The primary aim of this study is to establish the theoretical foundations for a solid-fluid biphasic mixture domain that can accommodate inertial effects and a viscous interstitial fluid, which can interface with a dynamic viscous fluid domain. Most mixture formulations consist of constituents that are either all intrinsically incompressible or compressible, thereby introducing inherent limitations. In particular, mixtures with intrinsically incompressible constituents can only model wave propagation in the porous solid matrix, whereas those with compressible constituents require internal variables, and related evolution equations, to distinguish the compressibility of the solid and fluid under hydrostatic pressure. In this study, we propose a hybrid framework for a biphasic mixture where the skeleton of the porous solid is intrinsically incompressible but the interstitial fluid is compressible. We define a state variable as a measure of the fluid volumetric strain. Within an isothermal framework, the Clausius-Duhem inequality shows that a function of state arises for the fluid pressure as a function of this strain measure. We derive jump conditions across hybrid biphasic interfaces, which are suitable for modeling hydrated biological tissues. We then illustrate this framework using confined compression and dilatational wave propagation analyses. The governing equations for this hybrid biphasic framework reduce to those of the classical biphasic theory whenever the bulk modulus of the fluid is set to infinity and inertia terms and viscous fluid effects are neglected. The availability of this novel framework facilitates the implementation of finite element solvers for fluid-structure interactions at interfaces between viscous fluids and porous-deformable biphasic domains, which can include fluid exchanges across those interfaces.

Transport of solute across the arterial wall is a process driven by both convection and diffusion. In disease, the elastic fibers in the arterial wall are disrupted and lead to altered fluid and mass transport kinetics. A computational mixture model was used to numerically match previously published data of fluid and solute permeation experiments in groups of mouse arteries with genetic (knockout of fibulin-5) or chemical (treatment with elastase) disruption of elastic fibers. A biphasic model of fluid permeation indicated the governing property to be the hydraulic permeability, which was estimated to be 1.52×10, 1.01×10, and 1.07×10 mm/μN.s for control, knockout, and elastase groups, respectively. A multiphasic model incorporating solute transport was used to estimate effective diffusivities that were dependent on molecular weight, consistent with expected transport behaviors in multiphasic biological tissues. The effective diffusivity for the 4 kDA FITC-dextran solute, but not the 70 or 150 kDa FITC-dextran solutes, was dependent on elastic fiber structure, with increasing values from control to knockout to elastase groups, suggesting that elastic fiber disruption affects transport of lower molecular weight solutes. The model used here sets the groundwork for future work investigating transport through the arterial wall.

The growth and treatment of tumors is an important problem to society that involves the manifestation of cellular phenomena at length scales on the order of centimeters. Continuum mechanical approaches are being increasingly used to model tumors at the largest length scales of concern. The issue of how to best connect such descriptions to smaller-scale descriptions remains open. We formulate a framework to derive macroscale models of tumor behavior using the thermodynamically constrained averaging theory (TCAT), which provides a firm connection with the microscale and constraints on permissible forms of closure relations. We build on developments in the porous medium mechanics literature to formulate fundamental entropy inequality expressions for a general class of three-phase, compositional models at the macroscale. We use the general framework derived to formulate two classes of models, a two-phase model and a three-phase model. The general TCAT framework derived forms the basis for a wide range of potential models of varying sophistication, which can be derived, approximated, and applied to understand not only tumor growth but also the effectiveness of various treatment modalities.

Most recently, the whole world is struggling against the virulent pandemic COVID-19. Due to the unbounded global spread of the disease, having biosensors with high performance such as high sensitivity and accuracy is of utmost importance. In this paper, the effects of various parameters on the behaviors of micro-biosensors are investigated in order to enhance their performance. These parameters are related to the geometry and material, and they are assumed to be gradually changing in the longitudinal direction of the biosensor according to a power law. Therefore, they are called functionally graded geometrical and material parameters. Another aspect is when considering microcantilever-based biosensors, the main behavior parameter is the deflection at the free end. In the analyses, the influences of the surface stress and van der Waals intermolecular forces are taken into account. Also, the total energy of the beam, which is the combination of the van der Waals energy and the elastic strain energy, is accomplished. In addition, the equivalent force causing the deflection is also evaluated using Castigliano method for two cases. These cases account for a concentrated force at the free end and a distributed load along the biosensor, respectively. Since the governing equations account for the size dependency and the considered parameters are functions of the position, the solution is too complex to be achieved analytically, and therefore, numerical methods are applied. For uniform biosensors made of homogeneous materials, or in other words when all parameters are not varying with the position, the obtained results are compared with those in the literature, and good agreement is obtained. On the other hand, the performance, which include sensitivity and limit of detection, of functionally graded biosensors can be enhanced by proper choices of the considered parameters and the corresponding exponent of the gradation function.

In this research, two alternative approaches to fractional derivatives, namely Caputo-Fabrizio (CF) and Atangana-Baleanu (AB) fractional operators, are used to propose a generalized model of thermoelastic heat transfer of a rigid cylinder with thermal characteristics. The proposed model can be constructed by combining the DPL model with phase delays and the two temperature theories. It will be taken into account that the solid cylinder has variable physical properties. It was also assumed that the surface of the cylinder is penetrated by a continuous magnetic field and is regularly exposed to thermal loading from a continuous heat source. The numerical solutions of the studied physical fields in the AB and CF fractional derivative cases were derived using the Laplace transform method and are compared visually and tabularly and discussed in detail.

Haemodynamics is a branch of fluid mechanics which investigates the features of blood when it flows not only via blood vessels of smaller/larger diameter, but also under normal as well as abnormal flow states, such as in the presence of stenosis, aneurysm, and thrombosis. This review aims to discuss the rheological properties of blood, geometry of constrictions, dilations and the emergence of single-layered fluid to four-layered fluid models. To discuss further the influence of the aforesaid parameters on the physiologically important flow quantities, the mathematical formulation and solution methodology of the two-layered and four layered arterial blood flow problems studied by the authors (Afiqah and Sankar in ARPN J Eng Appl Sci 15:1129--1143, 2020, Comput Methods Programs Biomed 199:105907, 2021. 10.1016/j.cmpb.2020.105907) are recalled. It should be pointed out that the increasing resistive impedance to flow in three distinct states encompassing healthy, anaemic, and diabetic demonstrates that the greater the restriction in the artery, very few blood is carried to the pathetic organs, leading to subjects' death. It is also discovered that the pulsatile nature of blood movement produces a dynamic environment that poses a slew of intriguing and unstable fluid mechanical state. It is hoped that the intriguing results gathered from this literature survey and review conducted may help the medical practitioners to forecast blood behaviour mobility in stenotic arteries. Furthermore, the physiological information gathered from the available clinical data from the literature on patients diagnosed with diabetes and anaemia may be beneficial to doctors in deciding the therapeutic procedure for treating some particular cardiovascular disease.