Hydrogels Based on Polyacrylamide and Calcium Alginate: Thermodynamic Compatibility of Interpenetrating Networks, Mechanical, and Electrical Properties

The synthesis and physicochemical properties of hydrogels with interpenetrated physical and chemical networks were considered in relation to their prospective application as biomimetic materials in biomedicine and bioengineering. The study was focused on combined hydrogels based on natural polysaccharide-calcium alginate (CaAlg) and a synthetic polymer-polyacrylamide (PAAm). The series of hydrogels with varying proportions among alginate and polyacrylamide have been synthesized, and their water uptake has been characterized depending on their composition. The equilibrium swelling and re-swelling in water after drying were considered. The compatibility of alginate and polyacrylamide in the combined blend was studied by the thermodynamic approach. It showed a controversial combination of negative enthalpy of mixing among PAAm and CaAlg with positive Gibbs energy of mixing. Mechanical and electrical properties of the combined gels with double networking were studied as relevant for their prospective use as scaffolds for tissue regeneration and working bodies in actuators. The storage modulus and the loss modulus were determined in the oscillatory compression mode as a function of proportions among natural and synthetic polymers. Both moduli substantially increased with the content of CaAlg and PAAm. The electrical (Donnan) potential of hydrogels was measured using the capillary electrode technique. The Donnan potential was negative at all compositions of hydrogels, and its absolute values increased with the content of CaAlg and PAAm.

Modelling of hemodynamics in bifurcation lesions of coronary arteries before and after myocardial revascularization

Modelling of patient-specific hemodynamics for a clinical case of severe coronary artery disease with the bifurcation stenosis was carried out with allowance for standard angiographic data obtained before and after successfully performed myocardial revascularization by stenting of two arteries. Based on a non-Newtonian fluid model and an original algorithm for fluid dynamics computation operated with a limited amount of initial data, key characteristics of blood flow were determined to analyse the features of coronary disease and the consequences of its treatment. The results of hemodynamic modelling near bifurcation sites are presented with an emphasis on physical, physiological and clinical phenomena to demonstrate the feasibility of the proposed approach. The main limitations and ways to minimize them are the subjects of discussion as well. This article is part of the theme issue 'Transport phenomena in complex systems (part 2)'.

Theory of static magnetization of magnetopolymer composites: The second virial approximation

This paper deals with a theoretical study of the static magnetization of a composite, consisting of nanodisperse single-domain ferromagnetic particles immobilized in a nonmagnetic medium. This situation is typical for magnetopolymer systems-smart materials, which found applications in high industrial and biomedical applications. It is supposed that the composite was polymerized without an external magnetic field; after curing the particles retain the spatial distribution and orientation of their axes of easy magnetization that they had before the host medium polymerization. Our results demonstrate that, in contrast to ferrofluids with a liquid host medium, a magnetic interparticle interaction provokes a decrease of the macroscopic magnetization of the system.

Variable-order fractional master equation and clustering of particles: non-uniform lysosome distribution

In this paper, we formulate the space-dependent variable-order fractional master equation to model clustering of particles, organelles, inside living cells. We find its solution in the long-time limit describing non-uniform distribution due to a space-dependent fractional exponent. In the continuous space limit, the solution of this fractional master equation is found to be exactly the same as the space-dependent variable-order fractional diffusion equation. In addition, we show that the clustering of lysosomes, an essential organelle for healthy functioning of mammalian cells, exhibit space-dependent fractional exponents. Furthermore, we demonstrate that the non-uniform distribution of lysosomes in living cells is accurately described by the asymptotic solution of the space-dependent variable-order fractional master equation. Finally, Monte Carlo simulations of the fractional master equation validate our analytical solution. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.

Effect of ring-shaped clusters on magnetic hyperthermia: modelling approach

Experiments demonstrate that magnetic nanoparticles, embedded in a tissue, very often form heterogeneous structures of various shapes and topologies. These structures (clusters) can significantly affect macroscopical properties of the composite system, in part its ability to generate heat under an alternating magnetic field (so-called magnetic hyperthermia). If the energy of magnetic interaction between the particles significantly exceeds the thermal energy of the system, the particles can form the closed ring-shaped clusters. In this work, we propose a relatively simple model of the heat production by the particles united in the 'ring' and immobilized in a host medium. Mathematically, this model is based on the phenomenological Debye equation of kinetics of the particles remagnetization. Magnetic interaction between all particles in the cluster is taken into account. Our results show that the appearance of the clusters can significantly decrease the thermal effect. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.

Nonlinear theory of macroscopic flow induced in a drop of ferrofluid

We present results of theoretical modelling of macroscopic circulating flow induced in a cloud of ferrofluid by an oscillating magnetic field. The cloud is placed in a cylindrical channel filled by a nonmagnetic liquid. The aim of this work is the development of a scientific basis for a progressive method of addressing drug delivery to thrombus clots in blood vessels with the help of the magnetically induced circulation flow. Our results show that the oscillating field can induce, inside and near the cloud, specific circulating flows with the velocity amplitude about several millimetres per second. These flows can significantly increase the rate of transport of the molecular non-magnetic impurity in the channel. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.

Transport phenomena in complex systems (part 1)

The issue, in two parts, is devoted to theoretical, computational and experimental studies of transport phenomena in various complex systems (in porous and composite media; systems with physical and chemical reactions and phase and structural transformations; in biological tissues and materials). Various types of these phenomena (heat and mass transfer; hydrodynamic and rheological effects; electromagnetic field propagation) are considered. Anomalous, relaxation and nonlinear transport, as well as transport induced by the impact of external fields and noise, is the focus of this issue. Modern methods of computational modelling, statistical physics and hydrodynamics, nonlinear dynamics and experimental methods are presented and discussed. Special attention is paid to transport phenomena in biological systems (such as haemodynamics in stenosed and thrombosed blood vessels magneto-induced heat generation and propagation in biological tissues, and anomalous transport in living cells) and to the development of a scientific background for progressive methods in cancer, heart attack and insult therapy (magnetic hyperthermia for cancer therapy, magnetically induced circulation flow in thrombosed blood vessels and non-contact determination of the local rate of blood flow in coronary arteries). The present issue includes works on the phenomenological study of transport processes, the derivation of a macroscopic governing equation on the basis of the analysis of a complicated internal reaction and the microscopic determination of macroscopic characteristics of the studied systems. This article is part of the theme issue 'Transport phenomena in complex systems (part 1)'.

On the theory of magnetic hyperthermia: clusterization of nanoparticles

Experiments show that clusters consisting of nano-sized ferromagnetic particles strongly affect the intensity of heat production during magnetic hyperthermia. In this paper, a theoretical study and mathematical modelling of the heat production by clusters of single-domain ferromagnetic particles, immobilized in a host medium, are presented. Two situations of strong and weak magnetic anisotropy of the particles are considered. Our results show that, in the case of strong anisotropy, the clusterization weakens the thermal effect, whereas in the case of weak anisotropy it enhances it. This article is part of the theme issue 'Patterns in soft and biological matters'.

Field-induced circulation flow in magnetic fluids

In this paper, we present results of a theoretical study of circulation flow in ferrofluids under the action of an alternating inhomogeneous magnetic field. The results show that the field with the amplitude of about 17 kA m^-1 and angular frequency 10 s^-1 can induce mesoscopic flow with a velocity amplitude of about 0.5 mm s^-1. This mechanism can be used for intensification of drag delivery in blood vessels. This article is part of the theme issue 'Patterns in soft and biological matters'.

Ferrogels Ultrasonography for Biomedical Applications

Ferrogels (FG) are magnetic composites that are widely used in the area of biomedical engineering and biosensing. In this work, ferrogels with different concentrations of magnetic nanoparticles (MNPs) were synthesized by the radical polymerization of acrylamide in stabilized aqueous ferrofluid. FG samples were prepared in various shapes that are suitable for different characterization techniques. Thin cylindrical samples were used to simulate the case of targeted drug delivery test through blood vessels. Samples of larger size that were in the shape of cylindrical plates were used for the evaluation of the FG applicability as substitutes for damaged structures, such as bone or cartilage tissues. Regardless of the shape of the samples and the conditions of their location, the boundaries of FG were confidently visualized over the entire range of concentrations of MNPs while using medical ultrasound. The amplitude of the reflected echo signal was higher for the higher concentration of MNPs in the gel. This result was not related to the influence of the MNPs on the intensity of the reflected echo signal directly, since the wavelength of the ultrasonic effect used is much larger than the particle size. Qualitative theoretical model for the understanding of the experimental results was proposed while taking into account the concept that at the acoustic oscillations of the hydrogel, the macromolecular net, and water in the gel porous structure experience the viscous Stocks-like interaction.

Stress relaxation in a ferrofluid with clustered nanoparticles

The formation of structures in a ferrofluid by an applied magnetic field causes various changes in the rheological behaviour of the ferrofluid. A ferrofluid based on clustered iron nanoparticles was investigated. We experimentally and theoretically consider stress relaxation in the ferrofluid under the influence of a magnetic field, when the flow is suddenly interrupted. It is shown that the residual stress observed in the fluid after the relaxation is correlated with the measured and theoretically predicted magnetic field-induced yield stress. Furthermore, we have shown that the total macroscopic stress in the ferrofluid after the flow is interrupted is defined by the presence of both linear chains and dense, drop-like bulk aggregates. The proposed theoretical approach is consistent with the experimentally observed behaviour, despite a number of simplifications which have been made in the formulation of the model. Thus, the obtained results contribute a lot to the understanding of the complex, magnetic field-induced rheological properties of magnetic colloids near the yield stress point.

Inverse magnetorheological fluids

We report a new kind of field-responsive fluid consisting of suspensions of diamagnetic (DM) and ferromagnetic (FM) microparticles in ferrofluids. We designate them as inverse magnetorheological (IMR) fluids for analogy with inverse ferrofluids (IFFs). Observations on the particle self-assembly in IMR fluids upon magnetic field application showed that DM and FM microparticles were assembled into alternating chains oriented along the field direction. We explain such assembly on the basis of the dipolar interaction energy between particles. We also present results on the rheological properties of IMR fluids and, for comparison, those of IFFs and bidispersed magnetorheological (MR) fluids. Interestingly, we found that upon magnetic field application, the rheological properties of IMR fluids were enhanced with respect to bidispersed MR fluids with the same FM particle concentration, by an amount greater than the sum of the isolated contribution of DM particles. Furthermore, the field-induced yield stress was moderately increased when up to 30% of the total FM particle content was replaced with DM particles. Beyond this point, the dependence of the yield stress on the DM content was non-monotonic, as expected for FM concentrations decreasing to zero. We explain these synergistic results by two separate phenomena: the formation of exclusion areas for FM particles due to the perturbation of the magnetic field by DM particles and the dipole-dipole interaction between DM and FM particles, which enhances the field-induced structures. Based on the second phenomenon, we present a theoretical model for the yield stress that semi-quantitatively predicts the experimental results.

To the theory of rheological properties of magnetopolymer suspensions

This paper deals with the theoretical study of the magnetorhelogical properties of dilute suspensions of polymer coils with ferromagnetic nanoparticles adsorbed on the macromolecules. The analysis shows that, under an applied magnetic field, these coils elongate in the field direction and swell. Both these factors lead to a significant increase in the effective viscosity of the system. Estimates show that in the magnetopolymer compositions, strong magnetoviscous effects are expected even though in standard ferrofluids these effects are negligible.

Dynamics of colloidal suspensions of ferromagnetic particles in plane Couette flow: comparison of approximate solutions with Brownian dynamics simulations

The stationary and oscillatory properties of dilute ferromagnetic colloidal suspensions in plane Couette flow are studied. Analytical expressions for the off-equilibrium magnetization and the shear viscosity are obtained within the so-called effective field approximation. We also investigate the predictions of a different approximation based on the linearized moment expansion. Direct numerical simulation of the kinetic model are performed in order to test the range of validity of these approximations.

Internal structure of colloidal aggregates

A nonlinear model of diffusion-limited growth of three-dimensional colloidal aggregate has been developed. The conditions of internal combination/recombination balance has been considered. Obtained solution shows that the aggregate contains the central dense core and the surrounding loose region, in which the aggregated particle concentration decreases as a power function, according to the fractal cluster properties. The fractal dimension d(f) has been found to be independent on physical and chemical properties of colloidal system. The obtained universal value d(f)=2.5 is in a good agreement with the known experimental and numerical results. The model may be useful for the analysis of a wide class of aggregation phenomena.

Dynamical susceptibility of solid ferrocolloids

A theoretical analysis of the dynamical magnetic susceptibility of a frozen nondilute ferrocolloid is presented. The steric and dipole-dipole interactions between ferroparticles are taken into account. Two systems are studied. The first is the homogeneous solid ferrocolloid with separate individual particles. The second is a ferrocolloid with heterogeneous chainlike aggregates. The effect of the magnetodipole interparticle interaction on the real and imaginary parts of the dynamical susceptibilities of these systems is estimated.