We show experimentally, and explain theoretically, what velocity is needed to break an elongated droplet entering a microfluidic T-junction. Our experiments on short droplets confirm previous... Show moreWe show experimentally, and explain theoretically, what velocity is needed to break an elongated droplet entering a microfluidic T-junction. Our experiments on short droplets confirm previous experimental and theoretical work that shows that the critical velocity for breakup scales with the inverse of the length of the droplet raised to the fifth power. For long elongated droplets that have a length about thrice the channel width, we reveal a drastically different scaling Taking into account that a long droplet remains squeezed between the channel walls when it enters a T-j unction, such that the gutters in the corners of the channel are the main route for the continuous phase to flow around the droplet, we developed a model that explains that the critical velocity for breakup is inversely proportional to the droplet length. This model for the transition between breaking and nonbreaking droplets is in excellent agreement with our experiments. Show less
Shah, M.S.; Steijn, V. van; Kleijn, C.R.; Kreutzer, M.T. 2019
Thermal fluctuations have been shown to influence the thinning dynamics of planar thin liquid films, bringing predicted rupture times closer to experiments. Most liquid films in nature and industry... Show moreThermal fluctuations have been shown to influence the thinning dynamics of planar thin liquid films, bringing predicted rupture times closer to experiments. Most liquid films in nature and industry are, however, non-planar. Thinning of such films not just results from the interplay between stabilizing surface tension forces and destabilizing van der Waals forces, but also from drainage due to curvature differences. This work explores the influence of thermal fluctuations on the dynamics of thin non-planar films subjected to drainage, with their dynamics governed by two parameters: the strength of thermal fluctuations,ย ๐๐ย , and the strength of drainage,ย ๐ ๐ ย . For strong drainage (ย ๐ ๐ ๐ โซ๐ trย ), we find that the film ruptures due to the formation of a local depression called a dimple that appears at the connection between the curved and flat parts of the film. For this dimple-dominated regime, the rupture time,ย trย , solely depends onย ๐ ๐ ย , according to the earlier reported scaling,ย ๐ trโผ๐ โ10/7ย . By contrast, for weak drainage (ย ๐ ๐ ๐ โช๐ trย ), the film ruptures at a random location due to the spontaneous growth of fluctuations originating from thermal fluctuations. In this fluctuations-dominated regime, the rupture time solely depends onย ๐๐ย asย ๐๐๐ผtrโผโ(1/๐max)lnโก(2๐)๐ผย , withย ๐ผ๐ผ=1.15ย . This scaling is rationalized using linear stability theory, which yieldsย ๐๐maxย as the growth rate of the fastest-growing wave andย ๐ผ๐ผ=1ย . These insights on if, when and how thermal fluctuations play a role are instrumental in predicting the dynamics and rupture time of non-flat draining thin films. Show less
Here, we investigate separately the dependence of the mixing time on the size and velocity of micro-droplets moving through serpentine channels. We find that the mixing time scales linearly with... Show moreHere, we investigate separately the dependence of the mixing time on the size and velocity of micro-droplets moving through serpentine channels. We find that the mixing time scales linearly with droplet size. All experimental data collapse on a master-line, when the convective time scale is multiplied by the dimensionless droplet size. Show less
Roghair, I.; Musterd, M.; Ende, D. van den; Kleijn, C.R.; Kreutzer, M.T.; Mugele, F. 2015
We present a numerical simulation technique to calculate the deformation of interfaces between a conductive and non-conductive fluid as well as the motion of liquid-liquid-solid three-phase contact... Show moreWe present a numerical simulation technique to calculate the deformation of interfaces between a conductive and non-conductive fluid as well as the motion of liquid-liquid-solid three-phase contact lines under the influence of externally applied electric fields in electrowetting configuration. The technique is based on the volume of fluid method as implemented in the OpenFOAM framework, using a phase fraction parameter to track the different phases. We solve the combined electrohydrodynamic problem by coupling the equations for electric effects-Gauss's law and a charge transport equation-to the Navier-Stokes equations of fluid flow. Specifically, we use a multi-domain approach to solving for the electric field in the solid and liquid dielectric parts of the system. A Cox-Voinov boundary condition is introduced to describe the dynamic contact angle of moving contact lines. We present several benchmark problems with analytical solutions to validate the simulation model. Subsequently, the model is used to study the dynamics of an electrowetting-based display pixel. We demonstrate good qualitative agreement between simulation results of the opening and closing of a pixel with experimental tests of the identical reference geometry. Show less
Musterd, M.; Steijn, V. van; Kleijn, C.R.; Kreutzer, M.T. 2015
We present a theoretical model to calculate the volume of non-wetting bubbles and droplets in segmented microflows from given dimensions of the microchannel and measured lengths of bubbles and... Show moreWe present a theoretical model to calculate the volume of non-wetting bubbles and droplets in segmented microflows from given dimensions of the microchannel and measured lengths of bubbles and droplets. Despite the importance of these volumes in interpreting experiments on reaction kinetics and transport phenomena, an accurate model like the one we present here did not yet exist. The model has its theoretical basis in the principle of interfacial energy minimization and is set up such that volume calculations are possible for a wide variety of channel geometries. We successfully validated our model with the 3D numerical energy minimization code SURFACE EVOLVER for the three most commonly used channel geometries in the field of microfluidics and provide accurate user-friendly equations for these geometries. Show less
Musterd, M.; Steijn, V. van; Kleijn, C.R.; Kreutzer, M.T. 2014
Local contact line pinning prevents droplets from rearranging to minimal global energy, and models for droplets without pinning cannot predict their shape. We show that experiments are much better... Show moreLocal contact line pinning prevents droplets from rearranging to minimal global energy, and models for droplets without pinning cannot predict their shape. We show that experiments are much better described by a theory, developed herein, that does account for the constrained contact line motion, using as an example droplets on tilted plates. We map out their shapes in suitable phase spaces. For 2D droplets, the critical point of maximum tilt depends on the hysteresis range and Bond number. In 3D, it also depends on the initial width, highlighting the importance of the deposition history. Show less
Rosso, M.; Steijn, V. van; Smet, L.C.PM. de; Sudholter, E.J.R.; Kleijn, C.R.; Kreutzer, M.T. 2011
A self-similar reaction front develops in reactive ion etching when the ions penetrate channels of shallow height h. This relates to the patterning of microchannels using a single-step etching and... Show moreA self-similar reaction front develops in reactive ion etching when the ions penetrate channels of shallow height h. This relates to the patterning of microchannels using a single-step etching and bonding, as described by Rhee et al. [Lab Chip 5, 102 (2005)]. Experimentally, we report that the front location scales as x(f) similar to ht(1/2) and the width is time-invariant and scales as delta similar to h. Mean-field reaction-diffusion theory and Knudsen diffusion give a semiquantitative understanding of these observations and allow optimization of etching times in relation to bonding requirements. (C) 2011 American Institute of Physics. [doi:10.1063/1.3578450] Show less
We describe the formation of water in oil droplets, which are commonly used in lab-on-a-chip systems for sample generation and dosing, at microfluidic T-shaped nozzles from elastic feed lines. A... Show moreWe describe the formation of water in oil droplets, which are commonly used in lab-on-a-chip systems for sample generation and dosing, at microfluidic T-shaped nozzles from elastic feed lines. A narrow nozzle forms a barrier for a liquid-liquid interface, such that pressure can build up behind the nozzle up to a critical pressure. Above this critical pressure, the liquid bursts into the main channel. Build-up of pressure is possible when the fluid before the nozzle is compressible or when the channel that leads to the nozzle is elastic. We explore the value of the critical pressure and the time required to achieve it. We describe the fluid flow of the sudden burst, globally in terms of flow rate into the channel and spatially resolved in terms of flow fields measured using micro-PIV. A total of three different stages-the lag phase, a spill out phase, and a linear growth phase-can be clearly discriminated during droplet formation. The lag time linearly scales with the curvature of the interface inside the nozzle and is inversly proportional to the flow rate of the dispersed phase. A complete overview of the evolution of the growth of droplets and the internal flow structure is provided in the digital supplement. Show less
We describe the breakup of a confined gas thread in a cross-flowing stream of liquid at capillary numbers Ca < 10(-2). The breakup is initiated, not by a Plateau-Rayleigh instability, but by... Show moreWe describe the breakup of a confined gas thread in a cross-flowing stream of liquid at capillary numbers Ca < 10(-2). The breakup is initiated, not by a Plateau-Rayleigh instability, but by liquid that flows from the tip of the thread to the neck where pinch-off occurs. This flow, faster than previously estimated, is driven by different curvatures at the tip and neck and runs through large gaps between thread and channel walls. Understanding how these curvatures evolve during bubble formation leads to accurate predictions of the moment of pinch-off. Show less
