Numerical study of collision modes of multi-core compound droplets in simple shear flow

Binh D. Pham,Truong V. Vu,Cuong T. Nguyen,Hoe D. Nguyen,Vinh T. Nguyen 대한기계학회 2020 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.34 No.5

Collisions of multi-core compound droplets have generated substantial interest in recent years because of their applications in the industry and academia. This study uses the front-tracking method to simulate the transition between the two collision modes of multi-core compound droplets in a simple shear flow. Compound droplets initially assumed identical have two sub-droplets of equal size. Given the shear flow, the droplets collide with one another and behave in two main modes, namely, passing-over and reversing. In the passing-over mode, the droplets pass over one another after coming into contact. The reversing mode appears with two compound droplets returning to their initial sides after the collision. During collision, the subdroplets circulate approximately at the center of their enclosing outer droplets. Some parameters, including capillary number Ca, viscosity ratios μ io and μ mo , radius ratio R io of the subdroplets to the outer droplets, and sub-droplet angle a 0 , are investigated to determine their impact on these modes of collisions. We find that the transition from a reversing to passingover mode occurs when we increase the value of Ca from 0.01 to 0.63, R io from 0.20 to 0.475, and μ io and μ mo in the range of 0.16-6.3. However, an increase in the value of a 0 between −75 oand 90 o leads to a change from a passing-over to reversing mode. Diagrams of the colliding modes are also presented in this research.

Thermocapillary migration of a fluid compound droplet

Vinh T. Nguyen,Truong V. Vu,Phan H. Nguyen,Nang X. Ho,Binh D. Pham,Hoe D. Nguyen,Hung V. Vu 대한기계학회 2021 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.35 No.9

Compound and simple droplets have been studied and appeared in many life applications, e.g., drug processing and microfluidic systems. Many studies have been conducted on the thermocapillary effects on simple droplets, but similar studies on compound droplets are quite rare. Filling this missing gap, this paper presents the front-tracking-based simulation results of the thermocapillary effects on compound droplets in a certain limited domain. The compound droplet consists of a single inner core that is initially concentric with the outer one. Various dimensionless parameters including Reynolds number from 1 to 50, Marangoni number from 1 to 100, droplet radius ratio from 0.3 to 0.8, and viscosity ratios from 0.1 to 6.4 are varied to reveal their influences on the migration of a compound droplet from cold to hot regions. Initially, the inner droplet moves faster than the outer one, and when the leading surface of the inner droplet touches the outer one, the inner and outer droplets migrate at the same speed. The effects of these parameters on the compound droplet eccentricity are also considered.

Numerical simulation of the freezing process of a water drop attached to a cold plate

Truong V. Vu,Khoa V. Dao,Binh D. Pham 대한기계학회 2018 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.32 No.5

This paper presents a direct numerical work on the freezing process of a water drop that is either sessile on or pendant from a cold plate. The numerical technique used is an axisymmetric front-tracking method to represent interfaces that separate different phases. The sessile drop corresponds to positive Bond numbers Bo (i.e., Bo > 0), and the pendant drop represents the other values of Bo. Numerical results show that pendant drops break up into liquid drops when gravity dominates the force induced by surface tension at Bo < 0. That is, a decrease in Bo enhances the breakup of the freezing drop. The breakup also depends significantly on the initial shape of the drop in terms of the contact angle at the plate f 0 , that is, increasing f 0 induces breakup. In addition, the drop rapidly completes freezing due to breakup. In the case of non-breakup, the increase in Bo reduces the solidified drop height and decreases the time to complete solidification. The freezing process also consumes minimal time with small f 0 . The solidified drop after solidification has a cone near the axis of symmetry due to volume expansion of water upon solidification. This shape of the solidified drop is in accordance with the experimental observation.

A multi-core compound droplet passing through a diffuser channel

Dang T. Bui,Hung V. Vu,Quang D. Nguyen,Truong V. Vu 대한기계학회 2021 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.35 No.11

This study‘s aim is to improve the understanding of the dynamical behavior of a multi-core compound droplet traveling in an axisymmetric channel consisting of a diffuser element. The compound droplet typically consisting of two inner droplets distributed one after another is initially located at a certain distance from the entrance of the channel. A front-tracking method is used to handle the movement and deformation of the droplet. The numerical simulation results show that the compound droplet is stretched in the channel, and it takes a certain time,“the transit time”, to pass through the diffuser. The compound droplet has the largest deformation in the diffuser region and tends to return to its nearly original shape after leaving the diffuser. The deformation and transit time of the compound droplet are affected by some typical parameters, such as the capillary number and the diffuser angle. For small capillary numbers, the leading inner droplet takes a shorter transit time than the rear one does. The transit time also increases with an increase in the diffuser angle and the number of inner droplets enclosed in the compound droplet.

Numerical investigation of dynamic behavior of a compound drop in shear flow

Truong V. Vu,Luyen V. Vu,Binh D. Pham,Quan H. Luu 대한기계학회 2018 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.32 No.5

We present a numerical investigation of the deformation and breakup of a compound drop in shear flow. The numerical method used in this study is a two-dimensional front-tracking/finite difference technique for representing the interface separating two fluids by connected elements. The compound drop with the initially circular and concentric inner and outer fronts is placed at the center of a domain whose top and bottom boundaries move in the opposite direction. Because of the shear rate, the compound drop deforms and can break up into drops, depending on the flow conditions based on the Reynolds number Re, the Capillary number Ca and the interfacial tension ratio s 21 of the outer to inner interfaces. We vary Re in the range of 0.1-3.16, Ca in the range of 0.05-0.6 and s 21 in the range of 0.8-3.2 to reveal the transition from the non-breakup to breakup regimes. Numerical results indicate that the compound drop breaks up into drops when there's an increase in Re or Ca or a decrease in s 21 beyond the corresponding critical values. We also propose a phase diagram of Ca versus Re that shows the region in which the compound drop changes from the deformation mode to the breakup mode.

Numerical investigations of solidification around a circular cylinder under forced convection

Truong V. Vu,Anh V. Truong,Ngoc T. B. Hoang,Duong K. Tran 대한기계학회 2016 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.30 No.11

We present numerical investigations of solidification around a cooled circular cylinder in the presence of forced convection. The numerical method is based on the front-tracking/finite difference and interpolation techniques. The solidification interface is represented by connected elements that move on a fixed, rectangular grid. The no-slip and Dirichlet temperature boundary conditions are imposed by the linear interpolation. The interpolation method was first validated through comparisons of the present results with some other numerical results for flow in an annulus, flow in an enclose with a conduction solid body and flow over a heated cylinder. We then used the method to investigate the solidification process around a cold cylinder by varying various parameters such as the Reynolds number Re, the Prandtl number Pr, the Stefan number, the thermal conductivity ratio k sl , the non-dimensional temperature of the introduced liquid q 0 , and the solid-to-liquid density ratio r sl . Numerical results indicate that an increase in any of Re, Pr and q 0 results in a decrease in the area of the solidification region around the cylinder. In contrast, increasing k sl increases the region of the solid phase. Investigation on St and r slreveals that the solidification rate increases with an increase in St or a decrease in r sl . However, St and r sl have a minor effect on the final product of the solidification process.

A hybrid interface tracking – level set technique for multiphase flow with soluble surfactant

Shin, Seungwon,Chergui, Jalel,Juric, Damir,Kahouadji, Lyes,Matar, Omar K.,Craster, Richard V. Elsevier 2018 Journal of computational physics Vol.359 No.-

<P><B>Abstract</B></P> <P>A formulation for soluble surfactant transport in multiphase flows recently presented by Muradoglu and Tryggvason (JCP 274 (2014) 737–757) is adapted to the context of the Level Contour Reconstruction Method, LCRM, (Shin et al. IJNMF 60 (2009) 753–778, ) which is a hybrid method that combines the advantages of the Front-tracking and Level Set methods. Particularly close attention is paid to the formulation and numerical implementation of the surface gradients of surfactant concentration and surface tension. Various benchmark tests are performed to demonstrate the accuracy of different elements of the algorithm. To verify surfactant mass conservation, values for surfactant diffusion along the interface are compared with the exact solution for the problem of uniform expansion of a sphere. The numerical implementation of the discontinuous boundary condition for the source term in the bulk concentration is compared with the approximate solution. Surface tension forces are tested for Marangoni drop translation. Our numerical results for drop deformation in simple shear are compared with experiments and results from previous simulations. All benchmarking tests compare well with existing data thus providing confidence that the adapted LCRM formulation for surfactant advection and diffusion is accurate and effective in three-dimensional multiphase flows with a structured mesh. We also demonstrate that this approach applies easily to massively parallel simulations.</P> <P><B>Highlights</B></P> <P> <UL> <LI> Extension of the LCRM Front-tracking method (Shin et al. IJNMF 60 (2009) 753–778) to flows with surfactant. </LI> <LI> Following Muradoglu and Tryggvason (JCP 274 (2014) 737–757) surfactant transport is solved on the interface and in the bulk. </LI> <LI> Accuracy demonstrated for mass conservation, surface advection and diffusion, bulk transport and Marangoni stresses. </LI> <LI> Large scale parallel calculations of two-phase annular film flow in the counter-current flow regime. </LI> </UL> </P>

Pairwise interaction of drops in shear-thinning inelastic fluids

Sadegh Mohammadi Masiri,Morteza Bayareh,Afshin Ahmadi Nadooshan 한국유변학회 2019 Korea-Australia rheology journal Vol.31 No.1

Inelasticity effects on the migration of a drop and pairwise interaction of drops in a simple shear flow are studied using a finite-difference front-tracking method. The Carreau-Yasuda model is used to adjust the shear-thinning behavior of fluids. Results showed that drop deformation and migration rate of drops in an inelastic system are smaller than those in a Newtonian one. It was revealed that inelasticity has larger effects for the case in which Newtonian drops suspended in a non-Newtonian phase. The time of collision process is shorter for an inelastic system in comparison with the Newtonian one. For two Newtonian drops in an elastic matrix, the results demonstrated that the drops exhibit reversible cross-flow migration at high inelasticity.

PROPAGATION OF PHASE BOUNDARIES: EXISTENCE AND ADMISSIBILITY OF SOLUTIONS VIA FRONT TRACKING METHOD

AHN, Hyeung-Won,LEE, Choon-Ho 한국전산응용수학회 2006 Journal of applied mathematics & informatics Vol.20 No.1

The existence of the admissible solution for conservation laws of trilinear type occurring material sciences was proved by Abeyaratne and Knowles. LeFloch proved the existence of admissible solutions of conservation laws of this type via Glimm's method. In this paper we introduce a front tracking solution and prove the existence of the front tracking solution. We also investigate the admissibility of solutions via the Front Tracking Method.

Front Tracking 방법과 기계학습을 이용한 다상유동의 수치적 해석

박재성(Jaesung Park),김재홍(Jaehong Kim),손기헌(Gihun Son) 대한기계학회 2020 대한기계학회 춘추학술대회 Vol.2020 No.12