External-field-induced directional droplet transport: A review.

It has been recently shown that small-volume droplets on lubricant-infused surfaces (LISs) can be analytically modeled using rotationally symmetric constant mean curvature (CMC) surfaces. While such an approach is available for noncloaked droplets, a similar approach is missing for cloaked droplets that are ubiquitous in a number of LIS-related applications. The presence of a thin cloaking film on the top spherical cap portion and its gradual transition to a bulk meniscus remain unaddressed for its implications on the interfacial profile of cloaked droplets. Here, we take into account the cloaking film tension and the disjoining pressure to present a mean curvature-based framework for modeling cloaked droplets on LISs. The transition of the bulk meniscus to a thin film is formulated as a transition regime, which is then modeled as a single imaginary point akin to the Neumann point of noncloaked droplets. We next show that the shape of a small droplet on a LIS essentially obeys a simple fundamental mean curvature relation that changes forms depending on the regimes of lubrication and whether the droplet is cloaked or noncloaked. We validate our framework with the droplet profiles recorded during the evaporation of cloaked droplets in our experiments, as well as those published in the literature. In addition, we also demonstrate the ability to model the shapes of floating droplets on LISs reported in the literature. In addition to quantifying the effect of disjoining pressure on interfacial profiles, we importantly unmask the behavior of the contact line, which is optically covered by the lubricant meniscus around the droplets on LISs.

Cloaked Droplets on Lubricant-Infused Surfaces: Union of Constant Mean Curvature Interfaces Dictated by Thin-Film Tension.

The manipulation of aqueous droplets has a profound significance in biochemical assays. Magnetic field-driven droplet manipulation, offering unique advantages, is consequently gaining attention. However, the phenomenon relating to diamagnetic droplets is not well understood. Here, we report the understanding of trapping and coalescence of flowing diamagnetic aqueous droplets in a paramagnetic (oil-based ferrofluid) medium using negative magnetophoresis. Our study revealed that the trapping phenomenon is underpinned by the interplay of magnetic energy (Em) and frictional (viscous) energy (Ef), in terms of magnetophoretic stability number, Sm = (Em/Ef). The trapping and nontrapping regimes are characterized based on the peak value of magnetophoretic stability number, Smp, and droplet size, D*. The study of coalescence of a trapped droplet with a follower droplet (and a train of droplets) revealed that the film-drainage Reynolds number (Refd) representing the coalescence time depends on the magnetic Bond number, Bom. The coalesced droplet continues to remain trapped or gets self-released obeying the Smp and D* criterion. Our study offers an understanding of the magnetic manipulation of diamagnetic aqueous droplets that can potentially be used for biochemical assays in microfluidics.

Trapping and Coalescence of Diamagnetic Aqueous Droplets Using Negative Magnetophoresis.

In this work, the localized photothermal effect of a focused infrared laser-induced migration and coalescence of the droplets in a microchannel was visually studied. Experimental results showed tha...

Droplet Migration and Coalescence in a Microchannel Induced by the Photothermal Effect of a Focused Infrared Laser

Biofabrication technologies are of importance for the construction of organ models and functional tissue replacements. Microfluidic manipulation, a promising biofabrication technique with micro-scale resolution, can not only help to realize the fabrication of specific microsized structures but also build biomimetic microenvironments for biofabricated tissues. Therefore, microfluidic manipulation has attracted attention from researchers in the manipulation of particles and cells, biochemical analysis, tissue engineering, disease diagnostics, and drug discovery. Herein, biofabrication based on microfluidic manipulation technology is reviewed. The application of microfluidic manipulation technology in the manufacturing of biomaterials and biostructures with different dimensions and the control of the microenvironment is summarized. Finally, current challenges are discussed and a prospect of microfluidic manipulation technology is given. The authors hope this review can provide an overview of microfluidic manipulation technologies used in biofabrication and thus steer the current efforts in this field.

Fabrication of Biomaterials and Biostructures Based On Microfluidic Manipulation.

Manipulation of aqueous droplets in microchannels has great significance in various emerging applications such as biological and chemical assays. Magnetic-field based droplet manipulation that offers unique advantages is consequently gaining attention. However, the physics of magnetic field-driven cross-stream migration and the coalescence of aqueous droplets with an aqueous stream are not well understood. Here, we unravel the mechanism of cross-stream migration and the coalescence of aqueous droplets flowing in an oil based ferrofluid with a coflowing aqueous stream in the presence of a magnetic field. Our study reveals that the migration phenomenon is governed by the advection (τa) and magnetophoretic (τm) time scales. Experimental data show that the dimensionless equilibrium cross-stream migration distance δ* and the length Lδ* required to attain equilibrium cross-stream migration depend on the Strouhal number, St = (τa/τm), as δ* = 1.1 St0.33 and Lδ*=5.3 St−0.50, respectively. We find that the droplet-stream coalescence phenomenon is underpinned by the ratio of the sum of magnetophoretic (τm) and film-drainage time scales (τfd) and the advection time scale (τa), expressed in terms of the Strouhal number (St) and the film-drainage Reynolds number (Refd) as ξ = (τm + τfd)/τa = (St−1 + Refd). Irrespective of the flow rates of the coflowing streams, droplet size, and magnetic field, our study shows that droplet-stream coalescence is achieved for ξ ≤ 50 and ferrofluid stream width ratio w* < 0.7. We utilize the phenomenon and demonstrated the extraction of microparticles and HeLa cells from aqueous droplets to an aqueous stream.

Cross-stream migration and coalescence of droplets in a microchannel co-flow using magnetophoresis

Handling and manipulation of particle-encapsulating droplets (PED) have profound applications in biochemical assays. Herein we report encapsulation of microparticles in aqueous ferrofluid droplets in a primary continuous phase (CP) and sorting of PED from empty droplets (ED) at the interface of the CP in coflow with a second continuous phase using a magnetic field. We find that the encapsulation process results in a size contrast between the PED and ED that depends on the flow regime – squeezing, dripping, or jetting – which in turn is governed by the ratio of the discrete phase to the continuous phase capillary number, Car. The difference between the volume fractions of ferrofluid in the PED and ED, ΔαPED, is utilized for sorting, and is found to depend on the ratio of the capillary numbers, Car. The difference ΔαPED is found to be maximum in the jetting regime, suggesting that the jetting regime is most suitable for encapsulation and sorting. The sorting criterion is represented in terms of a parameter ξ, which is a function of the ratios of the magnetic force to the interfacial force experienced by the PED and ED. Our study revealed that sorting is possible for ξ 0.25. The maximum sorting efficiency of our system is found to be ∼95% at a throughput of ∼100 drops per s.

Particle encapsulation in aqueous ferrofluid drops and sorting of particle-encapsulating drops from empty drops using a magnetic field.

We show that adjacent liquid droplets exhibit long-range attraction and repulsion on an immiscible liquid impregnating a surface when either the drop or the impregnating liquid is volatile. Remarka...

S. K. Jain

Papers

Cross-stream migration and coalescence of droplets in a microchannel co-flow using magnetophoresis

Particle encapsulation in aqueous ferrofluid drops and sorting of particle-encapsulating drops from empty drops using a magnetic field.

Attraction and Repulsion between Liquid Droplets over a Liquid-Impregnated Surface.