Three dimensional phase-field investigation of droplet formation in microfluidic flow focusing devices with experimental validation

Abstract

a b s t r a c tIn this paper, the droplet formation process at a low capillary number in a flow focusing micro-channel is studied by performing a three-dimensional phase field benchmark based on the Cahn-Hilliard NavierStokes equations and the finite element method. Dynamic moving contact line and wetting condition are considered, and generalized Navier boundary condition (GNBC) is utilized to demonstrate the dynamic motion of the interface on wall surface. It is found that the mobility parameter plays a very critical role in the squeezing and breakup process to control the shape and size of droplets. We define the characteristic mobility M c to represent the correct relaxation time of the interface. We also demonstrate that the characteristic mobility is associated with the physical process and should be kept as a constant as the product of the mobility tuning parameter χ and the square of interfacial thickness ε 2 . This criterion is applied for different interfacial thicknesses to correctly capture the physical process of droplet formation. Moreover, the size of the droplet, the velocity of the droplet along the downstream, and the period of droplet formation are compared between the numerical and experimental results which agree with each other both qualitatively and quantitatively. The presented model and criterion can be used to predict the dynamic behavior and movement of multiphase flows.

Study of imbibition in various geometries using phase field method

“…The phase field method combines Navier-Stokes equation with Cahn-Hilliard diffusion equation (Badalassi et al, 2003;Qin and Bhadeshia, 2010;Zhou et al, 2010;Bai et al, 2017;Rokhforouz and Akhlaghi Amiri, 2017):…”

“…On the other hand, it is difficult for volume-of-fluid method (Liu and Yu, 2016) to describe complex geometry on the interface and define the interfacial tension, while the evolution of a complicated free surface can be naturally followed without any special consideration for phase field method. Although phase field method is generally used for multiphase problems (Jacqmin, 1999;Yue et al, 2004;Qin and Bhadeshia, 2010;Akhlaghi Amiri and Hamouda, 2013;Bai et al, 2017), it will be shown in this paper that phase field method can be utilized to accurately solve imbibition problems and can readily accommodate various geometries. Through this research, it will be demonstrated that phase field method is a powerful tool in the study of imbibition in complex geometries.…”

Efficient Linear Schemes with Unconditional Energy Stability for the Phase Field Model of Solid-State Dewetting Problems

“…The phase field method now becomes one of the major modeling and computational tools for the study of interfacial phenomena (cf. [8,9,10,11,12,13,20,25,26]), and the references therein).…”

Discontinuous finite volume element method for a coupled Navier-Stokes-Cahn-Hilliard phase field model

“…Moreover, the presence of the energy law serves as a guide line for the design of energy stable numerical schemes. Various numerical methods have been developed and analyzed for different phase field models, such as the finite element method [3,30,35,40,45,52,54,100], finite difference method [14,16,99], spectral method [46,67,87,91,102], extended finite element method [18,32], discontinuous Galerkin finite element method [31,66,84], finite volume method [7,106], penalty-projection method [83], lattice Boltzmann method [26,107], and many others [13,50,53,63,71,77,79,80,98,105].…”