Abstract
Introduction: Compound fluid filaments appear in many applications, e.g., drug delivery and processing or microfluidic systems. This paper focuses on the numerical simulation of an incompressible, immiscible, and Newtonian fluid for the contraction process of a fluid compound filament by solving the Navier-Stokes equations. The front-tracking method is used to solve this problem, which uses connected segments (Lagrangian grid) that move on a fixed grid (Eulerian grid) to represent the interface between the liquids.
 Methods: The interface points are advected by the velocity interpolated from those of the fixed grid using the area weighting function. The coordinates of the interface points are used to construct the indicators specifying the different fluids and compute the interfacial tension force.
 Results: The simulation results show that under the effects of the interfacial tension, the capsuleshaped filament can transform into a spherical compound droplet (i.e., non-breakup) or can break up into smaller spherical compound and simple droplets (i.e., breakup). When the density ratio of the outer to middle fluids increases, the filament changes from non-breakup to breakup upon contraction.
 Conclusion: Increasing the density ratio enhances the breakup of the compound filament during contraction. The breakup is also promoted by increasing the initial length of the filament.
Highlights
Compound fluid filaments appear in many applications, e.g., drug delivery and processing or microfluidic systems
A typical grid resolution of 192×576 grid for a domain W×H = 4Ro× 12Ro is used in the simulation model to perform aspect ratio of the outer filament (Aro) = 10. Such a grid solution is selected through a grid refinement study, and it is found that the 192×576 grid gives results without variance in the compound fluid filament shape as compared to those obtained using finer grids
It is clear that increasing the density ratio ρom and increasing the initial length of the filament promote the breakup of the compound filament upon contraction
Summary
Compound droplets have been used in various applications, such as drug distribution, 1 microfluidic system, 2 food processing technology, 3 etc. 9 The initial conditions of the problem are significantly important, depending on the surface tension of the interface separating different fluids, the properties of the fluids such as viscosity and density. Two considered parameters for the deformation and breakup of fluid compound filament include the density ratio between the outer fluid and the middle fluid and the initial aspect ratio of the filament. This is a new problem that has not been explored in the literature. Instead of solving the density directly, we first move the interface between the different fluids and reconstruct indicator functions from its position Using these indicator functions is to specify the material properties at every location in the domain. Μim denoting the viscosity ratios, and σio denoting interfacial tension ratio between inner and outer filaments
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