A front-tracking method for viscous, incompressible, multi-fluid flows

This article describes the process of formation of droplets and bubbles in microfluidic T-junction geometries. At low capillary numbers break-up is not dominated by shear stresses: experimental results support the assertion that the dominant contribution to the dynamics of break-up arises from the pressure drop across the emerging droplet or bubble. This pressure drop results from the high resistance to flow of the continuous (carrier) fluid in the thin films that separate the droplet from the walls of the microchannel when the droplet fills almost the entire cross-section of the channel. A simple scaling relation, based on this assertion, predicts the size of droplets and bubbles produced in the T-junctions over a range of rates of flow of the two immiscible phases, the viscosity of the continuous phase, the interfacial tension, and the geometrical dimensions of the device.

http://ichf.pong.pl/i/publications/29.pdf

Formation of droplets and bubbles in a microfluidic T-junction-scaling and mechanism of break-up.

Jets, ie collimated streams of matter, occur from the microscale up to the large-scale structure of the universe Our focus will be mostly on surface tension effects, which result from the cohesive properties of liquids Paradoxically, cohesive forces promote the breakup of jets, widely encountered in nature, technology and basic science, for example in nuclear fission, DNA sampling, medical diagnostics, sprays, agricultural irrigation and jet engine technology Liquid jets thus serve as a paradigm for free-surface motion, hydrodynamic instability and singularity formation leading to drop breakup In addition to their practical usefulness, jets are an ideal probe for liquid properties, such as surface tension, viscosity or non-Newtonian rheology They also arise from the last but one topology change of liquid masses bursting into sprays Jet dynamics are sensitive to the turbulent or thermal excitation of the fluid, as well as to the surrounding gas or fluid medium The aim of this review is to provide a unified description of the fundamental and the technological aspects of these subjects

Physics of liquid jets

The dynamics and stability of thin liquid films have fascinated scientists over many decades: the observations of regular wave patterns in film flows down a windowpane or along guttering, the patterning of dewetting droplets, and the fingering of viscous flows down a slope are all examples that are familiar in daily life. Thin film flows occur over a wide range of length scales and are central to numerous areas of engineering, geophysics, and biophysics; these include nanofluidics and microfluidics, coating flows, intensive processing, lava flows, dynamics of continental ice sheets, tear-film rupture, and surfactant replacement therapy. These flows have attracted considerable attention in the literature, which have resulted in many significant developments in experimental, analytical, and numerical research in this area. These include advances in understanding dewetting, thermocapillary- and surfactant-driven films, falling films and films flowing over structured, compliant, and rapidly rotating substrates, and evaporating films as well as those manipulated via use of electric fields to produce nanoscale patterns. These developments are reviewed in this paper and open problems and exciting research avenues in this thriving area of fluid mechanics are also highlighted.

Dynamics and stability of thin liquid films

This article describes the dynamics of drop deformation and breakup in viscous flows at low Reynolds numbers. An attempt has been made to bring together a wide range of studies in the drop deformation literature, as well as to provide a large number of references to potential applications. In particular, a summary is provided of experimental, numerical, and theoretical investigations that examine drop breakup in externally­ imposed flows, e.g. uniaxial extensional fluid motion or more complicated time-periodic flows. For well-characterized flow conditions that lead to breakup, the effects of flow and material parameters on the drop size distribution are summarized. Also, a short discussion is given of the stability of the shapes of translating drops. The subject of deformation of neutrally buoyant drops in viscous shear flows at low particle Reynolds numbers was summarized by Acrivos ( 1983) and was reviewed in this series by Rallison ( 1 984). The Acrivos and Rallison papers present (a) theoretical descriptions of steady, nearly spheri­ cal shapes and steady, long slender shapes, (b) a description of efficient boundary integral numerical methods, and (e) a summary of the experi­ mental work performed prior to 1984. As documented in these review articles, many of the important ideas necessary for understanding drop

Dynamics of Drop Deformation and Breakup in Viscous Fluids

The deformation of a liquid capsule enclosed by an elastic membrane in an infinite simple shear flow is studied numerically at vanishing Reynolds numbers using a boundary-element method. The surface of the capsule is discretized into quadratic triangular elements that form an evolving unstructured grid. The elastic membrane tensions are expressed in terms of the surface deformation gradient, which is evaluated from the position of the grid points. Compared to an earlier formulation that uses global curvilinear coordinates, the triangular-element formulation suppresses numerical instabilities due to uneven discretization and thus enables the study of large deformations and the investigation of the effect of fluid viscosities. Computations are performed for capsules with spherical, spheroidal, and discoidal unstressed shapes over an extended range of the dimensionless shear rate and for a broad range of the ratio of the internal to surrounding fluid viscosities. Results for small deformations of spherical capsules are in quantitative agreement with the predictions of perturbation theories. Results for large deformations of spherical capsules and deformations of non-spherical capsules are in qualitative agreement with experimental observations of synthetic capsules and red blood cells. We find that initially spherical capsules deform into steady elongated shapes whose aspect ratios increase with the magnitude of the shear rate. A critical shear rate above which capsules exhibit continuous elongation is not observed for any value of the viscosity ratio. This behaviour contrasts with that of liquid drops with uniform surface tension and with that of axisymmetric capsules subject to a stagnation-point flow. When the shear rate is sufficiently high and the viscosity ratio is sufficiently low, liquid drops exhibit continuous elongation leading to breakup. Axisymmetric capsules deform into thinning needles at sufficiently high rates of elongation, independent of the fluid viscosities. In the case of capsules in shear flow, large elastic tensions develop at large deformations and prevent continued elongation, stressing the importance of the vorticity of the incident flow. The long-time behaviour of deformed capsules depends strongly on the unstressed shape. Oblate capsules exhibit unsteady motions including oscillation about a mean configuration at low viscosity ratios and continuous rotation accompanied by periodic deformation at high viscosity ratios. The viscosity ratio at which the transition from oscillations to tumbling occurs decreases with the sphericity of the unstressed shape. Results on the effective rheological properties of dilute suspensions confirm a non-Newtonian shear-thinning behaviour.

Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of fluid viscosities

The effect of interfacial bending stiffness on the deformation of liquid capsules enclosed by elastic membranes is discussed and investigated by numerical simulation. Flow-induced deformation causes the development of in-plane elastic tensions and bending moments accompanied by transverse shear tensions due to the non-infinitesimal membrane thickness or to a preferred configuration of an interfacial molecular network. To facilitate the implementation of the interfacial force and torque balance equations involving the hydrodynamic traction exerted on either side of the interface and the interfacial tensions and bending moments developing in the plane of the interface, a formulation in global Cartesian coordinates is developed. The balance equations involve the Cartesian curvature tensor defined in terms of the gradient of the normal vector extended off the plane of the interface in an appropriate fashion. The elastic tensions are related to the surface deformation gradient by constitutive equations derived by previous authors, and the bending moments for membranes whose unstressed shape has uniform curvature, including the sphere and a planar sheet, arise from a constitutive equation that involves the instantaneous Cartesian curvature tensor and the curvature of the resting configuration. A numerical procedure is developed for computing the capsule deformation in Stokes flow based on standard boundary-element methods. Results for spherical and biconcave resting shapes resembling red blood cells illustrate the effect of the bending modulus on the transient and asymptotic capsule deformation and on the membrane tank-treading motion.

Effect of membrane bending stiffness on the deformation of capsules in simple shear flow

Motion and deformation of liquid drops, and the rheology of dilute emulsions in simple shear flow

The transient deformation of liquid capsules enclosed by elastic membranes subject to simple shear flow is studied numerically using a new implementation of the boundary element method. The numerical results for capsules with spherical unstressed shapes and varying degrees of surface elasticity are compared with the predictions of an asymptotic theory for small deformations due to Barthes-Biesel and coworkers, and the significance of nonlinear effects due to finite deformation is assessed. It is found that the capsules exhibit continuous elongation when the dimensionless shear rate becomes larger than a critical threshold, in agreement with recent experimental observations of capsules with polymerized interfaces. Membrane failure at large deformations is discussed with respect to membrane thinning and development of excessive elastic tensions, and it is argued that the location where the membrane is likely to rupture due to continued deformation is insensitive to the precise mechanism of rupture. The numerical results suggest that a dilute suspension of capsules behaves like shear-thinning medium with some elastic properties. Results of oblate spheroidal capsules suggest that the points of maximum membrane thinning and tension coincide but their location depends upon the unstressed capsule shape.

Finite deformation of liquid capsules enclosed by elastic membranes in simple shear flow

Peristaltic flow in two-dimensional channels with sinusoidal waves is analysed. Under the assumption of creeping motion, the problem is formulated using the boundary integral method for Stokes flow. The effect of channel width, wave amplitude, phase shift, and mean pressure gradient on the streamline pattern and the properties of the flow is considered. The results are discussed with reference to various physiological and engineering processes. It is suggested that under the quasi-steady approximation, peristaltic flow with a varying mean pressure gradient offers an efficient method for molecular-convective transport.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112087001939

C. Pozrikidis

Papers

Deformation of liquid capsules enclosed by elastic membranes in simple shear flow: large deformations and the effect of fluid viscosities

Effect of membrane bending stiffness on the deformation of capsules in simple shear flow

Motion and deformation of liquid drops, and the rheology of dilute emulsions in simple shear flow

Finite deformation of liquid capsules enclosed by elastic membranes in simple shear flow

A study of peristaltic flow