Microchannels with curved geometries have been employed for many applications in microfluidic devices in the past decades. The Dean vortices generated in such geometries have been manipulated using different methods to enhance the performance of devices in applications such as mixing, droplet sorting, and particle/cell separation. Understanding the effect of the manipulation method on the Dean vortices in different geometries can provide crucial information to be employed in designing high-efficiency microfluidic devices. In this review, the physics of Dean vortices and the affecting parameters are summarized. Various Dean number calculation methods are collected and represented to minimize the misinterpretation of published information due to the lack of a unified defining formula for the Dean dimensionless number. Consequently, all Dean number values reported in the references are recalculated to the most common method to facilitate comprehension of the phenomena. Based on the converted information gathered from previous numerical and experimental studies, it is concluded that the length of the channel and the channel pathline, e.g., spiral, serpentine, or helix, also affect the flow state. This review also provides a detailed summery on the effect of other geometric parameters, such as cross-section shape, aspect ratio, and radius of curvature, on the Dean vortices\' number and arrangement. Finally, considering the importance of droplet microfluidics, the effect of curved geometry on the shape, trajectory, and internal flow organization of the droplets passing through a curved channel has been reviewed.

OBJECTIVE: Immiscible liquids are commonly used to achieve unique functions in many applications, where the breakup of compound droplets in airflow is an important process. Due to the existence of the liquid-liquid interface, compound droplets are expected to form different deformation and breakup morphologies compared with single-component droplets.
METHODS: We investigate experimentally the deformation and breakup of compound droplets in airflow. The deformation characteristics of compound droplets are quantitatively analyzed and compared with single-component droplets. Theoretical models are proposed to analyze the transition between breakup morphologies.
RESULTS: The breakup modes of compound droplets are classified into shell retraction, shell breakup, and core-shell breakup based on the location where the breakup occurs. The comparison with single-component droplets reveals that the compound droplet is stretched more in the flow direction and expands less in the cross-flow direction, and these differences occur when the core of the compound droplet protrudes into the airflow. The transition conditions between different breakup modes are obtained theoretically. In addition, the eccentricity of the compound droplet can lead to the formation of the thick ligament or the two stamens in the droplet middle.

The effects of surface wettability and viscoelasticity on the dynamics of liquid droplets under an electric field are studied experimentally. A needle-plate electrode system is used as the power source to polarize a dielectric plate by the corona discharge emitted at the needle electrode, creating a new type of steerable electric field realized. The dynamics of droplets between the dielectric plate and a conductive substrate include three different phenomena: equilibrium to a stationary shape on substrates with higher wettability, deformation to form a bridge between the top acrylic plate and take-off on the substrates with lower wettability. Viscoelastic droplets differ from water in the liquid bridge and takeoff phenomena in that thin liquid filaments appear in viscoelastic droplets, not observed for Newtonian droplets. The equilibrated droplet exhibits more pronounced heights for Newtonian droplets compared to viscoelastic droplets, with a decrease in height with the increase in the concentration of the elastic constituent in the aqueous solution. In the take-off phenomenon, the time required for the droplet to contact the upper plate decreases with the concentration of the elastic constituent increases. It is also found that the critical voltage required for the take-off phenomenon to occur decreases as the elasticity increases.

OBJECTIVE: A conducting droplet suspended in an insulating continuous phase, e.g. an aqueous electrolyte in an oil, is deformed by an applied electric field to nonspherical equilibrium shapes, and can even break-up under strong fields. Many technologies use electro-deformation to manipulate fluid dispersions, with surfactants present on the droplet interfaces forming stabilizing monolayers. While surfactants lower the interface tension which facilitates electro-deformation, the monolayer elasticity resists deformation. High molecular weight surfactants, with large dilatational viscosities, can potentially retard the deformation dynamics.
UNASSIGNED: A boundary integral method simulates the dynamic interfacial deformation of a perfectly conducting droplet in a dielectric in a uniform field. The interface contains an insoluble monolayer which is a Newtonian fluid with constant dilatational viscosity obeying a Langmuir state equation. A range of initial surfactant surface concentrations are studied, with elasticity proportional to concentration.
RESULTS: Equilibrium drop deformations, unaffected by surface viscosity, are strongly resisted by elasticity at high surface concentrations, and field strengths necessary for break-up increase with elasticity. Dilatational viscosity scales with the ratio, κ∗, the surface viscosity (divided by the droplet radius) to the bulk viscosity, and can extend the deformation time. Extended times are described by a time rescaling proportional to κ∗.

Controlled droplet manipulation by light has tremendous technological potential. We report here a method based on photothermally induced pyroelectric effects that enables manipulation and maneuvering of a water droplet on a superhydrophobic surface fabricated on lithium tantalite (LiTaO3). In particular, we demonstrate that the pyroelectric charge distribution has an essential role in this process. Evenly distributed charges promote a rapid hydrophobic to hydrophilic transition featuring a very large water contact angle (WCA) change of ∼76.5° in air. This process becomes fully reversible in silicone oil. In contrast, the localized charge distribution induced by guided laser illumination leads to very different and versatile functionalities, including droplet shape control and motion manipulation. The influence of a saline solution is also investigated and compared to the deionized water droplet. The focusing effect of the water droplet, a phenomenon that widely exists in nature, is particularly of interest. Simple tuning of the laser incident angle results in droplet deformation, jetting, splitting, and guided motion. Potential applications, such as droplet pinning and transfer, are presented. This approach offers a wide range of versatile functionalities and ready controllability, including contactless, electrodeless, and precise spatial and fast temporal control, with tremendous potential for applications requiring remote droplet control.

Droplet microfluidics provides a versatile tool for measuring interfacial tensions between two immiscible fluids owing to its abilities of fast response, enhanced throughput, portability and easy manipulations of fluid compositions, comparing to conventional techniques. Purely homogeneous extension in the microfluidic device is desirable to measure the interfacial tension because the flow field enables symmetric droplet deformation along the outflow direction. To do so, we designed a microfluidic device consisting of a droplet production region to first generate emulsion droplets at a flow-focusing area. The droplets are then trapped at a stagnation point in the cross junction area, subsequently being stretched along the outflow direction under the extensional flow. These droplets in the device are either confined or unconfined in the channel walls depending on the channel height, which yields different droplet deformations. To calculate the interfacial tension for confined and unconfined droplet cases, quasi-static 2D Darcy approximation model and quasi-static 3D small deformation model are used. For the confined droplet case under the extensional flow, an effective viscosity of the two immiscible fluids, accounting for the viscosity ratio of continuous and dispersed phases, captures the droplet deformation well. However, the 2D model is limited to the case where the droplet is confined in the channel walls and deforms two-dimensionally. For the unconfined droplet case, the 3D model provides more robust estimates than the 2D model. We demonstrate that both 2D and 3D models provide good interfacial tension measurements under quasi-static extensional flows in comparison with the conventional pendant drop method.

The deformation and breakup of a polymer solution droplet plays a key role in inkjet printing technology, tablet-coating process, and other spray processes. In this study, the bag breakup behavior of the polymer droplet is investigated numerically. The simple coupled level set and volume of fluid (S-CLSVOF) method and the adaptive mesh refinement (AMR) technique are employed in the droplet breakup cases at different Weber numbers and Ohnesorge numbers. The nature of the polymer solution is handled using Herschel-Bulkley constitutive equations to describe the shear-thinning behavior. Breakup processes, external flow fields, deformation characteristics, energy evolutions, and drag coefficients are analyzed in detail. For the bag breakup of polymer droplets, the liquid bag will form an obvious reticular structure, which is very different from the breakup of a Newtonian fluid. It is found that when the aerodynamic force is dominant, the increase of the droplet viscous force will prolong the breakup time, but has little effect on the final kinetic energy of the droplet. Moreover, considering the large deformation of the droplet in the gas flow, a new formula with the cross-diameter (Dcro) is introduced to modify the droplet drag coefficient.

Microelectromechanical system (MEMS) liquid sensors may be used under large acceleration conditions. It is important to understand the deformation of the liquid droplets under acceleration for the design and applications of MEMS liquid sensors, as this will affect the performance of the sensors. This paper presents an investigation into the deformation of a mercury droplet in a liquid MEMS sensor under accelerations and reports the relationship between the deformation and the accelerations. The Laminar level set method was used in the numerical process. The geometric model consisted of a mercury droplet of 2 mm in diameter and an annular groove of 2.5 mm in width and 2.5 mm in height. The direction of the acceleration causing the droplet to deform is perpendicular to the direction of gravity. Fabrication and acceleration experiments were conducted. The deformation of the liquid was recorded using a high-speed camera. Both the simulation and experimental results show that the characteristic height of the droplets decreases as the acceleration increases. At an acceleration of 10 m/s2, the height of the droplet is reduced from 2 to 1.658 mm, and at 600 m/s2 the height is further reduced to 0.246 mm. The study finds that the droplet can deform into a flat shape but does not break even at 600 m/s2. Besides, the properties of the material in the domain surrounding the droplet and the contact angle also affect the deformation of the droplet. This work demonstrates the deformation of the liquid metal droplets under acceleration and provides the basis for the design of MEMS droplet acceleration sensors.

We have developed a gene transfection method called water-in-oil droplet electroporation (EP) that uses a dielectric oil and a liquid droplet containing live cells and exogenous DNA. When a cell suspension droplet is placed between a pair of electrodes, an intense DC electric field can induce droplet deformation, resulting in an instantaneous short circuit caused by the droplet elongating and contacting the two electrodes simultaneously. Small transient pores are generated in the cell membrane during the short, allowing the introduction of exogenous DNA into the cells. The droplet EP was characterized by varying the following experimental parameters: applied voltage, number of short circuits, type of medium (electric conductivity), concentration of exogenous DNA, and size of the droplet. In addition, the formation of transient pores in the cell membrane during droplet EP and the transfection efficiency were evaluated.