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See Jo Kim(sjkim1@andong.ac.kr) , Wook Ryol Hwang*

Direct numerical simulations of droplet emulsions in sliding bi-periodic frames using the level-set method. See Jo Kim(sjkim1@andong.ac.kr) , Wook Ryol Hwang* School of Mechanical Engineering, Andong National University

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See Jo Kim(sjkim1@andong.ac.kr) , Wook Ryol Hwang*

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  1. Direct numerical simulations of droplet emulsions in sliding bi-periodic framesusing the level-set method See Jo Kim(sjkim1@andong.ac.kr), Wook Ryol Hwang* School of Mechanical Engineering, Andong National University *School of Mechanical and Aerospace Engineering, Gyeongsang National University

  2. Objective Rheology and flow-induced microstructural development in droplet emulsions in viscoelastic fluids by direct numerical simulations • A large number of small drops suspended freely in a viscoelastic fluid. • Fully coupled viscoelastic flow simulation with drops under sliding bi-periodic flows. • A well-defined sliding bi-periodic domain concept with drops is necessary.

  3. 2D, Circular disk-like drops, negligible inertia. • Inertialess drops in viscoelastic fluids in a sliding bi-periodic frame under simple shear . • Sliding bi-periodic frame of simple shear flow

  4. This problem represents a regular configuration of an infinite number of such a configuration in the unbounded domain Question 1: How to find INTERFACES ? Question 2: How to apply INTERFACIAL TENSION ?

  5. Question 1: How to find INTERFACES ? • Interface Tracking – Mesh Moves with Interface: Deformation characteristics of spherical bubble collapse in Newtonian fluids near the wall using the Finite Element Method with ALE formulation

  6. Andong National University Advanced Material Processing Lab. • Bowyer-Waston Algorithm

  7. Andong National University Advanced Material Processing Lab.

  8. Andong National University Advanced Material Processing Lab. Boundary Mark Node number : 437, element number : 814.

  9. (a) Show Number of Node (b) Show Number of Element (c) Show Number of Material Andong National University Advanced Material Processing Lab. • Mesh Generation for Two-Phase Fluid Systems • Graphic Display by OpenGL

  10. N T R Liquid Droplet Interfacial Boundary Conditions by Interface Tracking Normal Stress Balance : Shear Stress Balance : Local Mean Curvature:

  11. Question 1: How to find INTERFACES ? • Interface Capturing – Fixed Meshes across Interface: VOF: Diffuse Interface: Level Set Method:

  12. Interface Capturing by Level Set Method. Interface capturing based on a fixed mesh. Evolution Equation of the interface in terms of Level Set Function.

  13. Interfacial Boundary Conditions by Interface Capturing Continuum Surface Force (CSF): • Interfacial tension is treated as a body force Continuum Surface Stress (CSS): • Interfacial tension is treated as an additional stress

  14. Governing Equations Computational Domain (Oldroyd-B) • B.C. on computational domain Γ : • (Sliding bi-periodic frame constraints)

  15. Finite Element Formulation • Modification of combined weak formulation of Glowinski et al for right-ring • description of particles and sliding bi-periodic frame constraints • Both fluid and particle domains are described by the fluid problem; • 2. Force-free, torque-free, rigid-body motion is satisfied weakly with the constraint • on the particle boundary only; • Sliding bi-periodicity is applied weakly through the constraints of the sliding • bi-periodic frame; • The weak form has been coupled with the DEVSS/DG scheme to solve • emulsions in a viscoelastic fluid. • The weak form has been coupled with the DG scheme to solve • the Level set function.

  16. A single particle of radius r=0.2 in a sliding bi-periodic frame of size 1 x 1 in a • Newtonian fluid with • Regular configuration of an infinite number of drops of the same size in an • unbounded domain • Drops do not translate, but rotate with deformation. • Good example for study of rheology of emulsion. A Single Drop in Newtonian Fluid

  17. The pressure contour and streamline • Convergence to steady shape of deformed drop

  18. Distance function and drop deformation

  19. Time-dependent bulk suspension properties • Convergence to steady oscillation • bulk normal stress is zero for Particle-Newtonian medium system • bulk normal stress is not zero for Drop-Newtonian medium system • possibility of viscoelastic effects even for Drop-Newtonian medium system

  20. Two symmetrically located particles of radius 0.2 in a sliding bi-periodic frame Of size 1 x 1 in a Newtonian fluid with Two Drops in Newtonian Fluid

  21. Distance function and drop deformation

  22. Multiple Droplets in Newtonian Fluid

  23. Conclusions 1. Direct numerical methods of drop emulsions in a viscoelastic fluid has been developed and implemented. 2. Incorporation with the Level set scheme for interfacial tension of droplet. 3. Deformation phenomena were observed for a single droplet, and multiple droplets. 4. Bulk normal stress is not zero for Drop-Newtonian medium system.

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