor and can only be used for an incompressible fluid. As a result of this limitation, in the next part of the work, this approach is extended by the asymmetry of the stress tensor, depending on the angular velocity tensor. All constitutive equations are formulated in Cartesian coordinates in 3D space. The second approach to determining constitutive equations is more general: it takes the basis of non-equilibrium thermodynamics and is based on the physical approach, using the definition of density of the entropy production. The production of entropy is expressed by irreversible thermodynamic flows, which are caused by the effect of generalized thermodynamic forces after disturbance of the thermodynamic equilibrium. The dependence between fluxes and forces determines the constitutive equations between stress tensors, depending on the strain rate tensor and the magnetization vector, which depends on the intensity of the magnetic field. Their interdependencies are described in this article on the basis of the Curie principle and on the Onsager conditions of symmetry.

In this paper, new forms of Maxwell’s equations in vector and scalar variants are presented. The new forms are based on the use of Gauss’s theorem for magnetic induction and electrical induction. The equations are formulated in both differential and integral forms. In particular, the new forms of the equations relate to the non-stationary expressions and their integral identities. The indicated methodology enables a thorough analysis of non-stationary boundary conditions on the behavior of electromagnetic fields in multiple continuous regions. It can be used both for qualitative analysis and in numerical methods (control volume method) and optimization. The last Section introduces an application to equations of magnetic fluid in both differential and integral forms.

This paper deals with a mathematical modeling of flow stability of Newtonian and non-Newtonian fluids in the gap between two concentric cylinders, one of which rotates. A typical feature of the flow is the formation of a vortex flow, so-called Taylor vortices. Vortex structures are affected by the speed of the rotating cylinder and the physical properties of the fluids, i.e., viscosity and density. Analogy in terms of viscosity is assumed for non-Newtonian and magnetorheological fluids. Mathematical models of laminar, transient and turbulent flow with constant viscosity and viscosity as a function of the deformation gradient were formulated and numerically solved to analyze the stability of single-phase flow. To verify them, a physical experiment was performed for Newtonian fluids using visualizations of vortex structures-Taylor vortices. Based on the agreement of selected numerical and physical results, the experience was used for numerical simulations of non-Newtonian magnetorheological fluid flow.

Cyanobacterial water blooms represent toxicological, ecological and technological problems around the globe. When present in raw water used for drinking water production, one of the best strategies is to remove the cyanobacterial biomass gently before treatment, avoiding cell destruction and cyanotoxins release. This paper presents a new method for the removal of cyanobacterial biomass during drinking water pre-treatment that combines hydrodynamic cavitation with cold plasma discharge. Cavitation produces press stress that causes Microcystis gas vesicles to collapse. The cyanobacteria then sink, allowing for removal by sedimentation. The cyanobacteria showed no signs of revitalisation, even after seven days under optimal conditions with nutrient enrichment, as photosynthetic activity is negatively affected by hydrogen peroxide produced by plasma burnt in the cavitation cloud. Using this method, cyanobacteria can be removed in a single treatment, with no increase in microcystin concentration. This novel technology appears to be highly promising for continual treatment of raw water inflow in drinking water treatment plants and will also be of interest to those wishing to treat surface waters without the use of algaecides