Analytical model for managing hypotony after implantation surgery of a glaucoma drainage device.

The main aim of glaucoma treatment is to reduce the intraocular pressure (IOP). One of the most common surgical treatments of glaucoma is the implantation of a glaucoma drainage device to drain the aqueous humor from the anterior chamber to a filtration bleb, where the aqueous humor is absorbed. In some cases, the excess of drainage causes ocular hypotony, which constitutes a sight-threatening complication. To prevent hypotony after this intervention, surgeons frequently introduce a suture into the device tube, which increases the hydraulic resistance of the tube and, therefore, the IOP. This study aims to provide an analytical model to correct hypotony following implantation surgery of a glaucoma drainage device, which may help glaucoma surgeons decide on hypotony treatment. The results indicate that the IOP after implanting a cylindrical tube around 300 µm in diameter is essentially the same as that built up in the filtering bleb and can hardly be controlled by introducing a straight suture unless the suture diameter is slightly lower than that of the tube. On the contrary, when the tube diameter is smaller than, for example, 100 µm, significant reductions of the IOP can be obtained by introducing a thin suture into the tube.

Viscoelastic liquid bridge breakup and liquid transfer between two surfaces.

We studied experimentally the breakup of liquid bridges made of aqueous solutions of Poly(acrylic acid) between two separating solid surfaces with freely moving contact lines. For polymer concentrations higher than a certain threshold (~30 ppm), the contact line on the surface with the highest receding contact angle fully retracts before the liquid bridge capillary breakup takes place at its neck. This means that all the liquid remains attached to the opposing surface when the surfaces are separated. This behavior occurs regardless of the range of liquid volume and stretching speed studied. Such behavior is very different from that observed for Newtonian liquids or non-Newtonian systems where contact lines are intentionally pinned. It is shown that this behavior stems from the competition between thinning of bridge neck (delayed by extensional thickening) and receding of contact line (enhanced by shear thinning) on the surface with lower receding contact angle. If the two surfaces exhibit the same wetting properties, the upper contact line fully retracts before the capillary breakup due to the asymmetry caused by gravity, and, therefore, all the liquid remains on the lower surface.

Influence of the surface viscous stress on the pinch-off of free surfaces loaded with nearly-inviscid surfactants.

We analyze the breakup of a pendant water droplet loaded with SDS. The free surface minimum radius measured in the experiments is compared with that obtained from a numerical solution of the Navier-Stokes equations for different values of the shear and dilatational surface viscosities. This comparison shows the small but measurable effect of the surface viscous stresses for sufficiently small spatiotemporal distances from the breakup point, and allows to establish upper bounds for the values of the shear and dilatational viscosities. We study numerically the distribution of Marangoni and viscous stresses over the free surface as a function of the time to the pinching, and describe how surface viscous stresses grow in the pinching region as the free surface approaches its breakup. When Marangoni and surface viscous stresses are taken into account, the surfactant is not swept away from the thread neck in the time interval analyzed. Surface viscous stresses eventually balance the driving capillary pressure in the pinching region for small enough values of the time to pinching. Based on this result, we propose a scaling law to account for the effect of the surface viscosities on the last stage of temporal evolution of the neck radius.

Dripping, jetting and tip streaming.

Dripping, jetting and tip streaming have been studied up to a certain point separately by both fluid mechanics and microfluidics communities, the former focusing on fundamental aspects while the latter on applications. Here, we intend to review this field from a global perspective by considering and linking the two sides of the problem. First, we present the theoretical model used to study interfacial flows arising in droplet-based microfluidics, paying attention to three elements commonly present in applications: viscoelasticity, electric fields and surfactants. We review both classical and current results of the stability of jets affected by these elements. Mechanisms leading to the breakup of jets to produce drops are reviewed as well, including some recent advances in this field. We also consider the relatively scarce theoretical studies on the emergence and stability of tip streaming in open systems. Second, we focus on axisymmetric microfluidic configurations which can operate on the dripping and jetting modes either in a direct (standard) way or via tip streaming. We present the dimensionless parameters characterizing these configurations, the scaling laws which allow predicting the size of the resulting droplets and bubbles, as well as those delimiting the parameter windows where tip streaming can be found. Special attention is paid to electrospray and flow focusing, two of the techniques more frequently used in continuous drop production microfluidics. We aim to connect experimental observations described in this section of topics with fundamental and general aspects described in the first part of the review. This work closes with some prospects at both fundamental and practical levels.

A method for measuring the interfacial tension for density-matched liquids.

We propose a method to measure the interfacial tension characterizing the interface between two immiscible liquids of practically the same density. In this method, a cylindrical liquid bridge made of one the liquids is vibrated laterally inside a tank filled with the other. The first resonance frequency is determined and equated to the first eigenfrequency of the m=1 linear mode to infer the interfacial tension value. The method does not involve the density jump across the interface. Therefore, its accuracy is affected neither by the smallness of the Bond number nor by errors of the density difference. The experimental setup is relatively simple, and the procedure does not use image processing techniques. The results satisfactorily agree with those measured by TIFA-AI (Theoretical Fitting Image Analysis-Axisymmetric Interfaces) for the same liquid bridges when the density difference is sufficiently large for TIFA-AI to be valid. We conduct numerical simulations of the Navier-Stokes equations to determine the best parameter conditions for the proposed method. The transfer function characterizing the frequency response of the fluid configuration is measured in some experiments to quantify non-linear effects and to study the role played by the outer bath vibration.

Influence of an iris-fixed phakic intraocular lens on the transport of nutrients by the aqueous humor.

We study numerically the influence of an iris-fixed phakic intraocular lens (PIOL) on the transport of nutrients by the aqueous humor across a realistic model of the human eye. The Boussinesq equations are solved to calculate the velocity field both in the anterior and posterior chambers. The transport of the nutrient is modeled as that of a passive scalar convected by that velocity field and diffused by the concentration gradient. The nutrient is assumed to be adsorbed at the non-vascularized tissues, i.e., the crystalline lens and cornea endothelium. The adsorption rates at the crystalline and cornea endothelium are supposed to be proportional to the nutrient concentration there. The comparison between the results obtained with and without the PIOL allows us to quantify the influence of this device on the nutrient supply from the aqueous humor. The amount of nutrient adsorbed onto the crystalline is hardly affected by the presence of the PIOL in the anterior chamber, even though there is an iridotomy in this case. When the PIOL is implanted, the flux adsorbed onto the cornea endothelium increases up to around 32% for the highest value of the adsorption coefficient, and hardly varies for the other values of this parameter. This counterintuitive effect is explained by the efficient role played by the iridotomy in evacuating the nutrient from the posterior to the anterior chamber. Based on these results, one can estimate the variation of glucose available in the cornea endothelium after implanting the PIOL, and discuss potential effects on the cell metabolism. These simulations can be regarded as a first attempt to shed light on the mechanisms responsible for the supply of oxygen and glucose to eye avascular structures like the cornea endothelium and crystalline.

Numerical analysis of the pressure drop across highly-eccentric coronary stenoses: application to the calculation of the fractional flow reserve.

BACKGROUND: Fractional flow reverse (FFR) is the gold standard assessment of the hemodynamic significance of coronary stenoses. However, it requires the catheterization of the coronary artery to determine the pressure waveforms proximal and distal to the stenosis. On the contrary, computational fluid dynamics enables the calculation of the FFR value from relatively non-invasive computed tomography angiography (CTA). METHODS: We analyze the flow across idealized highly-eccentric coronary stenoses by solving the Navier-Stokes equations. We examine the influence of several aspects (approximations) of the simulation method on the calculation of the FFR value. We study the effects on the FFR value of errors made in the segmentation of clinical images. For this purpose, we compare the FFR value for the nominal geometry with that calculated for other shapes that slightly deviate from that geometry. This analysis is conducted for a range of stenosis severities and different inlet velocity and pressure waveforms. RESULTS AND CONCLUSIONS: The errors made in assuming a uniform velocity profile in front of the stenosis, as well as those due to the Newtonian and laminar approximations, are negligible for stenosis severities leading to FFR values around the threshold 0.8. The limited resolution of the stenosis geometry reconstruction is the major source of error when predicting the FFR value. Both systematic errors in the contour detection of just 1-pixel size in the CTA images and a low-quality representation of the stenosis surface (coarse faceted geometry) may yield wrong outcomes of the FFR assessment for an important set of eccentric stenoses. On the contrary, the spatial resolution of images acquired with optical coherence tomography may be sufficient to ensure accurate predictions for the FFR value.

Erratum: Influence of the Surface Viscosity on the Breakup of a Surfactant-Laden Drop [Phys. Rev. Lett. 118, 024501 (2017)].

This corrects the article DOI: 10.1103/PhysRevLett.118.024501.

Stabilization of axisymmetric liquid bridges through vibration-induced pressure fields.

Previous theoretical studies have indicated that liquid bridges close to the Plateau-Rayleigh instability limit can be stabilized when the upper supporting disk vibrates at a very high frequency and with a very small amplitude. The major effect of the vibration-induced pressure field is to straighten the liquid bridge free surface to compensate for the deformation caused by gravity. As a consequence, the apparent Bond number decreases and the maximum liquid bridge length increases. In this paper, we show experimentally that this procedure can be used to stabilize millimeter liquid bridges in air under normal gravity conditions. The breakup of vibrated liquid bridges is examined experimentally and compared with that produced in absence of vibration. In addition, we analyze numerically the dynamics of axisymmetric liquid bridges far from the Plateau-Rayleigh instability limit by solving the Navier-Stokes equations. We calculate the eigenfrequencies characterizing the linear oscillation modes of vibrated liquid bridges, and determine their stability limits. The breakup process of a vibrated liquid bridge at that stability limit is simulated too. We find qualitative agreement between the numerical predictions for both the stability limits and the breakup process and their experimental counterparts. Finally, we show the applicability of our technique to control the amount of liquid transferred between two solid surfaces.

Numerical and experimental analysis of the transitional flow across a real stenosis.

In this paper, we present a numerical study of the pulsatile transitional flow crossing a severe real stenosis located right in front of the bifurcation between the right subclavian and right common carotid arteries. The simulation allows one to determine relevant features of this subject-specific flow, such as the pressure waves in the right subclavian and right common carotid arteries. We explain the subclavian steal syndrome suffered by the patient in terms of the drastic pressure drop in the right subclavian artery. This pressure drop is caused by both the diverging part of the analyzed stenosis and the reverse flow in the bifurcation induced by another stenosis in the right internal carotid artery.

Influence of the Surface Viscosity on the Breakup of a Surfactant-Laden Drop.

We examine both theoretically and experimentally the breakup of a pendant drop loaded with an insoluble surfactant. The experiments show that a significant amount of surfactant is trapped in the resulting satellite droplet. This result contradicts previous theoretical predictions, where the effects of surface tension variation were limited to solutocapillarity and Marangoni stresses. We solve numerically the hydrodynamic equations, including not only those effects but also those of surface shear and dilatational viscosities. We show that surface viscosities play a critical role to explain the accumulation of surfactant in the satellite droplet.

Monosized dripping mode of axisymmetric flow focusing.

We identify and analyze the perfectly regular dripping mode of flow focusing. This mode occurs within narrow intervals of injected flow rates and applied pressure drops and leads to homogeneous-size droplets with diameters similar to or smaller than that of the discharge orifice. The balance between the local acceleration of the fluid particle and the applied pressure drop yields the scaling law for the droplet diameter. This scaling law is validated experimentally with excellent accord.

The onset of electrospray: the universal scaling laws of the first ejection.

The disintegration of liquid drops with low electrical conductivity and subject to an electric field is investigated both theoretically and experimentally. This disintegration takes place through the development of a conical cusp that eventually ejects an ultrathin liquid ligament. A first tiny drop is emitted from the end of this ligament. Due to its exceptionally small size and large electric charge per unit volume, that drop has been the object of relevant recent studies. In this paper, universal scaling laws for the diameter and electric charge of the first issued droplet are proposed and validated both numerically and experimentally. Our analysis shows how charge relaxation is the mechanism that differentiates the onset of electrospray, including the first droplet ejection, from the classical steady cone-jet mode. In this way, our study identifies when and where charge relaxation and electrokinetic phenomena come into play in electrospray, a subject of live controversy in the field.

Convective-to-absolute instability transition in a viscoelastic capillary jet subject to unrelaxed axial elastic tension.

The convective-to-absolute instability transition in an Oldroyd-B capillary jet subject to unrelaxed axial stress is examined theoretically. There is a critical Weber number below which the jet is absolutely unstable under axisymmetric perturbations. We analyze the dependence of this critical parameter with respect to the Reynolds and Deborah numbers, as well as the unrelaxed axial stress. For small Deborah numbers, the unrelaxed stress destabilizes the viscoelastic jet, increasing the critical Weber number for which the convective-to-absolute instability transition takes place. If the Deborah number takes higher values, then the transitional Weber number decreases as the unrelaxed stress increases until two solution branches cross each other. The dominant branch for large axial stress leads to a threshold of this quantity above which the viscoelastic jet becomes absolutely unstable independently of the Weber number. The threshold depends on neither the Reynolds nor the Deborah number for sufficiently large values of these parameters.

Dynamics of an axisymmetric liquid bridge close to the minimum-volume stability limit.

We analyze both theoretically and experimentally the dynamical behavior of an isothermal axisymmetric liquid bridge close to the minimum-volume stability limit. First, the nature of this stability limit is investigated experimentally by determining the liquid bridge response to a mass force pulse for volumes just above that limit. In our experiments, the liquid bridge breakup takes place only when the critical volume is surpassed and is never triggered by the mass force pulse. Second, the growth of the small-amplitude perturbation mode initiating the liquid bridge breakage is measured experimentally and calculated from the linearized Navier-Stokes equations. The results of the linear stability analysis allow one to explain why liquid bridges with volumes just above the stability limit are so robust. Finally, the nonlinear process leading to the liquid bridge breakup is described from both experimental data and the solution of the full Navier-Stokes equations. Special attention is paid to the free-surface pinchoff. The results show that the flow becomes universal (independent of both the initial and boundary conditions) sufficiently close to that singularity and suggest that the transition from the inviscid to the viscous regime is about to take place in the final stage of both the experiments and numerical simulations.

Production of microbubbles from axisymmetric flow focusing in the jetting regime for moderate Reynolds numbers.

We analyze both experimentally and numerically the formation of microbubbles in the jetting regime reached when a moderately viscous liquid stream focuses a gaseous meniscus inside a converging micronozzle. If the total (stagnation) pressure of the injected gas current is fixed upstream, then there are certain conditions on which a quasisteady gas meniscus forms. The meniscus tip is sharpened by the liquid stream down to the gas molecular scale. On the other side, monodisperse collections of microbubbles can be steadily produced in the jetting regime if the feeding capillary is appropriately located inside the nozzle. In this case, the microbubble size depends on the feeding capillary position. The numerical simulations for an imposed gas flow rate show that a recirculation cell appears in the gaseous meniscus for low enough values of that parameter. The experiments allow one to conclude that the bubble pinch-off comprises two phases: (i) a stretching motion of the precursor jet where the neck radius versus the time before the pinch essentially follows a potential law, and (ii) a final stage where a very thin and slender gaseous thread forms and eventually breaks apart into a number of micron-sized bubbles. Because of the difference between the free surface and core velocities, the gaseous jet breakage differs substantially from that of liquid capillary jets and gives rise to bubbles with diameters much larger than those expected from the Rayleigh-type capillary instability. The dependency of the bubble diameter upon the flow-rate ratio agrees with the scaling law derived by A. M. Gañán-Calvo [Phys. Rev. E 69, 027301 (2004)], although a slight influence of the Reynolds number can be observed in our experiments.

Theoretical investigation of a technique to produce microbubbles by a microfluidic T junction.

A microfluidic technique is proposed to produce microbubbles. A gaseous stream is injected through a T junction into a channel transporting a liquid current. The gas adheres to a hydrophobic strip printed on the channel surface. When the gas and liquid flow rates are set appropriately, a gaseous rivulet flows over that strip. The rivulet breaks up downstream due to a capillary pearling instability, which leads to a monodisperse collection of microbubbles that can be much smaller than the channel size. The physics of the process is theoretically investigated, using both full numerical simulation of the Navier-Stokes equations and a linear stability analysis of an infinite gaseous rivulet driven by a coflowing liquid stream. This stability analysis allows one to determine a necessary condition to get this effect in a T junction device. It also provides reasonably good predictions for the size of the produced microbubbles as obtained from numerical experiments.

Building functional materials for health care and pharmacy from microfluidic principles and Flow Focusing.

In this review, we aim at establishing a relationship between the fundamentals of the microfluidics technologies used in the Pharmacy field, and the achievements accomplished by those technologies. We describe the main methods for manufacturing micrometer drops, bubbles, and capsules, as well as the corresponding underlying physical mechanisms. In this regard, the review is intended to show non-specialist readers the dynamical processes which determine the success of microfluidics techniques. Flow focusing (FF) is a droplet-based method widely used to produce different types of fluid entities on a continuous basis by applying an extensional co-flow. We take this technique as an example to illustrate how microfluidics technologies for drug delivery are progressing from a deep understanding of the physics of fluids involved. Specifically, we describe the limitations of FF, and review novel methods which enhance its stability and robustness. In the last part of this paper, we review some of the accomplishments of microfluidics when it comes to drug manufacturing and delivery. Special attention is paid to the production of the microencapsulated form because this fluidic structure gathers the main functionalities sought for in Pharmacy. We also show how FF has been adapted to satisfy an ample variety of pharmaceutical requirements to date.