A note on couette flow of nematic crystals according to the Ericksen–Leslie theory

In order to model the flow of nematic crystals, the theoretical framework according to Ericksen and Leslie is applied. The essentials of the theory are compiled and then specialized to Couette flow. The profiles for linear velocity and orientation angle will be computed and, in particular, we shall also study the rise in temperature due to viscous dissipation, which is frequently ignored by mechanicians. Analytical and numerical solutions for the fields are derived for different boundary conditions and will subsequently be discussed.TU Berlin, Open-Access-Mittel - 201

Electrodynamics from the viewpoint of modern continuum theory—A review

This paper wants to draw attention to several issues in electrodynamic field theory and to make way for a rational continuum approach to the subject. The starting point are the balances for magnetic flux and electric charge, both in a very general formulation for volumes and for open surfaces, all of which can deform and be immaterial or material. The spatial point-of-view for the description of fields is favored and its advantages in comparison to the concept of material particles is explained. A straightforward answer to the question of how to choose units for the electromagnetic fields most suitably is also presented. The transformation properties of the electromagnetic fields are addressed by rewriting the balances in space–time notation. Special attention is paid to the connection between the two sets of electromagnetic fields through the so-called Maxwell–Lorentz–æther relations. The paper ends with an outlook into constitutive theory of matter under the influence of electromagnetic fields and a discussion on curious developments in context with Maxwell's equations

Thence the moment of momentum

Fifty years have passed since Truesdell's seminal paper on the origin and status of the balance for the moment of momentum was published in ZAMM. It is time to take stock: Important new developments in the theory of generalized continua with internal degrees of freedom and some fascinating fundamental applications need to be pointed out. Is there new evidence from classical papers regarding its independence from the balance of linear momentum? Can micropolar theory be used to “explain” electromagnetism? How is the conservation of the moment of momentum viewed in today's physics textbooks? In this paper an attempt is made to answer these and many more interesting questions.TU Berlin, Open-Access-Mittel – 202

FUNNEL FLOW OF A NAVIER-STOKES-FLUID WITH POTENTIAL APPLICATIONS TO MICROPOLAR MEDIA

In this paper foundations are laid for a future solution of a fully coupled flow problem for the micropolar medium undergoing structural change in a funnel-shaped crusher. Initially the fundamental equations of micropolar media are revisited and the problem of structural changes of micropolar media moving in a crusher is explained. Then a review of the current state-of-the-art is presented and a necessary extension of the problem is motivated. The need for using numerical methods of fluid mechanics is emphasized. As a prerequisite for the study of the fully coupled initial boundary value 2D-flow problem of a micropolar fluid the funnel flow of a Navier-Stokes fluid is investigated based on an implicit finite difference scheme using the Thomas algorithm. Numerical results for velocities, stresses, and for the pressure dependence of the funnel flow are presented. The correctness of the algorithm is checked by specializing to the case of a flow through a tunnel of constant cross-section under the influence of gravity, for which an analytical solution is available

Drug Delivery From Polymer-Based Nanopharmaceuticals—An Experimental Study Complemented by Simulations of Selected Diffusion Processes

The success of medical therapy depends on the correct amount and the appropriate delivery of the required drugs for treatment. By using biodegradable polymers a drug delivery over a time span of weeks or even months is made possible. This opens up a variety of strategies for better medication. The drug is embedded in a biodegradable polymer (the “carrier”) and injected in a particular position of the human body. As a consequence of the interplay between the diffusion process and the degrading polymer the drug is released in a controlled manner. In this work we study the controlled release of medication experimentally by measuring the delivered amount of drug within a cylindrical shell over a long time interval into the body fluid. Moreover, a simple continuum model of the Fickean type is initially proposed and solved in closed-form. It is used for simulating some of the observed release processes for this type of carrier and takes the geometry of the drug container explicitly into account. By comparing the measurement data and the model predictions diffusion coefficients are obtained. It turns out that within this simple model the coefficients change over time. This contradicts the idea that diffusion coefficients are constants independent of the considered geometry. The model is therefore extended by taking an additional absorption term into account leading to a concentration dependent diffusion coefficient. This could now be used for further predictions of drug release in carriers of different shape. For a better understanding of the complex diffusion and degradation phenomena the underlying physics is discussed in detail and even more sophisticated models involving different degradation and mass transport phenomena are proposed for future work and study

Modeling of blood flow in the framework of micropolar theory

In this paper, we study the blood flow through blood vessels of various radii (including the case of variable cross section as well as modeling the blood flow through venae and arteries). Two approaches are discussed in order to mimic the dependence of blood viscosity on red blood cells aggregation, which changes with the shear rate and position inside the vessel: Two microstructural parameters together with empirical constitutive equations as a characteristic of aggregation are proposed, namely the microinertia as well as the volume fraction of blood particles (erythrocytes, platelets and leukocytes). Consequently, the Navier–Stokes system of equations for an incompressible fluid is supplemented by a constitutive equation for the moment of inertia in one case and for the volume fraction in another. The problems are solved numerically by the finite volume method for vessels of various geometries in spatial description. A comparison with experimental data for a narrow capillary shows the efficiency of the proposed constitutive equations for describing blood flow. Also, velocity profiles are obtained on the basis of compiled empirical formula for various sections of a blood vessel of variable radius. In addition, the flow through vessels of the human circulatory system, such as the inferior vena cava and the carotid artery, are studied

Micropolar medium in a funnel-shaped crusher

In this paper, the solution to a coupled flow problem for a micropolar medium undergoing structural changes is presented. The structural changes occur because of a grinding of the medium in a funnel-shaped crusher. The standard macroscopic equations for mass and linear momentum are solved in combination with a balance equation for the microinertia tensor containing a production term. The constitutive equations of the medium describe a linear viscous material with a viscosity coefficient depending on the characteristic particle moment of inertia, the so-called microinertia. A coupled system of equations is presented and solved numerically in order to determine the distribution of the fields for velocity, pressure, viscosity coefficient, and microinertia in all points of the continuum. The numerical solution to this problem is found by using the implicit finite difference method and the upwind scheme.TU Berlin, Open-Access-Mittel – 202