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Notes: Red blood cells are known to change shape in response to local flow conditions. Deformability affects red blood cell physiological function and the hydrodynamic properties of blood. The immersed boundary method is used to simulate three-dimensional membrane–fluid flow interactions for cells with the same internal and external fluid viscosities. The method has been validated for small deformations of an initially spherical capsule in simple shear flow for both neo-Hookean and the Evans-Skalak membrane models. Initially oblate spheroidal capsules are simulated and it is shown that the red blood cell membrane exhibits asymptotic behavior as the ratio of the dilation modulus to the extensional modulus is increased and a good approximation of local area conservation is obtained. Tank treading behavior is observed and its period calculated. © 1998 American Institute of Physics.

Notes: Abstract Outer hair cell electromotility is crucial for the amplification, sharp frequency selectivity, and nonlinearities of the mammalian cochlea. Current modeling efforts based on morphological, physiological, and biophysical observations reveal transmembrane potential gradients and membrane tension as key independent variables controlling the passive and active mechanics of the cell. The cell's mechanics has been modeled on the microscale using a continuum approach formulated in terms of effective (cellular level) mechanical and electric properties. Another modeling approach is nanostructural and is based on the molecular organization of the cell's membranes and cytoskeleton. It considers interactions between the components of the composite cell wall and the molecular elements within each of its components. The methods and techniques utilized to increase our understanding of the central role outer hair cell mechanics plays in hearing are also relevant to broader research questions in cell mechanics, cell motility, and cell transduction.

Notes: Abstract The steady rotation of a disk of infinite radius in a conducting incompressible fluid in the presence of an axial magnetic field leads to the formation on the disk of a three-dimensional axisymmetric boundary layer in which all quantities, in view of the symmetry, depend only on two coordinates. Since the characteristic dimension is missing in this problem, the problem is self-similar and, consequently, reduces to the solution of ordinary differential equations. Several studies have been made of the steady rotation of a disk in an isotropically conductive fluid. In [1] a study was made of the asymptotic behavior of the solution at a large distance from the disk. In [2] the problem is linearized under the assumption of small Alfven numbers, and the solution is constructed with the aid of the method of integral relations. In the case of small magnetic Reynolds numbers the problem has been solved by numerical methods [3,4]. In [5] the method of integral relations was used to study translational flow past a disk. The rotation of a weakly conductive fluid above a fixed base was studied in [6,7], The effect of conductivity anisotropy on a flow of a similar sort was studied approximately in [8], In the following we present a numerical solution of the boundary-layer problem on a disk with account for the Hall effect.

Notes: Abstract One of the basic mechanisms through which biological cells preserve the consistency of their structure is the regulation of material exchange between cell and surrounding medium. The regulation is performed by a thin semipermeable membrane surrounding the cell; it passes some materials freely, while allowing only slight transmission of others, or completely blocking passage. Water shows the maximum penetrating power. If there exists on both sides of the membrane an aqueous solution of some material which does not penetrate the membrane, then under the influence of osmotic pressure water flows into that region where the material concentration is higher, as long as the difference in hydrostatic pressure does not suppress the motion [1, 2]. The viscous flow which develops may lead to displacement of a particle.

Notes: Abstract Several experiments have been reported that indicate a significant difference between the hydrodynamic properties of suspensions and conventional viscous fluids. According to measurements made with different types of viscometers, the viscosity of the suspension in many cases exhibits anomalous behavior that is not compatible with descriptions of the suspension as a conventional Newtonian or non-Newtonian fluid [1–3]. Stratification into solid and liquid phases also plays an important role in the flow of suspensions. In particular, in the significant practical case of Poiseuille flow of an equidense suspension in a circular pipe, wall and core effects were observed. The wall effect, i. e., the migration of suspended particles toward the pipe centerline and the corresponding reduction of the solid phase concentration near the walls, was observed in suspensions of different nature (particles of different nature and form in a viscous liquid [4] and in blood, i.e., suspensions of blood corpuscles in blood plasma [3, 5]) over a wide range of values of average concentration. In contrast with the wall effect, the core effect, which involves an increase of the solid phase concentration in an annular region at a distance of 0.5–0.7 R from the pipe centerline (R is the pipe radius), was observed only for small values of the average concentration [6, 7]. An experiment [8] showed that the presence of the core effect is associated with rotation of the solid particles. When the center of gravity of each of the particles was shifted, their rotation was hindered. In the absence of rotation the particles always migrated toward the tube centerline. Many studies have been devoted to explanation of the wall effect. The magnitude of the transverse force acting on a sphere rotating in a translational viscous liquid flow was calculated in [9] (the limits of applicability of the resulting formula do not permit examination of those values of the parameters for which the core effect is observed in practice). If we substitute the expression for force into the particle equation of motion and integrate, we find that the particle trajectory approaches the tube axis asymptotically [10], regardless of the initial position of the particle. Another approach is the averaged description of the suspension behavior. The Navier-Stokes equation, with a coefficient of viscosity that depends in known fashion on the local solid phase concentration, was written as the equation of motion for the steady flow of a suspension in a circular tube. The variational principle (the principle of minimum energy dissipation) was formulated to find the concentration distribution. The wall effect was also obtained using this approach [11, 12]. An analogous study using the Kessonmodel yielded practically no results [13]. The complete system of equations of two-fluid hydrodynamics was recently constructed in which the fluid and the dispersed phase are considered as two interpenetrating, interacting continua, with rotation and deformation of the dispersed phase particles being taken into consideration (Nguen Van D'ep, Candidate's dissertation: Some questions on the Hydrodynamics of Structured Fluids [in Russian], Voronezh State University, Voronezh, 1968). However, the practical use of this system for solving, for example, the Poiseuille problem appears to be difficult, since it is necessary to know in detail the interaction forces between the phases. In the present study we use the single-fluid approximation, i.e., the quantities introduced (velocity, density, and so on) characterize the motion of the suspensions as a whole, and not any single phase. Only two quantities characterize the solid phase proper: the bulk concentration and the local angular velocity of the solid particles. This approach does not require knowledge of the interaction forces between the phases, and the final equations are considerably simpler than those for the two-fluid description. The thermodynamics of irreversible processes is used to construct a closed system of equations that includes the diffusion equations and the generalized moment of momentum equation, which make it possible to find the three-dimensional distribution of the concentration and the angular velocity of the solid particles. The generalized Fick law, which contains three additional diffusion coefficients, is obtained. In contrast with classical models, the viscous stress tensor is asymmetric, and its antisymmetric part is proportional to the difference in the angular rates of rotation of the solid particles and the suspension as a whole. From these equations follow under certain particular assumptions the equations of the theory of a fluid with internal rotation [14]. As an example of the application of the theory, the Poiseuille problem of flow in a flat channel is solved. The concentration distributions obtained agree well with the experimental data described above.

Notes: Abstract A fluid model with internal rotation (micropolar fluid) was proposed in [1–5], in which the general equations were derived and solutions of certain steady-state problems were presented (the equations presented in [5] and the steady-state solutions of these equations [5–7] differ somewhat from the corresponding results of [1–4, 8]). The essential feature of this model is the account for the proper rotation of the fluid molecules or particles suspended in the fluid, which makes possible a more detailed description of the behavior of fluids with complex internal structure—for example, suspensions and biological fluids [5, 8]. In the following we present some results of a study of Poisseuille and Couette flow of a fluid with internal rotation between parallel plates.

Notes: Abstract Results are presented of an experimental investigation of light scattering by blood flow. The relationship between the observed dependence of the scattering on the time and strain rate and the aggregation of particles (erythrocytes) and hydrodynamic characteristics is discussed.