Session GR: Drops VI

Generation of micron-sized bubbles at the entrance region of PDMS microchannels

Here we present a new regime of operation of PDMS-based flow focusing microfluidic devices. We show that bubbles with diameters below one tenth the channel width, which we fix here to $w=50$ $\mu$m, can be produced in low viscosity liquids thanks to the strong pressure gradient existing at the entrance region of the channel. Our theory, which is in good agreement with experiments, predicts that bubble size can be expressed as $d_b/w\propto \left(Q_g/Q_g\right)^{5/12}$, where $Q_g$ and $Q_l$ indicate, respectively, the gas and liquid flow rates.   

Velocimetry techniques on Newtonian droplets and jets

Experiments on the dynamics of Newtonian droplets and jets are described. Laser Doppler Anemometry (LDA), Particle Image Velocimetry (PIV) and shadowgraph imaging studies were performed in experimental setups in which important parameters such as pressure and velocity can be measured, in order to generate understanding and data to validate numerical models for jet and drop behavior in ink-jet printing systems. For jets with millimeter diameter, simple setups are described to obtain velocity fields within modulated and un-modulated continuous jets by the use of LDA and PIV. A drop-on-demand system capable of generating millimeter-size droplets was used with a simple novel PIV arrangement to obtain the velocity fields within impacting and coalescing droplets. These experimental setups and their instrumentation are simple to reproduce and use conventional and commercially available techniques.   

The onset of microscale tipstreaming with soluble nonionic surfactants

Surfactants play a significant role in the formation of emulsion droplets in microfluidic devices. At specific concentrations and flow rates, tipstreaming is observed and micron-scale droplets are formed. To date, the role of the surfactant itself is not well understood. The timescales for surfactant mass transport including diffusion, adsorption, and desorption can all be significant in determining the local, instantaneous surface concentration. In this talk, we present microfluidic tipstreaming experiments using nonionic CiEj surfactants in which the hydrophobic tail length varies. We show that tipstreaming occurs only when adsorption is rapid enough for surfactant to adsorb but viscous stresses are strong enough to maintain a surface tension gradient. The experiments indicate that the allowable surface coverage for tipstreaming is very small, even though the bulk concentration is greater than the critical micelle concentration. We use a one-dimensional kinetic-limited transport model to demonstrate that small surface coverages can lead to highly nonlinear effects like tipstreaming at these length and time scales.   

Scaling in two-fluid pinch-off

The physics of two-fluid pinch-off, which arises whenever drops, bubbles, or jets of one fluid are ejected from a nozzle into another fluid, is scientifically important and technologically relevant. While the breakup of a drop in a passive environment is well understood, the physics of pinch-off when both the inner and outer fluids are dynamically active remains inadequately understood. Here, the breakup of a compound jet whose core and shell are incompressible Newtonian fluids is analyzed computationally when the interior is a ``bubble'' and the exterior is a liquid. The numerical method employed is an implicit method of lines ALE algorithm which uses finite elements with elliptic mesh generation and adaptive finite differences for time integration. Thus, the new approach neither starts with a priori idealizations, as has been the case with previous computations, nor is limited to length scales above that set by the wavelength of visible light as in any experimental study. In particular, three distinct responses are identified as the ratio $m$ of the outer fluid's viscosity to the inner fluid's viscosity is varied. For small $m$, simulations show that the minimum neck radius $r$ initially scales with time $\tau$ before breakup as $r \sim \tau^{0.58}$ (in accord with previous experiments and inviscid fluid models) but that $r \sim \tau$ once $r$ becomes sufficiently small. For intermediate and large values of $m$, $r \sim \tau^\alpha$, where the exponent $\alpha$ may not equal one, once again as $r$ becomes sufficiently small.   

A method to generate picoliter droplets out of a microliter drop, on-demand using satellite formation

We investigated a simple, robust way to generate pico- to femtoliter drops out of a single 1microliter droplet for the use of generating monodisperse droplets in droplet-based microfluidics. A single drop is placed between glass substrates, immersed in silicone oil with different viscosities, moved with constant velocities from 50micron/s to 1500micron/s. As two plates separates, liquid bridge breaks and smaller droplets, or satellites are formed. We have found that for a fixed viscosity, nearly same size of droplets are generated over several orders of velocities. Using this method, single cell encapsulation is also possible without any other complex control and we successively captured a single Arabidopsis Protoplast with this method. This method can be used to divide smal l bio sample on-demand, to several smaller droplets for further analysis.   

Experimental and numerical investigation of microjet breakup of dilute polymer solutions

Droplet formation from the breakup of a microjet of dilute polymer solution is investigated using ultra high-speed imaging up to 1 million frames per second and by means of a one-dimensional model based on the slender-jet approximation. A liquid emanating from a nozzle at sufficiently large velocity forms a jet that is inherently unstable and spontaneously breaks up into droplets to minimize its surface energy. The addition of a small amount of long flexible polymers (\emph{i.e.}~polyethylene oxide) to the liquid dramatically influences this breakup process. In the final stage of the collapse -- when the shear rate in the liquid increases -- the polymer chains stretch and parallelize in the direction of the main flow, which results in a significantly increase of the local viscosity, and hence strong non-Newtonian behaviour. In this work we make a direct comparison between the ultra high-speed imaging results and those obtained from a simplified one-dimensional model.   

A model for predicting drop size distribution in effervescent jet breakup by bubble-bursting

This paper deals with the problem of prediction of mean drop size in effervescent atomizers with bubbly flow. Current studies in literature indicate that the progress in the development of a model for drop size prediction in effervescent sprays is not satisfactory. This model, which gives the drop size distribution of effervescent spray generated by rapid expansion of bubbles, is based on energy and entropy principles. A spherical control volume of liquid jet with bubble inside is considered as the initial state. The final state is taken as the fine droplets formed after the breakup. The model works with the constraints of conserving mass and energies of the system. The objective of obtaining the drop size distribution is transformed to a new constraint of maximization of entropy of the system (i.e. finding drop size classes with maximum probability of occurrence). Thus, it becomes an optimization problem to which a method of Lagrange multipliers is applied. The outcome of this exercise is the most probable distribution of droplets in various size classes and it can be converted into more meaningful averages such as SMD that is useful for mixing and combustion applications.   

Exploring the effect of liquid crystalline phase on droplet breakup

We investigate droplet breakup of a thermotropic liquid crystal in the smectic, nematic, and isotropic phases. The experiment consists of varying the ambient temperature to control the liquid crystalline phase and imaging breakup using a fast video camera. We find breakup of the smectic phase is well described by existing theory for a shear thinning power-law fluid. These theories predict the stress/strain dependence measured in bulk rheology coincides with the minimum radius dependence on time to breakup. For the nematic and isotropic phases, we find the minimum radius dependence on time to breakup does not agree with bulk rheological measurements that indicate Newtonian behavior. Instead, breakup occurs in two stages, with extensional thickening preceding extensional thinning. Finally, we will comment on a possible flow induced ordering mechanism and make comparisons to two other rod-like systems exhibiting similar behavior.   

Breakup of double emulsions in wedge-shaped microfluidic channels

Double emulsion droplets can serve as drug delivery vehicles and individual compartments for chemical reactions, and such materials are relevant to new kinds of microfluidic applications. We study experimentally the dynamics and breakup of double emulsion droplets flowing through poly(dimethylsiloxane) (PDMS) channels. As water-in-oil-in-water (W/O/W) double emulsion droplets flow through such wedge-shaped channels, the breakup of the droplets is controlled by the capillary number and the droplet-to-orifice size ratio. We obtain a phase diagram of droplet breakup morphology from the experimental results, and explain the results via a combination of the capillary instability and thin film dynamics. The phase diagram is useful for predicting and controlling the breakup of the droplet. Finally, differences between results obtained in PDMS channels and capillary channels are discussed.   

Evolution, Pinch-off, and Classification of the Steady-State Solutions of an Axisymmetric Drop in Stokes Flow

The evolution of an Axisymmetric viscous drop immersed in a strain field is examined numerically using higher order boundary integral simulation followed the work of Nitsche et al. [J. Comp. 229, 2010]. The effect of three parameters is examined, namely: the capillary number, the viscosity ratio and the relative nonlinearity in background flow. A classification of the steady-state solutions in parameter space for sufficiently small capillary number is presented including the regimes of oval, canonical and bell-shaped steady-states. The non-steady evolution for larger capillary number is also studied and classified. New results include the effect of the nonlinearity in background flow. The presence of a positive nonlinear term leads to corner formation as time goes to infinity. Negative nonlinearity on the other hand leads to a finite time singularity. Either the drop pinches at two points on the axis in finite time or the curvature blows up at a point away from the axis. Pinch-off is also investigated in detail.