Jetting Dynamics of Viscous Droplets on Superhydrophobic Surfaces.

We investigated the dynamics of liquid jets engendered by the impact of droplets on a fractal superhydrophobic surface. Depending on the impact conditions, jets emanate from the free liquid surface with several different shapes and velocities, sometimes accompanied by droplet ejection. Experimental outcomes exhibit two different regimes: the singular jet and columnar jet. We found that droplet impacts at a lower impact velocity and low viscosity result in singular jets, attaining a maximum velocity nearly 20-fold higher than the impact velocity. The high-speed video frames reveal that the formation and subsequent collapse of the cylindrical air cavities within the droplet favor the formation of these high-speed singular jets. In contrast, the capillary wave focusing engenders columnar jets at a moderate to high impact velocity. With an increase in viscosity, singular jets are suppressed at lower impact velocities, whereas columnar jets are seen regularly. The columnar jets ascend and grow over time, feeding a bulbous mass, and subsequently the bulb separates itself from the parent jet due to capillary pinch-off phenomena. The quantitative analysis shows that columnar jets' top jet drop size varies nonmonotonically and is influenced by preceding jetting dynamics. At moderate viscosity, the drop size varies with jet velocity, following a power-law scaling. At very high viscosities, both singular and columnar jetting events are inhibited. The results are relevant to several recent technologies, including microdispensing, thermal management, and disease transmission.

Understanding Deformation and Breakup Tendency of Shear-Thinning Viscoelastic Drops in Constricted Microchannels.

The study of drop deformation in response to various stresses has long piqued the interest of several academics. The deformation behavior of cells, drug carriers, and even drug particles moving via microcapillaries inside the human body can be modeled using a viscoelastic drop model. A drop breakup study can also provide better design guidance for nanocarriers that can deliver on-demand burst drug releases at specific cancer sites. Thus, we attempted to investigate the deformation and breakup of a shear-thinning finitely extensible nonlinear elastic-peterlin (FENE-P) drop moving through the constricted microchannel. The computational simulation suggested that drop deformation and breakup can be manipulated by varying of parameters like channel confinement, Deborah number, solvent viscosity ratio, viscosity ratio, and capillary number. We attempted to find the critical capillary number for initiation of drop breakup. Observations from present study will give valuable insights into deformation and breakup patterns of drug carriers inside constricted microcapillaries. The simulations of the two-phase viscoelastic drop─Newtonian matrix system were performed on an open-source solver, Basilisk.

Magnetic-Field Mediated Active Propulsion of Ferrofluid Droplets on a Wire.

Droplet actuation on wires or fibers is highly relevant to digital microfluidics applications. Several different passive or active actuation mechanisms have been studied, including capillary pressure, thermal gradient, tilting, acoustics, and electrowetting, to name a few. However, the lack of precise control and accurate droplet positioning during its actuation on a wire limits the use of earlier methods. On the other hand, using a nonuniform magnetic field to actuate a droplet on a micrometer-size wire helps overcome the above limitations. In this context, we elucidate the motion of microliter-size ferrofluid droplets, smaller than the capillary length, in the presence of a permanent magnet using a simple yet robust experimental setup, wherein the clamshell shape droplets hang on a wire at a predetermined distance from the magnet. Beyond a critical volume, the droplet starts moving toward the magnet while exhibiting shape evolution continuously. Using a high-speed videography technique, we uncover the intricate relationship between the magnetowetting, favoring continuous shape evolution of droplets of different sizes, and their actuation dynamics (velocity) on a wire, which has scarcely been explored. The most significant contribution of this study is the detailed evaluation of the shape factor (k), relating the shape evolution of the droplet to its velocity through the contact angle hysteresis force. A theoretical framework has also been proposed, comprising different forces in action, which is found to set forth a good match with the experimental results. The results from this study are expected to open up new avenues in digital microfluidics, specifically in drug delivery, ferrobotics, and droplet logic gates, to name a few.

Magnetowetting dynamics of sessile ferrofluid droplets: a review.

The fascinating behavior of ferrofluids in a magnetic field has been intriguing researchers for many years. With the advancement in digital microfluidics, ferrofluid droplets have been extensively used in different applications ranging from biomedical to mechanical systems. Notably, the magnetic field can change the wetting dynamics of sessile ferrofluid droplets, leading to a plethora of interesting hydrodynamic phenomena. In the recent past, the spatiotemporal evolution of the droplet shape and contact line dynamics of a ferrofluid droplet in different magnetowetting scenarios has been explored widely. The relevant studies elucidate several critical aspects, such as the role of magnetic nanoparticles, carrier fluid, and the interaction of the magnetic fluid with the solid surface, among many others. Hence a systematic review of the progress made in understanding the fundamental and practical aspects of magnetowetting in the past decade (2010-2020) would be a helpful resource to the scientific community in the near future. Drawn by this motivation, an honest effort has been made in this Review to highlight the significant scientific findings concerning the sessile droplet magnetowetting phenomena within the timeline of interest. Several cutting-edge applications developed from the scientific findings in the purview of magnetowetting have also been discussed before outlining the conclusions and future areas of scope.

Transport Behavior of Commercial Anticancer Drug Protein-Bound Paclitaxel (Paclicad) in a Micron-Sized Channel.

Protein-bound paclitaxel has been developed clinically as one of the most successful chemotherapy drugs for the treatment of a wide variety of cancers. However, these medications, due to their nanoscale properties, may often induce capillary blocking while migrating through minute blood vessels. Considering the detrimental impact of this restriction, we investigated the transport of protein-bound paclitaxel, Paclicad, in a 7 µm microchannel mimicking the identical mechanical confinement of the blood capillaries. The drug was reported to migrate through a constricted microchannel without obstruction at a solution flow rate of 20-50 µL/h. The onset of an agglomeration site was observed at higher flow rates of 70-90 µL/h, while complete capillary obstruction was observed at 100 µL/h. The mobility of the particles was also calculated, and the results suggested that the presence of varying cross-sections affects the mobility of the drug particles. The trajectory of the particle migration was observed to be less tortuous at the higher flow rate, but the tortuous nature appeared to increase with the presence of agglomeration sites in the flow field. The experimental results were also compared with the computational model of the drug particle. The drug particle was modeled both as Newtonian and as an FENE-P viscoelastic drop. The drop interface tracking was done by the VOF method using the open source software Basilisk. The particle displacement was better estimated by both the FENE-P and Newtonian model at a flow rate of 30 µL/h, while deviation was observed at a flow rate of 50 µL/h. The FENE-P model was observed to show higher deformation than the Newtonian model at both flow rates. The experimental results provided better insight into the agglomeration tendency of Paclicad, migrating through a constricted microchannel at higher flow rates. The numerical model could be further employed to understand the more complex intravenous transport of drugs.

Magnetowetting dynamics of sessile ferrofluid drops on soft surfaces.

We investigate the magnetowetting behaviour of sessile ferrofluid droplets on elastomeric surfaces with different stiffness. The non-uniform magnetic field engenders deformation and splitting of the ferrofluid droplet, which is greatly influenced by the softness of the substrate. We observe that the decrease in the dynamic contact angle is maximum on the softest substrate, while the contact line remains pinned. Again, for an apparently rigid substrate, the contact radius decreases almost linearly, whereas the decrease in the contact angle appears to be lower than that of soft substrates. The contact line experiences a transition from "stick-slip" on rigid surfaces to "pinned" motion on soft surfaces, which is favoured by the formation of a large wetting ridge and smaller receding contact angle on the latter. We also find that the splitting time and splitting ratio (the ratio of the volume of the daughter droplet to that of the residual droplet) increase with an increase in the softness of the underlying substrate.

Experimental characterization of the growth dynamics during capillarity-driven droplet generation.

The transient dynamics of a growing droplet in a yarn is explored following the spatiotemporal evolution of the three-phase contact line as well as the liquid-air interface with the help of videographic techniques and subsequent image analyses. The spontaneous capillary flow of liquids in a porous network is used to generate a droplet on the freely hanging end of a yarn whose other end is dipped continuously in a liquid reservoir. The growing droplet initially moves upward due to surface tension until the attainment of a critical volume, beyond which gravity is able to pull it downward until detachment. Based upon the spatiotemporal trajectory of the three-phase contact line of the droplet, the entirety of the associated growth dynamics can be divided in three distinct regimes, namely, "radial growth," "axial growth," and "motion" stages. The transition from one to the other is governed by the subtle interplay between the capillary and the gravity forces. Several experimental fluids are considered to elucidate the effect of the fluid properties on the transient contact line and interfacial dynamics of drops. The kinetics of the three-phase contact line and the radius of the droplet is found to follow two distinct exponential scaling laws, developed through the combination of the relevant forces. A mathematical model has also been proposed to predict the critical volume of the growing droplet in relation to its final volume, beyond which gravity controls the transient dynamics.

Deciphering Hydrodynamic and Drug-Resistant Behaviors of Metastatic EMT Breast Cancer Cells Moving in a Constricted Microcapillary.

Epithelial to mesenchymal transition (EMT) induces cell migration, invasion, and drug resistance, and consequently, contributes to cancer metastasis and disease aggressiveness. This study attempted to address crucial biological parameters to correlate EMT and drug-treated cancer cells traversing through microcapillaries, reminiscent of metastatic conditions. MDA-MB-468 breast cancer cells induced to undergo EMT by treatment with 20 ng/mL of epidermal growth factor (EGF) were initially passed through several blockages and then through a constricted microchannel, mimicking the flow of invasive metastatic cells through constricted blood microcapillaries. EMT cells acquired enhanced migratory properties and retained 50% viability, even after migration through wells 10-15 µm in size and a constricted passage of 7 µm and 150 µm in length at a constant flow rate of 50 µL/h. The hydrodynamic properties revealed cellular deformation with a deformation index, average transit velocity, and entry time of 2.45, 12.3 mm/s, and 31,000 µs, respectively for a cell of average diameter 19 µm passing through one of the 7 µm constricted sections. Interestingly, cells collected at the channel outlet regained epithelial character, undergoing reverse transition (mesenchymal to epithelial transition, MET) in the absence of EGF. Remarkably, real-time polymerase chain reaction (PCR) analysis confirmed increases of 2- and 2.7-fold in the vimentin and fibronectin expression in EMT cells, respectively; however, their expression reduced to basal level in the MET cells. A scratch assay revealed the pronounced migratory nature of EMT cells compared with MET cells. Furthermore, the number of colonies formed from EMT cells and paclitaxel-treated EMT cells after passing through a constriction were found to be 95 ± 10 and 79 ± 4, respectively, confirming that the EMT cells were more drug resistant with a concomitant two-fold higher expression of the multi-drug resistance (MDR1) gene. Our results highlight the hydrodynamic and drug-evading properties of cells that have undergone an EMT, when passed through a constricted microcapillary that mimics their journey in blood circulation.

Understanding flow dynamics, viability and metastatic potency of cervical cancer (HeLa) cells through constricted microchannel.

To understand the burgeoning challenges of metastasis, a microchannel of 35 µm diameter, constricted to 7 µm for a distance of 200 µm in a total length of 3 mm, was designed and fabricated using a mask aligner made of polydimethylsiloxane (PDMS) to mimic in vivo capillaries. A thin glass cover-slide was mounted on top to monitor the motion of single or aggregated malignant HeLa cells (size 17-30 µm) microscopically through the constricted microchannel at a constant flow rate of 30 µl/h. Quantitative deconvolution of high-speed videographs of a single cell of 30 µm revealed cellular deformation while passing through constriction, having elongation index, average transit velocity and entry time of 2.67, 18 mm/s and 5.1 ms, respectively. Morphological analysis of live and apoptotic cells by dual staining with Acridine Orange/Ethidium Bromide demonstrated retention of a significant viable cell population after exit through the constriction and a viability index of 50% was quantified by dye exclusion assay. The cumulative data for microfluidic parameters, morphology and relevant metastatic MMP2 gene expression efficiency measured by real-time polymerase chain reaction revealed retention of virulence potency that could possibly cause metastasis, would be beneficial in developing futuristic MEMS device for cancer theranostics.

Cross-stream migration of drops suspended in Poiseuille flow in the presence of an electric field.

The present study focuses on the cross-stream migration of a neutrally buoyant two-dimensional drop in a Poiseuille flow in a channel under the influence of an electric field. In the absence of an electric field, the important nondimensional parameters describing this problem are the viscosity ratio (λ) between the drop fluid and the surrounding medium, the ratio of drop diameter to channel height (a^{*}), and the capillary number (Ca). The influence of all these parameters on drop migration is investigated. It is observed that a large drop moves slowly as compared to a smaller drop, but attains a steady shape at the center line of the channel. The increase in value of the capillary number enhances the cross-stream migration rate, while the increase in viscosity ratio reduces the tendency of the drops to move towards the channel center line. The presence of an electric field introduces additional interfacial stresses at the drop interface, which in turn alters the dynamics observed in the absence of an electric field. Extensive computations are carried out to analyze the combined effect of the electric field and the shear flow on the cross-stream migration of the drop. The computational results for a perfect dielectric indicate that the droplet migration enhances in the presence of an electric field. The permittivity ratio (S) and the electric field strength (E) play major roles in drop migration and deformation. Computations using the leaky dielectric model also show that for certain combinations of electrical properties the drop undergoes immense elongation along the direction of the electric field. The conductivity ratio (R) is again a vital parameter in such a system of fluids. It is further observed that for certain conditions the leaky dielectric drops exhibit rotation together with translation.

Migration of a droplet in a cylindrical tube in the creeping flow regime.

The migration of a neutrally buoyant droplet in a tube containing another immiscible liquid is investigated numerically in the creeping flow regime. A fully developed velocity profile is imposed at the inlet of the tube. The interface between the two immiscible fluids is captured using a coupled level-set and volume-of-fluid approach. The deformation and breakup dynamics of the droplet are investigated in terms of three dimensionless parameters, namely, the ratio between the radius of the undeformed droplet and the radius of the capillary tube, the viscosity ratio between the dispersed and the continuous phases, and the capillary number that measures the relative importance of the viscous force over the surface tension force. It has been observed that the droplet, while traversing through the tube, either approaches a steady bulletlike shape or develops a prominent reentrant cavity at its rear. Depending on the initial droplet size, there exists a critical capillary number for every flow configuration beyond which the drop fails to maintain a steady shape and breaks into fragments. The deformation and breakup phenomena depend primarily on the droplet size, the viscosity ratio, and the capillary number. Special attention has been given to the case where the drop diameter is comparable with the tube diameter. A thorough computational study has been conducted to find the critical capillary number for a range of droplets of varied sizes suspended in systems having different viscosity ratios.

Field induced anomalous spreading, oscillation, ejection, spinning, and breaking of oil droplets on a strongly slipping water surface.

Application of an electric field on an oil droplet floating on the surface of a deionized water bath showed interesting motions such as spreading, oscillation, and ejection. The electric field was generated by connecting a pointed platinum cathode at the top of the oil droplet and a copper anode coated with polymer at the bottom of the water layer. The experimental setup mimicked a conventional electrowetting setup with the exception that the oil was spread on a soft and deformable water isolator. While at relatively lower field intensities we observed spreading of the droplet, at intermediate field intensities the droplet oscillated around the platinum cathode, before ejecting out at a speed as high as ∼5 body lengths per second at even stronger field intensities. The experiments suggested that when the electric field was ramped up abruptly to a particular voltage, any of the spreading, oscillation, or ejection motions of the droplet could be engendered at lower, intermediate and higher field intensities, respectively. However, when the field was ramped up progressively by increasing by a definite amount of voltage per unit time, all three aforementioned motions could be generated simultaneously with the increase in the field intensity. Interestingly, when the aforementioned setup was placed on a magnet, the droplet showed a rotational motion under the influence of the Lorentz force, which was generated because of the coupling of the weak leakage current with the externally applied magnetic field. The spreading, oscillation, ejection, and rotation of the droplet were found to be functions of the oil-water interfacial tension, viscosity, and size of the oil droplet. We developed simple theoretical models to explain the experimental results obtained. Importantly, rotating at a higher speed broke the droplet into a number of smaller ones, owing to the combined influence of the spreading due to the centripetal force and the shear at the oil-water interface. While the oscillatory and rotational motions of the incompressible droplet could be employed as stirrers or impellers inside microfluidic devices for mixing applications, the droplet ejection could be employed for futuristic applications such as payload transport or drug delivery.

Wettability effects on contact line dynamics of droplet motion in an inclined channel.

The present work discusses the implications of wall wettability and inclination of the surface on droplet dynamics. In this work, mesoscopic illustration of droplet dynamics in a duct with different inclination angles, based on the two-phase lattice Boltzmann model, is reported. Temporal evolution of wetted length, wetted area, and maximum height of the droplet for surfaces with different inclination angles and wettabilities is furnished in detail in order to elucidate the droplet displacement dynamics. It has been observed that the effect of inclination of the surface on droplet dynamics is more pronounced on a hydrophobic surface as compared to a hydrophilic surface. The time evolution of height and contact line motion of the droplet shows that higher angle of inclination of substrate affects the dynamics strongly irrespective of wettability.