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Register a new userUniversality in microdroplet nucleation during solvent exchange in Hele-Shaw like channels
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Micro and nanodroplets have many important applications such as in drug delivery, liquid-liquid extraction, nanomaterial synthesis and cosmetics. A commonly used method to generate a large number of micro or nanodroplets in one simple step is solvent exchange (also called nanoprecipitation), in which a good solvent of the droplet phase is displaced by a poor one, generating an oversaturation pulse that leads to droplet nucleation. Despite its crucial importance, the droplet growth resulting from the oversaturation pulse in this ternary system is still poorly understood. We experimentally and theoretically study this growth in Hele-Shaw like channels by measuring the total volume of the oil droplets that nucleates out of it. In order to prevent the oversaturated oil from exiting the channel, we decorated some of the channels with a porous region in the middle. Solvent exchange is performed with various solution compositions, flow rates and channel geometries, and the measured droplets volume is found to increase with the Peclet number $Pe$ with an approximate effective power law $Vpropto Pe^{0.50}$. A theoretical model is developed to account for this finding. With this model we can indeed explain the $Vpropto Pe^{1/2}$ scaling, including the prefactor, which can collapse all data of the porous channels onto one universal curve, irrespective of channel geometry and composition of the mixtures. Our work provides a macroscopic approach to this bottom-up method of droplet generation and may guide further studies on oversaturation and nucleation in ternary systems.
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Solvent exchange (also called solvent shifting or Ouzo effect) is a generally used bottom-up process to mass-produce nanoscale droplets. In this process, a good solvent for some oil is displaced by a poor one, leading to oil nanodroplet nucleation and subsequent growth. Here we perform this process on a hydrophobic substrate so that sessile droplets so-called surface nanodroplets-develop, following the work of Zhang et al. [Zhang, X.; Lu, Z.; Tan, H.; Bao, L.; He, Y.; Sun, C.; Lohse, D. Proc. Natl. Acad. Sci. U.S.A. 2015, 122, 9253-9257]. In contrast to what was done in that paper, we chose a very well-controlled Hele-Shaw geometry with negligible gravitational effects, injecting the poor solvent in the center of the Hele-Shaw cell, and characterize the emerging nanodroplets as a function of radial distance and flow rates. We find that the mean droplet volume per area <Vol>_area strongly depends on the local Peclet number Pe and follows a universal scaling law <Vol>_area~Pe^(3/4). Moreover, the probability distribution function of the droplet volume strongly depends on the local Pe as well, regardless of the flow rates and radial distance, giving strong support to the theoretical model of the solvent exchange process developed in Zhang et al.s work.
Water vapor condensation is common in nature and widely used in industrial applications, including water harvesting, power generation, and desalination. As compared to traditional filmwise condensation, dropwise condensation on lubricant-infused surfaces (LIS) can lead to an order-of-magnitude increase in heat transfer rates. Small droplets (with the diameter below 100 $mu$m) account for nearly 85 percent of the total heat transfer and droplet sweeping plays a crucial role in clearing nucleation sites, allowing for frequent re-nucleation. Here, we focus on the dynamic interplay of microdroplets with the thin lubricant film during water vapor condensation on LIS. Coupling high-speed imaging, optical microscopy, and interferometry, we show that the initially uniform lubricant film re-distributes during condensation. Governed by lubricant height gradients, microdroplets as small as 2 $mu$m in diameter undergo rigorous and gravity-independent self-propulsion, travelling distances multiples of their diameters at velocities up to 1100 $mu$m/s. Although macroscopically the movement appears to be random, we show that on a microscopic level capillary attraction due to asymmetrical lubricant menisci causes this gravity-independent droplet motion. Based on a lateral force balance analysis, we quantitatively find that the sliding velocity initially increases during movement, but decreases sharply at shorter inter-droplet spacing. The maximum sliding velocity is inversely proportional to the oil viscosity and is strongly dependent of the droplet size, which is in excellent agreement with the experimental observations. This novel and non-traditional droplet movement is expected to significantly enhance the sweeping efficiency during dropwise condensation, leading to higher nucleation and heat transfer rates.
We study microfluidic self digitization in Hele-Shaw cells using pancake droplets anchored to surface tension traps. We show that above a critical flow rate, large anchored droplets break up to form two daughter droplets, one of which remains in the anchor. Below the critical flow velocity for breakup the shape of the anchored drop is given by an elastica equation that depends on the capillary number of the outer fluid. As the velocity crosses the critical value, the equation stops admitting a solution that satisfies the boundary conditions; the drop breaks up in spite of the neck still having finite width. A similar breaking event also takes place between the holes of an array of anchors, which we use to produce a 2D array of stationary drops in situ.
We present an analytical study, validated by numerical simulations, of electroosmotic flow in a Hele-Shaw cell with non-uniform surface charge patterning. Applying the lubrication approximation and assuming thin electric double layer, we obtain a pair of uncoupled Poisson equations which relate the pressure and the stream function, respectively, to gradients in the zeta potential distribution parallel and perpendicular to the applied electric field. We solve the governing equations for the fundamental case of a disk with uniform zeta potential and show that the flow-field in the outer region takes the form of a pure dipole. We illustrate the ability to generate complex flow-fields around smooth convex regions by superposition of such disks with uniform zeta potential and a uniform pressure driven flow. This method may be useful for future on-chip devices, allowing flow control without the need for mechanical components.
The flow in a Hele-Shaw cell with a time-increasing gap poses a unique shrinking interface problem. When the upper plate of the cell is lifted perpendicularly at a prescribed speed, the exterior less viscous fluid penetrates the interior more viscous fluid, which generates complex, time-dependent interfacial patterns through the Saffman-Taylor instability. The pattern formation process sensitively depends on the lifting speed and is still not fully understood. For some lifting speeds, such as linear or exponential speed, the instability is transient and the interface eventually shrinks as a circle. However, linear stability analysis suggests there exist shape invariant shrinking patterns if the gap $b(t)$ is increased more rapidly: $displaystyle b(t)=left(1-frac{7}{2}tau mathcal{C} tright)^{-{2}/{7}}$, where $tau$ is the surface tension and $mathcal{C}$ is a function of the interface perturbation mode $k$. Here, we use a spectrally accurate boundary integral method together with an efficient time adaptive rescaling scheme, which for the first time makes it possible to explore the nonlinear limiting dynamical behavior of a vanishing interface. When the gap is increased at a constant rate, our numerical results quantitatively agree with experimental observations (Nase et al., Phys. Fluids, vol. 23, 2011, pp. 123101). When we use the shape invariant gap $b(t)$, our nonlinear results reveal the existence of $k$-fold dominant, one-dimensional, web-like networks, where the fractal dimension is reduced to almost one at late times. We conclude by constructing a morphology diagram for pattern selection that relates the dominant mode $k$ of the vanishing interface and the control parameter $mathcal{C}$.
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