In this study, analytical calculation formula of radial coordinate of the region where the velocity of flow is maximum in the space between the concentric annuli as an empirical approach is proposed. In general, the graphic drawn according to the formula which depends on rheological conduct of the fluid environment ( ) and the ratio of radii of tubes ( ) is obtained on the following picture. Figure A. The variation of parameter λ(n, δ) with respect to δ.In Figure A the symbols are numerical values from [11,12] for n = 0.1, 0.5, 1. The lines are the theoretical curves calculated according to Equation 9 in these values of n; n = 0.1(blue), n = 0.5 (black), n = 1 (red). As seen in Figure A, the theoretical results are agree with the results given in the literature in the form of approximate tables/graphs. Thus, the graphical solutions proposed [11][12] nearly half a century ago were integrated with the analytical solution we proposed. Purpose:The main purpose of this study is to create an analytical calculation of the instantaneous flow rate or pressure drop, which is important for non-Newtonian flow in the space between the concentric annuli. For this, an analytical formula is proposed for calculating the λ(n,δ) radial coordinate, which is important for determining the non-Newtonian flow profile. This formula completes the previous formulas presented in the literatüre. Theory and Methods:The solution of the problem was made by determining the radial coordinate of the point where the velocity profile is maximum, by following the approximate expression of the shear stress-shear rate characteristics according to the Power-Law model for the flow in the concentric annuli. Results:The results showed that it is possible to determine the flow rate or pressure drop analytically in concentric cylindrical annuli. The analytical approach proposed for this purpose has been found to include other approximate solutions presented in the literature to date. Conclusion:Simple empirical formula given in Equation 9 is proposed to calculate the parameter λ(n,δ) easily, which is the coordinate of the region where the flow velocity is the maximum in the axial flows of non-Newtonian rheological fluids in concentric annuli. Although this equation is not an expression derived from the solution of the hydrodynamic problem, it applies at all variation intervals (n = 0 ⋯ ∞) for non-Newtonian behavior parameter n of rheological fluids, and satisfies all hydrodynamic and rheological boundary conditions. Therefore, the approximate analytical calculation method proposed in this study will allow the calculation of basic parameters such as pressure change and flow rate without using complex methods such as interpolation, graph and table data.

Biyomühendislikte yapılan çalışmalarda in vitro deneyler için gerçek kanın kullanılması; elde edilmesi, saklanması, manipülasyonu, büyük miktarlarda gerekli olması, hava ile temas ettiğinde yapısının değişmesi ve toksisitesi gibi nedenlerden dolayı pek mümkün değildir. Bu yüzden in vitro ortamda yapılan deneylerde kan yerine kullanılacak sıvıların araştırılması önemli bir konudur. Bu sıvıların insan kanına benzer reolojik özellikler göstermesi beklenir. Fakat kan reolojisi son derece karmaşık olduğundan, kanın tüm reolojik özelliklerini karşılayan analog sıvılar geliştirmek oldukça zordur. Tek bir analog sıvısı ile kanın bütün özellikleri aynı anda sağlanamadığından, laboratuvar ortamında yapılacak çalışmanın özelliğine bağlı olarak kan yerine geçecek farklı kan analoglarının seçimi yapılmaktadır. Yapılan çoğu çalışmalarda, bu kan analogları için hazırlanan bileşimlere Xanthan Gum (XG) ilavesiyle kanın reolojik özelliklerine en yakın davranış sergileyen analoglar ön plana çıkmaktadır. Bu çalışmamızda in vitro koşullarda kanın yerine geçebilecek kan analog sıvılarının araştırılması yapılmış, bu analogların reolojik özellikleri tablolarla sunulmuş ve önerilerde bulunulmuştur.

The kinetic equation of the accumulation of magnetic particles from axial flow on a magnetized ferromagnetic wire in an external homogeneous magnetic field has been developed in this study. A new differential equation of the evolution of the accumulation radius over time, which considers both the capture and the detachment of the particles in the accumulation profile on the wire, has been formulated. The evolution of the radius of the accumulation profile over time was obtained from both the differential kinetic equation based on population theory and from the stochastic Fokker–Planck equation. In the limit approach (t→∞), it was observed that the expressions of the saturation radius of the accumulation radius on the magnetized wire of the particles obtained from both models were the same. It is emphasized that the obtained results are valid for both the initial and steady-state build-up of the particle capture process. These results were compared with the experimental results from the literature, and it was observed that the theoretical and experimental results were in good agreement. The effects of both capture and detachment events on the accumulation of particles on the magnetized wire were evaluated.

Separation processes are widely used in chemical and biotechnical processes. Especially biomagnetic separation is an important issue among effective separation processes to separate the magnetic micron and submicron particles. It is necessary to establish and determine a high magnetic field or field gradient in the separation cell. However, it is not easy to determine the magnetic field gradient in the working region for different separation in practice. The reason for these difficulties is that the magnetic cells used in biochemical separation have different geometries and there are no simple and useful systems to easily measure these magnetic fields. Two main objectives are aimed in this study. First, a simple measuring device design can measure gradient magnetic fields with high precision of about 0,01mm and, secondly, obtain simple empirical expressions for the magnetic field. A magnetometer with Hall probes that works with the 3D printer principle was designed and tested to measure the magnetic field. Magnetic field changes were measured according to the surface coordinates on the measurement platform or measuring cell. Numerous experimental measurements of gradient magnetic fields generated by permanent magnets have been taken. The results obtained from the studies and results from the proposed empirical models were compared.