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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.

Compound droplets with different sizes are increasingly used in industrial production and academic research. This study aims to improve understanding of the dynamical behaviors of the compound droplet moving in microchannels. The compound droplet consisting of one inner core is initially concentric and placed at the entrance of a circular channel with a cone at the downstream region. Following this primary channel is a secondary channel that is circular and straight. Manipulation of the droplet is assisted by a flow introduced via the gap between two channels. The numerical results show that when passing through these confined channels, the droplet experiences a finite deformation or breakup mode. In each mode, the deformation or breakup of the compound droplet is also different when changing the values of the parameters including the capillary number, the ratio of the droplet radii, the ratio of the interfacial tension, the size of the secondary channel, the gap size and the cone angle. The finitely deformed droplet can be either nearly ellipsoidal with a deformation index D of around unity (i.e., first deformation mode) or highly elongated with a high D (i.e., second deformation mode). Breakup of the compound droplet happens to the outer droplet, and the breakup point is located either in front of the inner droplet (i.e., first breakup mode) or behind it (i.e., second breakup mode). The simple droplets yielded in the first breakup mode has a higher total volume than those in the second breakup mode. It is found that the droplet experiences the first deformation mode to the first breakup mode, then the second deformation mode and finally the second breakup mode when Ca increases. The regime diagrams of these modes, based on these parameters, are also presented.

A compound droplet deforming in a constricted tube widely appears in drug delivery and microfluidic devices. In such a constriction, an indentation can present at the trailing surface of the droplet. However, this aspect has not been fully investigated and understood so far. This study focuses on the effects of some dimensionless parameters on the negative curvature, i.e., indentation, at the trailing surface of a compound droplet moving through a constricted tube. The presence of the constriction at the middle of the tube length enhances the droplet indentation. Numerical results were obtained for the capillary number Ca (varied in range of 0.1–1.0), the inner-to-outer droplet radius ratio R21 (varied in range of 0.2–0.9), the droplet-to-tube radius ratio R10 (varied in range of 0.2–0.9), the inner-to-outer interfacial tension coefficient ratio σ21 (varied in range of 0.1–6.4), and the normalized depth of the constriction d/R (varied in range of 0.0–0.8). The results reveal that the most influencing factor is Ca, increasing its value leads to the increment of the maximum indentation at the trailing surface of the inner and outer droplets. The indentation is also increased with increasing the value of R10 and d/R. In contrast, increasing R21 results in a decrease in the indentation at the trailing surface of the outer droplet. When increasing σ21, the indentation at the trailing surface of the inner one is quickly suppressed, while the outer droplet is minorly affected. We also point out the patterns of the trailing surface of the inner and outer droplets and their transitions from one to the other patterns in the diagrams based on these parameters.

This paper presents the results of numerical simulations of the coalescence and solidification of two hollow droplets. A base droplet (i.e., a pre-solidified droplet) stays on a supercool surface that causes its shell liquid to solidify. An incoming droplet then flows toward and coalesces with the base droplet. After coalescence of the droplets, the two hollow cores can coalesce depending on the momentum of the incoming hollow core and the solidification rate. A high solidification rate corresponding to a high Stefan number St prevents the hollow cores from coalescing and thus induces a discrete hollow-core solidified product, whereas a low St number results in a coalesced hollow-core (CH) droplet. However, the coalescence of two droplets and/or their hollow cores does not affect the apex at the top of the final solidified droplet, which is created by volume expansion upon phase change. Some other parameters including the Peclet number Pe, the Weber number We, the size Ris of the incoming inner core, the position Hs of the incoming droplet and the number of cores Ni of the incoming droplet also affect the coalescence and phase transition of the droplets. It is found that transition from a CH region to a discrete hollow-core region occurs for lower Pe, Ris, or Ni. In contrast, decreasing the value of We or Hs enhances the CH region. Moreover, we provide regime diagrams based on the supercooling degree, the Peclet number, and the size of the inner core of the incoming droplet.

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.

In this study, we present the three-phase numerical simulation results of an axisymmetric compound drop solidifying on a cold plate by the front-tracking method. The compound drop initially has a hemispherical shape with a concentric inner gas core (i.e. gas bubble). The temperature of the plate is lower than the fusion temperature of the shell liquid and thus causes the shell liquid to solidify from the plate surface. It is found that the solid-liquid interface propagates parallelly to the plate during the initial stage of solidification. Then, the region near the outer interface moves faster than that near the inner gas core does. The solidification process completes around the inner core first, and the drop top is the last region to be solidified. Accordingly, a break point is available on the temporal variation of the average height of the solid-liquid interface. Besides, in the presence of volume expansion, the solidified compound drop also has an apex at the top. The numerical results show that the presence of the inner gas bubble prolongs the solidification time. We also find that varying the Stefan number St (in the range of 0.032 – 1.0) or the Bond number Bo (in the range of 0.18 – 3.2) has a minor effect on the inner gas core after complete solidification even though the solidification time decreases with an increase in St or Bo. The effects of the Prandtl number and volume change on the final product of the solidification process are also considered.

Droplets resulting from liquid filament contraction have been widely used in industrial processes. However, detailed investigations of liquid compound filament contraction processes are lacking in the literature. Therefore, this study provides a numerical investigation of the contraction of a two-layered compound filament. The simulations are based on an axisymmetric front-tracking method. It is found that because of the interfacial tension force, the initially long cylindrical filament contracts to a compound droplet without any breakup or breaks up into smaller droplets during contraction. Unlike simple filaments, the presence of the inner filament inside the compound filament results in a more complicated compound filament breakup process with various droplet types, e.g., simple droplets, single-core compound droplets, and multi-core compound droplets. We find that the inner filament breaks up into droplets, while the outer does not induce breakup. Such a breakup mode produces a multi-core compound droplet after contraction. In some cases, while the inner filament only contracts to a single droplet, its enclosing filament breaks up to produce simple droplets at each end. We also find a breakup mode that combines these two modes, where both the inner and outer filaments perform breakup. In addition, the breakup of the compound filament occurs via one of two mechanisms: end-pinching and necking. These breakup modes and mechanisms are affected by various parameters such as the inner and outer aspect ratios, the Ohnesorge number, the interfacial tension ratio, and the viscosity ratios. Based on these parameters, various regime diagrams of breakup and non-breakup are proposed.

The rheological behaviors of a compound droplet in a confined geometry are of importance in many industrial and natural processes. However, a detailed numerical simulation of the finite deformation and its transition to the breakup of the multi-core compound droplet in an axisymmetric T-junction channel is still lacking. The present study is to fill this gap through the numerical simulations of a two-core compound droplet that deforms and breaks up in this channel configuration. The numerical results are obtained by the axisymmetric front-tracking method. Our new finding is that the compound droplet in the channel can experience the finite deformation or the breakup depending on the flow condition or the configuration of the channel. In the finite deformation mode (i.e. non-breakup mode), the droplet rapidly reaches the maximum deformation before approaching the perpendicular rigid wall. The most deformation occurs with the outer droplet, and the inner droplet closer to the wall is less deformed than the other inner core droplet. In the breakup mode, three breakup patterns are recognized: (i) breakup type I occurring when breaking up only the outer droplet; (ii) breakup type 2 occurring when breaking up only the inner droplets; (iii) breakup type 3 occurring when breaking up both inner and outer droplets. The transition from the non-breakup mode to the breakup mode is available when increasing the Reynolds number Re (from 0.16 to 40.0), the capillary number Ca (from 0.04 to 4.0), the size Ro of the outer droplet and the middle-to-outer fluid viscosity ratio μ21, or decreasing the size Ri of the inner droplets, the radial size C2 of the channel (normalized by the channel axial size C1) and the interfacial tension ratio of the inner to the outer droplets. The transition diagrams based on some of these parameters are also proposed to provide a more complete picture of the two-core compound droplet behaving in the axisymmetric T-junction channel. .