PurposeThis paper sets out to present a fully explicit smoothed particle hydrodynamics (SPH) method to solve non‐Newtonian fluid flow problems.Design/methodology/approachThe governing equations are momentum equations along with the continuity equation which are described in a Lagrangian framework. A new treatment similar to that used in Eulerian formulations is applied to viscous terms, which facilitates the implementation of various inelastic non‐Newtonian models. This approach utilizes the exact forms of the shear strain rate tensor and its second principal invariant to calculate the shear stress tensor. Three constitutive laws including power‐law, Bingham‐plastic and Herschel‐Bulkley models are studied in this work. The imposition of the incompressibility is fulfilled using a penalty‐like formulation which creates a trade‐off between the pressure and density variations. Solid walls are simulated by the boundary particles whose positions are fixed but contribute to the field variables in the same way as the fluid particles in flow field.FindingsThe performance of the proposed algorithm is assessed by solving three test cases including a non‐Newtonian dam‐break problem, flow in an annular viscometer using the aforementioned models and a mud fluid flow on a sloping bed under an overlying water. The results obtained by the proposed SPH algorithm are in close agreement with the available experimental and/or numerical data.Research limitations/implicationsIn this work, only inelastic non‐Newtonian models are studied. This paper deals with 2D problems, although extension of the proposed scheme to 3D is straightforward.Practical implicationsThis study shows that various types of flow problems involving fluid‐solid and fluid‐fluid interfaces can be solved using the proposed SPH method.Originality/valueUsing the proposed numerical treatment of viscous terms, a unified and consistent approach was devised to study various non‐Newtonian flow models.
Droplet-based microfluidic logic gates have many applications in diagnostic assays and biosciences due to their automation and the ability to be cascaded. In spite of many bio-fluids, such as blood exhibit non-Newtonian characteristics, all the previous studies have been concerned with the Newtonian fluids. Moreover, none of the previous studies has investigated the operating regions of the logic gates. In this research, we consider a typical AND/OR logic gate with a power-law fluid. We study the effects of important parameters such as the power-law index, the droplet length, the capillary number, and the geometrical parameters of the microfluidic system on the operating regions of the system. The results indicate that AND/OR states mechanism function in opposite directions. By increasing the droplet length, the capillary number and the power-law index, the operating region of AND state increases while the operating region of OR state reduces. Increasing the channel width will decrease the operating region of AND state while it increases the operating region of OR state. For proper operation of the logic gate, it should work in both AND/OR states appropriately. By combining the operating regions of these two states, the overall operating region of the logic gate is achieved. Microfluidics lab-on-chip devices have many applications in diagnostic assays, analytical chemistry, and biosciences. Using droplet-based microfluidic devices may offer various benefits 1. One of the advantages is encapsulating the important fluids as a droplet in order to prevent them from chemical reactions and pollutions. Another advantage of these systems is a better mixing of the reactant inside the droplet and increasing the reaction speed 2. In this manner the sample volume decreases significantly, the cost of operation is reduced drastically, and diagnostic results are obtained in a much shorter time, higher precision, sensitivity, and portability 3. For the droplet-based microfluidic devices, one needs to consider various components such as the valves and the mixers to perform certain functions. Electric, magnetic and thermocapillary forces are some types of forces that are used to control and manipulate fluid in microfluidic circuits 4-6. Thus, these circuits may contain many components that will make their construction complicated. Furthermore, some external equipment such as the permanent magnet or wire coils should be considered 7-11. Additional components limit the portability, scalability and parallel operations. The solution is automation. In electronics, complex operations are obtained using logic gates. Logic gates have many applications like sound and molecular computing 12,13. By analogy to logic gates (in which the pressure can be analogous to the voltage, the flow rate to the electric current and the hydrodynamic resistance to the electrical resistance) one can derive their functionalities for the microfluidics 14,15. Fabricating fluidics devices that are similar to logic circuits, began in the 1960s 16,17. These devices...
We investigate an efficient method (T-junction with valve) to produce nonuniform droplets in micro- and nano-fluidic systems. The method relies on breakup of droplets in a T-junction with a valve in one of the minor branches. The system can be simply adjusted to generate droplets with an arbitrary volume ratio and does not suffer from the problems involved through applying the available methods for producing unequal droplets. A volume of fluid (VOF) based numerical scheme is used to study the method. Our results reveal that by decreasing the capillary number, smaller droplets can be produced in the branch with valve. Also, we find that the droplet breakup time is independent of the valve ratio and decreases with the increase of the capillary number. Also, the results indicate that the whole breakup length does not depend on the valve ratio. The whole breakup length decreases with the decrease of the capillary number at the microscales, but it is independent of the capillary number at the nanoscales. In the breakup process, if the tunnel forms the pressure drop does not depend on the valve ratio. Otherwise, the pressure drop reduces linearly by increasing the valve ratio.
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