Abstract: Multicellular tumor spheroids (MCTS) are used as organotypic models of normal and solid tumor tissue. Traditional techniques for generating MCTS, such as growth on nonadherent surfaces, in suspension, or on scaffolds, have a number of drawbacks, including the need for manual selection to achieve a homogeneous population and the use of nonphysiological matrix compounds. In this study we describe a mild method for the generation of MCTS, in which individual spheroids form in hanging drops suspended from a microtiter plate. The method has been successfully applied to a broad range of cell lines and shows nearly 100% efficiency (i.e., one spheroid per drop). Using the hepatoma cell line, HepG2, the hanging drop method generated well-rounded MCTS with a narrow size distribution (coefficient of variation [CV] 10% to 15%, compared with 40% to 60% for growth on nonadherent surfaces). Structural analysis of HepG2 and a mammary gland adenocarcinoma cell line, MCF-7, composed spheroids, revealed highly organized, three-dimensional, tissue-like structures with an extensive extracellular matrix. The hanging drop method represents an attractive alternative for MCTS production, because it is mild, can be applied to a wide variety of cell lines, and can produce spheroids of a homogeneous size without the need for sieving or manual selection. The method has applications for basic studies of physiology and metabolism, tumor biology, toxicology, cellular organization, and the development of bioartificial tissue.

Abstract: The apparent contact angle of a drop on a rough surface is often modeled using either Wenzel's or Cassie's formulas. Previous experiments are not conclusive regarding which formula to use and when. This information is critical in designing a superhydrophobic substrate for applications in microscale devices. A drop on a rough substrate can occupy multiple equilibrium states. These equilibrium states denote respective local minima in energy. The particular shape that a drop attains depends on how the drop is formed. We propose a design procedure to develop a rough superhydrophobic substrate that accounts for the multiple equilibrium drop shapes. The theory is expected to work well to maximize the advancing contact angle of a drop. It is noted in the end that appropriate models for the receding contact angles on rough substrate must be investigated further before appropriate design procedures, which will maximize the receding contact angle or minimize hysteresis (i.e., minimize the difference between the adv...

Abstract: Many-body dissipative particle dynamics is constructed to exhibit vapor-liquid coexistence, with a sharp interface, and a vapor phase of vanishingly small density. The application to fluid mechanics problems involving free surfaces is illustrated by simulation of a pendant drop. The model is an unusual example of a soft-sphere liquid with a potential energy built out of local-density-dependent one-particle self-energies.

Abstract: It has been shown that a water drop can bounce persistently, when thrown on a super-hydrophobic substrate. We present here scaling arguments which allow us to predict the maximal deformation and the contact time of the drop. This approach is completed by a model describing the flow inside the drop, and by original experimental data.

Abstract: The full spray emitted by Taylor cones of the ionic liquid 1-ethyl-3-methyl imidazolium tetrafluoroborate (EMI+BF4−) held in a vacuum is investigated at room temperature by time of flight mass spectrometry. The current is composed mainly of ions under most conditions studied, but contains a small component of nanometer drops that tends to dominate the emitted mass flow. Exceptionally, drop ejection vanishes close to the smallest flow rate at which the Taylor cone is steady. The present discovery of a stable strictly ionic regime in Taylor cones of substances other than liquid metals owes much to earlier observations with sulfuric acid, where most but not all the current was ionic. Most striking is the fact that this purely ionic regime is obtained at an electrical conductivity K of only 1.3 S/m, much smaller than that of sulfuric acid, and smaller than that at which formamide electrolytes with K>2 S/m do still emit substantial drop currents. The ion emission includes primarily the dimer (EMI–BF4)EMI+, acc...

Abstract: Nucleation is the first step in granulation where the powder and liquid first contact. Two types of nucleation in wet granulation processes are proposed. Drop controlled nucleation, where one drop forms one nucleus, occurs when drops hitting the powder surface do not overlap (low spray flux Psi(a)) and the drop must wet quickly into the bed (short drop penetration time t(p)). If either criterion is not met, powder mixing characteristics will dominate (mechanical dispersion regime). Granulation experiments were performed with lactose powder, water, PEG200, and 7% HPC solution in a 6 L and a 25 L mixer granulator. Size distributions were measured as the drop penetration time and spray flux were varied. At short penetration times, decreasing Psi(a) caused the nuclei distribution to become narrower. When drop penetration time was high, the nuclei size distribution was broad independent of changes in dimensionless spray flux. Nucleation regime maps were plotted for each set of experiments in each mixer as a function of the dimensionless distribution width delta. The nucleation regime map demonstrates the interaction between drop penetration time and spray flux in nucleation. The narrowest distribution consistently occurred at low spray flux and low penetration time, proving the existence of the drop controlled regime. The nucleation regime map provides a rational basis for design and scale-up of nucleation and wetting in wet granulation.

Abstract: When a drop impacts on a liquid surface it entraps a small amount of air under its centre as the two liquid surfaces meet. The contact occurs along a ring enclosing a thin disk of air. We use the next-generation ultra-high-speed video camera, capable of 1 million f.p.s. (Etoh et al. 2002), to study the dynamics of this air sheet as it contracts due to surface tension, to form a bubble or, more frequently, splits into two bubbles. During the contraction of the air disk an azimuthal undulation, resembling a pearl necklace, develops along its edge. The contraction speed of the sheet is accurately described by a balance between inertia and surface tension. The average initial thickness of the air sheet decreases with higher impact Reynolds numbers, becoming less than one micron. The total volume of air entrapped depends strongly on the bottom curvature of the drop at impact. A sheet of micro-bubbles is often observed along the original interface. Oguz–Prosperetti bubble rings are also observed. For low Weber numbers (We<20) a variety of other entrapment phenomena appear.

Abstract: Partial wetting of chemically heterogeneous substrates is simulated. Three-dimensional sessile drops in equilibrium with smooth surfaces supporting ordered chemical patterns are considered. Significant features are observed as a result of changing the drop volume. The number of equilibrated drops is found either to remain constant or to increase with growing drop volume. The shape of larger drops appears to approach that of a spherical cap and their three-phase contact line seems, on a larger scale, more circular in shape than that of smaller drops. In addition, as the volume is increased, the average contact angle of drops whose free energy is lowest among all equilibrium-shaped drops of the same volume appears to approach the angle predicted by Cassie. Finally, contrary to results obtained with two-dimensional drops, contact angle hysteresis observed in this system is shown to exhibit a degree of volume dependence in the advancing and receding angles. Qualitative differences in the wetting behavior associated with the two different chemical patterns considered here, as well as differences between results obtained with two-dimensional and three-dimensional drops, can possibly be attributed to variations in the level of constraint imposed on the drop by the different patterns and by the dimensionality of the system.

Abstract: [1] We investigate the extent to which aerosol extinction is a suitable proxy for the aerosol affecting drop formation. First we use multiple realizations of a cloud model to investigate the sensitivity of cloud drop effective radius re to aerosol parameters (size distribution and composition) and dynamical parameters (updraft and liquid water content). In general, re is most sensitive to cloud liquid water, a parameter often ignored in indirect effect analyses. The relative importance of the other parameters varies for different conditions but aerosol concentration Na is consistently important. Updraft plays an increasingly important role under high aerosol loadings. A breakdown of the individual aerosol terms contributing to drop size change shows that use of aerosol extinction as a proxy for size distribution and composition tends to underestimate the magnitude of the first indirect effect. This may influence interpretation of current satellite and surface remote measurements of the indirect effect.

Abstract: The insoluble surfactant pentadecanoic acid is spread at the interface of aqueous droplets, which are then deposited on a well-defined substrate and allowed to evaporate. The surface state of the s...

Abstract: The large shape distortions that occur during the drying of sessile drops of polymer solution are shown to be related to a buckling instability. As solvent evaporates, polymers accumulate near the vapor/drop interface and, depending on the experimental conditions, can form a glassy skin which bends as the volume it encloses decreases. A comparison of the times that characterize drying kinetics and glassy skin formation enables us to predict instability occurrence. Good agreement is found with measurements performed at different polymer concentrations, drop volumes and drying rates.

Abstract: A liquid drop placed on a vibrating diaphragm will burst into a fine spray of smaller secondary droplets if it is driven at the proper frequency and amplitude. The process begins when capillary waves appear on the free surface of the drop and then grow in amplitude and complexity as the acceleration amplitude of the diaphragm is slowly increased from zero. When the acceleration of the diaphragm rises above a well-defined critical value, small secondary droplets begin to be ejected from the free-surface wave crests. Then, quite suddenly, the entire volume of the drop is ejected from the vibrating diaphragm in the form of a spray. This event is the result of an interaction between the fluid dynamical process of droplet ejection and the vibrational dynamics of the diaphragm. During droplet ejection, the effective mass of the drop–diaphragm system decreases and the resonance frequency of the system increases. If the initial forcing frequency is above the resonance frequency of the system, droplet ejection causes the system to move closer to resonance, which in turn causes more vigorous vibration and faster droplet ejection. This ultimately leads to drop bursting. In this paper, the basic phenomenon of vibration-induced drop atomization and drop bursting will be introduced, demonstrated, and characterized. Experimental results and a simple mathematical model of the process will be presented and used to explain the basic physics of the system.

Abstract: We report a study on the deformation and breakup of drops in an impulsively started shear flow under Stokes flow conditions using boundary-integral simulations and video-microscopy experiments. Two independent techniques are used for determining the physical parameters of the system from the combined use of numerical simulations and experiments. Accurate breakup criteria (critical capillary numbers) are presented for a range of viscosity ratios. The time required for breakup events has a broad minimum corresponding to moderate shear rates. The size distribution of droplets produced by breakup events is shown to scale with the critical size drop for breakup in shear. A simplified model, based on this finding, is developed for the size distribution in a sheared emulsion. According to the model, the drop size distribution in a given emulsion depends only on the average initial drop size and the shear rate.

Abstract: The problem of a drop of arbitrary density and viscosity moving close to a vertical wall under the effect of buoyancy is analysed theoretically. The case where the suspending fluid is at rest far from the drop and that of a linear shear flow are both considered. Effects of inertia and deformation are assumed to be small but of comparable magnitude, so that both of them contribute to the lateral migration of the drop. Expressions for the drag, deformation and migration valid down to separation distances from the wall of a few drop radii are established and discussed. Inertial and deformation-induced corrections to the drag force and slip velocity of a buoyant drop moving in a linear shear flow near a horizontal wall are also derived.

Abstract: Reliabilit!- perfonnance of IC packages during drop impact is critical, especially for handheld electronic products. Currently. thcrc is no detailed test standard in the industry to advise on the procedures for board level dmp test. nor there is any model Ilia1 providcs good correlation with experimental ineasiircinents of acceleration and impact life. In this paper; detailed drop tests and simulations are pcrfonned on TFBGA (Thin-profile Fine-pitch BGA) and VFBGA (Vey-thinprofile Fine-pitch BGA) packages at board level using testing procediires developed in-house. The packages are susceptible to solder joint failures, induced by a combination of PCB bending and iueclwnical shock during impact. The critical solder ball is obsewed to occur at the outennost comer solder .joint_ and fails along the solder and PCB pad interface. Various testing parameters are studied experimentally and analytically. to understand the effects of drop heightl drop oricntation, number of PCB mounting screws to fixture. position of component on board: PCB bending: solder material, and etc. Drop height, fclt thickness, and contact conditions are used to fine-tune the shape aud level of shock pulse required. Board level drop test can be better controlled. compared with system or product level test such as impact of mobile phone. which sometimes has rather unpredictable results due to higher complexity and variations in drop orientation. At tlie same time, dynamic simulation is perfonncd to compare with esperiniental results. The model established has close values of peak acceleration and impact duration as measured in actual drop test. The failure mode and critical solder ball location predicted by modeling correlate well with testing. For the first time, an accurate life prediction model is proposed for board level drop test to estiinatc the number of drops to failure for a package. For the correlation cases studied. the nminmm nonual peeling stresses of critical solder joints correlate well with the mean impact lives measured during the drop test. The uncertainty of impact life prediction is within M drops, for a typical test of 50 drops. With this new model, a failure-free state can be detennined, and drop test performance of new package design can be quantified. and fuliher enhanced through modeling. This quantitative approach is different from traditional qualitative modeling. as it provides both accurate relative and absolute impact life prediction. The relative performance of package may be different under board level drop test ,and thennal cycling test. Different design guidelines should be considered, depcnding on application and area of concern

Abstract: In Part 2 of the two-part article, the impact dynamics of a liquid drop on a flat surface with heat transfer is numerically simulate d with the immersed boundary method. Computations with both static and dynamic contact angles are adopted to assess the importance and implications of the modeling aspect. Both water and ink droplets are considered, with direct experimental visualization and quantitative measurement employed to assess the computation. The effects of wettability, viscosity, surface tension, and impact velocity on the droplet spreading and recoiling behavior and wall heat transfer are assessed. It is found that the drop inertia directly influences the spread characteristics, the surface tension plays a major role in the recoil frequency, the drop viscosity damps out the drop spread and recoil, and the contact angle affects both the spreading and recoiling processes. Overall, the dynamic contact angle model attenuates the recoiling of the drop. The wall heat flux distribution is clearly affecte...

Abstract: The device enables a second drop to be mixed in a first drop deposited on an electrically insulating layer of an analysis support, in a viscous liquid environment and to mix the resulting drop. The device comprises at least one injector forming the second drop above the first drop. After formation of the second drop, a voltage impulse is applied between a first electrode, arranged under the electrically insulating layer of the analysis support, underneath the first drop, and a second electrode arranged near the outlet orifice of the injector. The voltage impulse fosters the coalescence phenomenon between the two drops, while preventing risks of contamination of the injector by the reagent of the first drop.

Abstract: Drying of a sessile drop of a complex liquid can lead to intriguing complex shapes. We report here a study dealing with a model system, made of a hydrosoluble polymer that is glassy when pure. Under solvent evaporation, polymers accumulate near the vapor/drop interface and may form a glassy skin, which bends as the volume of liquid it encloses decreases. The conditions for the occurrence of this buckling instability have been investigated; the experimental results are well explained by a model that compares the characteristic times for drying and for the formation of a glassy skin. Depending on the experimental conditions, different types of shape distortion take place; secondary instabilities that break the axisymmetry are also observed.

Abstract: Flotation of liquid droplets on pool surfaces, in the presence of temperature differences, is studied experimentally and numerically. Coalescence or sinking of the droplet is prevented by the thermal Marangoni motion, owing to the surface tension imbalance at the pool surface. The mechanism is the same as that investigated in previous works on coalescence and wetting prevention in the presence of temperature differences. If the droplet is colder than the liquid surface, the flow is directed radially towards the drop; this radial flow field drags the ambient air under the drop, thus creating an air film and avoiding a direct contact between the droplet and the pool molecules.The surface velocities are measured visually with a CCD camera to image the motion of tracers floating on the pool surface; the surface temperature distributions along the pool and the droplet surfaces are measured by an infrared thermocamera. The experimental results are correlated by numerical results obtained under the assumption of spherical drop and axisymmetric flow regime. Different liquids are considered and the influence of evaporation is discussed, showing a good agreement between the experiments and the numerical simulations.

Abstract: Drying kinetics of low molecular weight sugars such as fructose, glucose, sucrose and organic acid such as citric acid and high molecular weight carbohydrate such as maltodextrin (DE 6) were determined experimentally using single drop drying experiments as well as predicted numerically by solving the mass and heat transfer equations. The predicted moisture and temperature histories agreed with the experimental ones within 6% average relative (absolute) error and average difference of ± 1°C, respectively. The stickiness histories of these drops were determined experimentally and predicted numerically based on the glass transition temperature (T g ) of surface layer. The model predicted the experimental observations with good accuracy. A nonsticky regime for these materials during spray drying is proposed by simulating a drop, initially 120 µm in diameter, in a spray drying environment.