3D Droplet Research Articles

Controlled packing and single-droplet resolution of 3D-printed functional synthetic tissues

3D-printing networks of droplets connected by interface bilayers are a powerful platform to build synthetic tissues in which functionality relies on precisely ordered structures. However, the structural precision and consistency in assembling these structures is currently limited, which restricts intricate designs and the complexity of functions performed by synthetic tissues. Here, we report that the equilibrium contact angle (θDIB) between a pair of droplets is a key parameter that dictates the tessellation and precise positioning of hundreds of picolitre-sized droplets within 3D-printed, multi-layer networks. When θDIB approximates the geometrically-derived critical angle (θc) of 35.3°, the resulting networks of droplets arrange in regular hexagonal close-packed (hcp) lattices with the least fraction of defects. With this improved control over droplet packing, we can 3D-print functional synthetic tissues with single-droplet-wide conductive pathways. Our new insights into 3D droplet packing permit the fabrication of complex synthetic tissues, where precisely positioned compartments perform coordinated tasks.

Compaction Dynamics during Progenitor Cell Self-Assembly Reveal Granular Mechanics

Summary We study the self-assembly dynamics of human progenitor cells in agarose microwells that are used for production of chondrogenic organoids. Using image analysis on time-lapse microscopy, we estimate the aggregate area in function of time for a large number of aggregates. In control conditions, the aggregate radius follows an exponential relaxation that is consistent with the dewetting dynamics of a liquid film. Upon introducing Y-27632 Rho kinase inhibitor, the compatibility with the liquid model is lost, and slowed-down relaxation dynamics are observed. We demonstrate that these aggregates behave as granular piles undergoing compaction, with density relaxation that follows a stretched exponential. Using simulations with an individual cell-based model, we construct a phase diagram of cell aggregates that suggests that the aggregate in presence of Rho kinase inhibitor approaches glass transition.

Squeezed metallic droplet with tunable Kubo gap and charge injection in transition metal dichalcogenides

Shrinking the size of a bulk metal into nanoscale leads to the discreteness of electronic energy levels, the so-called Kubo gap δ. Renormalization of the electronic properties with a tunable and size-dependent δ renders fascinating photon emission and electron tunneling. In contrast with usual three-dimensional (3D) metal clusters, here we demonstrate that Kubo gap δ can be achieved with a two-dimensional (2D) metallic transition metal dichalcogenide (i.e., 1T'-phase MoTe2) nanocluster embedded in a semiconducting polymorph (i.e., 1H-phase MoTe2). Such a 1T'/1H MoTe2 nanodomain resembles a 3D metallic droplet squeezed in a 2D space which shows a strong polarization catastrophe while simultaneously maintaining its bond integrity, which is absent in traditional δ-gapped 3D clusters. The weak screening of the host 2D MoTe2 leads to photon emission of such pseudometallic systems and a ballistic injection of carriers in the 1T'/1H/1T' homojunctions which may find applications in sensors and 2D reconfigurable devices.

Pinch-off location and time during 2D droplet impact onto a wetted stationary cylinder using the lattice Boltzmann method

This paper focuses on pinch-off location and time during 2D droplet impact onto a wetted stationary cylinder using the lattice Boltzmann method. A general off-lattice boundary condition is implemented for the curved boundary. The boundary condition is examined by comparing the steady-state velocity profile of the Taylor–Couette flow with its analytical solution. Additionally, the spreading length of a droplet impacting a wetted stationary cylinder is shown to be in good agreement with the numerical data of the literature. In the results section, the effects of Reynolds, Weber, and Froude numbers, as well as the droplet/cylinder diameter ratio, on the pinch-off length and time are investigated. The simulations revealed that as the Froude number increases, the pinch-off time increases with a slope 1.39 times more than that of the pinch-off length decrease. Moreover, it is shown that the critical Weber number for onset of dripping process increases with increasing the Froude number or decreasing the Reynolds number.

Demixing in Membranes and their Encapsulated Solutions

Liquid-liquid phase separation drives a range of biophysical processes in many locations throughout cells, from the interior of nuclei to outer membranes. It is known that phase separation in a cell's interior creates 3D liquid droplets composed of proteins, which are sensitive to the system's physiochemical conditions. In membranes, such as those of giant plasma membrane vesicles (GPMVs) and living vacuole membranes, phase separation is two dimensional. The composition of lipids and cholesterol in the membrane determines the temperature (Tmix) at which the system transitions from a mixed to phase separated system. When 3D droplets and membranes physically touch, actin-independent endocytosis can occur. Together, these observations lead to the question: How does demixing in the solution affect demixing in the membrane? We investigate this question using giant unilamellar vesicles (GUVs) and an aqueous two-phase system of polyethylene glycol and dextran.

Conservative Allen–Cahn equation with a nonstandard variable mobility

In this article, we present the conservative Allen–Cahn equation with a nonstandard variable mobility. Unlike the classical variable mobility, the proposed nonstandard variable mobility has small value at the interface and large value away from the interface. As benchmark tests, we perform temporal evolutions of two droplets without velocity field, 2D droplet deformation under a simple shear flow, 2D droplet deformation under a swirling flow, and 3D droplet deformation under a shear flow. The numerical results of the proposed method demonstrate a remarkable accuracy in preserving interfaces. Moreover, the proposed method not only captures interface location but also maintains uniform interface transition layer thickness.

Rotation and propulsion in 3D active chiral droplets

Chirality is a recurrent theme in the study of biological systems, in which active processes are driven by the internal conversion of chemical energy into work. Bacterial flagella, actomyosin filaments, and microtubule bundles are active systems that are also intrinsically chiral. Despite some exploratory attempt to capture the relations between chirality and motility, many features of intrinsically chiral systems still need to be explored and explained. To address this gap in knowledge, here we study the effects of internal active forces and torques on a 3-dimensional (3D) droplet of cholesteric liquid crystal (CLC) embedded in an isotropic liquid. We consider tangential anchoring of the liquid crystal director at the droplet surface. Contrary to what happens in nematics, where moderate extensile activity leads to droplet rotation, cholesteric active droplets exhibit more complex and variegated behaviors. We find that extensile force dipole activity stabilizes complex defect configurations, in which orbiting dynamics couples to thermodynamic chirality to propel screw-like droplet motion. Instead, dipolar torque activity may either tighten or unwind the cholesteric helix and if tuned, can power rotations with an oscillatory angular velocity of 0 mean.

Forming a Large-Scale Droplet Array in a Microcage Array Chip for High-Throughput Screening.

Forming a large-scale droplet array plays an important role for microfluidic droplet-based high-throughput screening and analysis. Herein, we describe a simple and rapid method to form a large-scale two-dimension (2D) droplet array by using a microcage array chip. Differing from the previous droplet array formation methods, microcages formed by being surrounded by multiple micropillars could rapidly spread the oil phase through the gaps between the micropillars and trap droplets with fast speed and convenient operation. We formed a large-scale 2D monolayer droplet array containing approximately 1 000 000 droplets on a 5.5 cm × 5.5 cm microcage array chip within 90 s. The droplets in the droplet array could be further incubated for performing biochemical reactions and detected by a fluorescence microscope in real time. Due to the exact trapping and positioning functions of the microcages to the droplets, single targeted fluorescent droplets in the array could be individually picked out and transferred to culture medium by a microfluidic droplet-handling robot with a success rate of 100% and a picking operation time of 2.0 s for one droplet under the optimized conditions. This system was validated in the screening of the bacterium expressing the esterase AFEST from a mixture of AFEST-expressing and phosphotriesterase-expressing E. coli cells, achieving a success rate of 100% for single-droplet picking while maintaining the bacterial cell viability. The present system has the potential to be applied in high-throughput screening and analysis, such as single cell analysis, directed evolution, and drug screening.

Numerical study of wetting stability and sliding behavior of liquid droplets on microgrooved surfaces

3D droplet models are developed to numerically investigate the droplet stability and hysteresis of the three-phase contact line on both horizontal and inclined microgrooved solid surfaces. A numerical method is applied to study the shapes and energies of liquid droplets, with a particular focus on the stability of the suspended wetting state. A normalized form of droplet energy is used to compare the relative stabilities of multiple metastable wetting states and a numerical approach is found to reliably predict the wetting stability of droplets on horizontal microgrooved substrates. For wetting on inclined surfaces, numerical simulations of sliding behavior of liquid droplets on flat and periodic microgrooved surfaces with a range of groove geometry are conducted. A numerical model capable of predicting the critical sliding angle of the drop from the knowledge of advancing and receding angles is developed. The effects of microgroove topography, droplet size, and inclination angle on the droplet dynamic behavior are analyzed. Droplet shape and critical sliding angle, obtained from the numerical models, are compared with those of experimental results and are found to be in very good agreement.

Post-pinch-off relaxation of two-dimensional droplets in a Hele-Shaw cell

We report on the shape relaxation of 2D droplets, formed right after the spontaneous pinch-off of a capillary bridge-droplet confined within a Hele-Shaw cell. An array of bridge-droplets confined within a microchip device first undergo neck thinning due to the evaporation driven volume change. Subsequently, an abrupt topological change transforms each bridge-droplet into a small central satellite droplet and the twin-droplets pinned at the edges of the cell. We monitor the shape relaxation with high temporal resolution optical microscopy. Capillary action drives the 2D shape relaxation, while the viscous dissipation in the film retards it. As a result, the tip of the twin-droplets exhibit a self-similar parabolic shape evolution. Based on these observations, the lubrication-approximation model accurately predicts the internal pressure evolution and the droplet tip displacement. The geometrical confinement substantially slows down the dynamics, facilitating visualization of the capillary-viscous regime, even for low viscosity liquids. The characteristic relaxation timescale shows an explicit dependence on the confinement ratio (width/gap) and the capillary-velocity of liquid. We verify the broad applicability of the model using different liquids.

Interacting coalescence avalanches in a 2D droplet assembly

A 2D droplet assembly can undergo destabilization through a series of coalescence events that propagate like an avalanche. Multiple avalanches can get triggered during the course of an experiment, which interact as they propagate in the system. In this article, the avalanching phenomenon as a function of the number of avalanches triggered is investigated. The dynamics of interaction between the avalanches is studied as a function of the propensity for propagation of an avalanche and the proximity and asynchrony in triggering. This article shows that when the propagation propensity of avalanches is small, they are uncorrelated and independent allowing one to predict the effect of multiple triggers by a superposition of the results of the single‐avalanche case. However, for large propagation propensities, the avalanches compete for droplets to coalesce due to the finite‐sized nature of the droplet assembly and behave like a single autocatalytically propagating avalanche. © 2018 American Institute of Chemical Engineers AIChE J, 65: 1111–1118, 2019

A lattice Boltzmann study on dripping process during 2D droplet impact onto a wetted rotating cylinder

In this study, two dimensional droplet impact onto a wetted rotating circular cylinder is investigated using the lattice Boltzmann method for the first time. A general off-lattice boundary treatment is implemented for this purpose. The curved boundary condition is validated by comparing the velocity profile of the circular Couette flow with the analytical results. In addition, variations of the wetted length after droplet impact onto the stationary cylinder is shown to be in a good agreement with the numerical results reported in the literature. In the results section, effects of the Reynolds (Re) and Weber numbers (We), velocity ratio (V*), and droplet eccentricity (Ec) on dripping volume fraction is investigated in the ranges of 0 <Re < 1000, 0 <We < 70, 0 <V* < 1.5, − 0.8 <Ec < 0.8, while the Froude number is kept constant at Fr = 2. The simulation results show that the dripping volume fraction is independent of the velocity ratio for We ≥ 50. It was found that for the counter-clockwise rotation, the minimum dripping volume fraction decreases with increasing the velocity ratio and occurs at higher positive eccentricities. However, in the examined range of |Ec|≤ 0.8, the maximum dripping fraction occurs at Ec = −0.8 for all velocity ratios. Finally, investigation of the dripping angle indicates that it increases with the velocity ratio.

A Novel Approach to Droplet's 3D Shape Recovery Based on Mask R-CNN and Improved Lambert⁻Phong Model.

Aiming at the demand for extracting the three-dimensional shapes of droplets in microelectronic packaging, life science, and some related fields, as well as the problems of complex calculation and slow running speed of conventional shape from shading (SFS) illumination reflection models, this paper proposes a Lambert–Phong hybrid model algorithm to recover the 3D shapes of micro-droplets based on the mask regions with convolutional neural network features (R-CNN) method to extract the highlight region of the droplet surface. This method fully integrates the advantages of the Lambertian model’s fast running speed and the Phong model’s high accuracy for reconstruction of the highlight region. First, the Mask R-CNN network is used to realize the segmentation of the highlight region of the droplet and obtain its coordinate information. Then, different reflection models are constructed for the different reflection regions of the droplet, and the Taylor expansion and Newton iteration method are used for the reflection model to get the final height of all positions. Finally, a three-dimensional reconstruction experimental platform is built to analyze the accuracy and speed of the algorithm on the synthesized hemisphere image and the actual droplet image. The experimental results show that the proposed algorithm based on mask R-CNN had better precision and shorter running time. Hence, this paper provides a new approach for real-time measurement of 3D droplet shape in the dispensing state.

Axisymmetric lattice Boltzmann simulation of droplet impact on solid surfaces.

Droplet-solid interaction is a ubiquitous fluid phenomenon that underpins a wide range of applications. To further the understanding of this important problem, we use an axisymmetric lattice Boltzmann method (LBM) to model the droplet impact on a solid surface with different wettability. The method applies a popular free-energy LBM developed by Lee and Liu [T. Lee and L. Liu, J. Comput. Phys. 229, 8045 (2010)10.1016/j.jcp.2010.07.007] to simulate incompressible binary fluids with physical density and viscosity contrasts. The formulation is recast in cylindrical coordinates for modeling the normal impact of a three-dimensional (3D) droplet in the no-splashing regime, in which an axisymmetric flow is considered. The droplet deposits on or rebounds from the surface, governed by three key parameters: Weber number, Ohnesorge number, and equilibrium contact angle, which quantifies the surface wettability. We elucidate the distinct impact dynamics by probing droplet morphology and contact line behavior in great detail, which are quantitatively characterized by spreading factor, droplet aspect ratio, and dynamic contact angle. The simulations also resolve fluid velocity field inside and outside the droplet, which provides additional insight into the morphological evolution and mass-momentum transfer during impact. Explicit comparison between axisymmetric and conventional 2D LBM highlights the importance of axisymmetric terms in governing equations for reproducing physical impact behavior. The axisymmetric LBM significantly reduces computational cost as compared with 3D LBMs and offers an effective means to study droplet impact in applicable conditions.

Image analysis of axisymmetric droplets in wetting experiments: A new tool for the study of 3D droplet geometry and droplet shape reconstruction

A new software tool is developed for droplet image analysis for the study of wetting of solid substrates. The tool extracts information exclusively from images and does not require the use of any properties of the system. Moreover, its applicability covers both axisymmetric and non-axisymmetric droplets. The developed software processes independently droplet images taken from side and top perspectives. Processing of side-view images is made by polynomial fitting to the droplet shape and provides important 2D geometrical features such as contact angles, length, height, contact point coordinates and contour outline. The analysis of top-view images is achieved through active contours (snakes) and yields droplet dimensions, centroid position and contour outline. The combination of synchronized side and top images provides the reconstruction of the droplet 3D shape by means of slices of circular arc shape, which allows estimation of droplet volume and of the distribution of contact angles along its perimeter. The above is an important feature that has not been delivered by other software tools. Experimental results to support the applicability of the new tool are presented for two distinct substrates having different surface properties (glass and Teflon).

Lattice Boltzmann simulation of the spreading behavior of a droplet impacting on inclined solid wall

The spreading behavior of a 3D droplet impacting on inclined solid wall is presented by using a lattice Boltzmann method (LBM) with single component multiphase pseudopotential model. The time evolution of spreading factor, dimensionless spreading width, dimensionless height, dimensionless bottom area and adhesion force are obtained. Our numerical results show that when increasing the contact angle or inclination angle, the dimensionless height and the dimensionless bottom area increases but the dimensionless spreading length and spreading width decreases. In addition, the progresses of circumferential spreading in starting-up and spreading stages and the aggregation at front edge in retracting stage would be more obvious by decreasing the viscosity or increasing the Bond number.

초소수성 실린더 표면에 충돌하는 액적의 움직임에 관한 수치해석 연구

Droplet impact is widely used in various engineering applications. Various conditions could affect the droplet evolution during impacting process. We have focused on geometrical effect from curved surface. Due to curvature of the wall, dynamics of the droplet would be quite different compared to the flat surface. We also paid great attentions to the contact line behavior. To augment the curvature effect, cylindrical surface with superhydrophobic characteristic was considered in this study. Very high advancing (165o) and receding angle (160o) associated with superhydrophobic surface makes distinctive difference in its behavior between axial and circumferential direction. We have numerical studied the impact process of the 3D droplet on cylindrical surface using Level Contour Reconstruction(LCRM) method. We found that impact behavior is pretty much same as flat surface in the axial direction. In circumferential direction, contact diameter has certain limit for higher impact velocity. Contact time of the droplet is also quite different compared to the flat surface in circumferential direction. At lower impact velocity, contact time of the droplet decrease rapidly with increased impact velocity but has negligible change at higher values.

A Metallographic Review of 3D Printing/Additive Manufacturing of Metal and Alloy Products and Components

Applications and examples of light and electron micrographs illustrating microstructures, which describe metallurgical phenomena in 3D printing/additive manufacturing of metal and alloy products and components, are presented along with extensive process and processing parameter descriptions and review. Examples include microstructures that have defined turbine blade fabrication and optimization over the past half century, including contemporary electron beam melting fabrication of turbine blade alloys and other novel microstructures and architectures, which result from layer by layer, non-equilibrium melt solidification and epitaxial growth involving powder bed laser and electron beam fabrication. Phase transformations and second-phase formation by rapid cooling in metal and alloy components fabricated by laser and electron beam melting technologies are illustrated for a range of high-temperature materials. Using a range of examples, the advantages of fabricating complex (especially porous) biomedical and related commercial products are described. Prospects for future developments of direct 3D metal and alloy droplet printing, as a key component of the digital factory of the future, are described. This technology is compared with more conventional solidification and powder bed layer building thermo-kinetics, especially in the context of large structure and component fabrication.

3D-glass molds for facile production of complex droplet microfluidic chips.

In order to leverage the immense potential of droplet microfluidics, it is necessary to simplify the process of chip design and fabrication. While polydimethylsiloxane (PDMS) replica molding has greatly revolutionized the chip-production process, its dependence on 2D-limited photolithography has restricted the design possibilities, as well as further dissemination of microfluidics to non-specialized labs. To break free from these restrictions while keeping fabrication straighforward, we introduce an approach to produce complex multi-height (3D) droplet microfluidic glass molds and subsequent chip production by PDMS replica molding. The glass molds are fabricated with sub-micrometric resolution using femtosecond laser machining technology, which allows directly realizing designs with multiple levels or even continuously changing heights. The presented technique significantly expands the experimental capabilities of the droplet microfluidic chip. It allows direct fabrication of multilevel structures such as droplet traps for prolonged observation and optical fiber integration for fluorescence detection. Furthermore, the fabrication of novel structures based on sloped channels (ramps) enables improved droplet reinjection and picoinjection or even a multi-parallelized drop generator based on gradients of confinement. The fabrication of these and other 3D-features is currently only available at such resolution by the presented strategy. Together with the simplicity of PDMS replica molding, this provides an accessible solution for both specialized and non-specialized labs to customize microfluidic experimentation and expand their possibilities.

Rate Dependence of Elementary Rearrangements and Spatiotemporal Correlations in the 3D Flow of Soft Solids.

We use a combination of confocal microscopy, rheology, and molecular dynamics simulations to investigate jammed emulsions under shear, by analyzing the 3D droplets rearrangements in the shear frame. Our quantitative analysis of local dynamics reveals elementary nonaffine rearrangements that underlie the onset of the flow at small strains. We find that the mechanism of unjamming and the upturn in the material flow curve are associated to a qualitative change in spatiotemporal correlations of such rearrangements with the applied shear rate. At high shear rates, droplet clusters follow coordinated, stringlike motion. Conversely, at low shear rates, the elementary nonaffine rearrangements exhibit longer-ranged correlations, with complex spatiotemporal patterns. The 3D microscopic details provide novel insights into the specific features of the material flow curve, common to a large class of technologically relevant soft disordered solids and new fundamental ingredients for constitutive models.