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

Precise and effective control of droplet generation is critical for applications of droplet microfluidics ranging from materials synthesis to lab-on-a-chip systems. Methods for droplet generation can be either passive or active, where the former generates droplets without external actuation, and the latter makes use of additional energy input in promoting interfacial instabilities for droplet generation. A unified physical understanding of both passive and active droplet generation is beneficial for effectively developing new techniques meeting various demands arising from applications. Our review of passive approaches focuses on the characteristics and mechanisms of breakup modes of droplet generation occurring in microfluidic cross-flow, co-flow, flow-focusing, and step emulsification configurations. The review of active approaches covers the state-of-the-art techniques employing either external forces from electrical, magnetic and centrifugal fields or methods of modifying intrinsic properties of flows or fluids such as velocity, viscosity, interfacial tension, channel wettability, and fluid density, with a focus on their implementations and actuation mechanisms. Also included in this review is the contrast among different approaches of either passive or active nature.

Passive and active droplet generation with microfluidics: a review

Ink-jet printing is a method for directly patterning and fabricating patterns without the need for masks. To achieve this, the fluids used as inks must have the capability of being stably and accurately printed by ink-jetting. We have investigated the inter-relationship between ink-jet printability and physical fluid properties by monitoring droplet formation dynamics. The printability of the fluids was determined using the inverse (Z) of the Ohnesorge number (Oh) which relates to the viscosity, surface tension, and density of the fluid. We have experimentally defined the printable range as 4 ≤ Z ≤ 14 by considering characteristics such as single droplet formability, positional accuracy, and maximum allowable jetting frequency.

Influence of fluid physical properties on ink-jet printability.

The dynamics of the piezo inkjet printhead operation

Purpose – The purpose of this paper is to present an exhaustive review of research studies and activities in the inkjet printing of conductive materials.Design/methodology/approach – This paper gives a detailed literature survey of research carried out in inkjet printing of conductive materials.Findings – This article explains the inkjet printing process and the various types of conductive inks. It then examines the various factors that affect the quality of inkjet printed interconnects such as printing parameters, materials and substrate treatments. Methods of characterising both the inkjet printing process and the electrical properties of printed conductive materials are also presented. Finally relevant applications of this technology are described.Originality/value – Inkjet printing is currently one of the cheapest direct write techniques for manufacturing. The use of this technique in electronic manufacturing, where interconnects and other conductive features are required is an area of increasing rele...

Inkjet printing of conductive materials: a review

http://absimage.aps.org/image/DFD05/MWS_DFD05-2005-000822.pdf

\textbf{Surfactant effects in dynamics and breakup of a contracting liquid filament}

Motivated by the desire to improve the theoretical understanding of drop-on-demand (DOD) ink-jet printing, a computational analysis is carried out to simulate the formation of liquid drops of incompressible Newtonian fluids from a simple capillary tube by imposing a transient flow rate upstream of the nozzle exit. Since the flow in a typical ink-jet nozzle is toward the nozzle outlet during part of the time and away from the nozzle outlet at other times, an inflow rate is adopted here that captures the essential physics and is given in dimensionless form by Q=(πWe∕2)sinΩt, where We is the Weber number (inertial/surface tension force), Ω is the frequency, and t is time. The dynamics are studied as functions of We, Ω, and the Ohnesorge number Oh (viscous/surface tension force). For a common ink forming from a nozzle of 10μm radius, Oh=0.1. For this typical case, a phase or operability diagram in (We,Ω)-space is developed that shows that three regimes of operation are possible. In the first regime, where We ...

Computational analysis of drop-on-demand drop formation

The drop weight method is an accurate yet simple technique for determining surface tension σ. It relies on dripping a liquid of density ρ at a low flow rate Q from a capillary of radius R into air and measuring the combined volumes of the primary and satellite drops that are formed. The method’s origin can be traced to Tate, who postulated that the volume Videal of the drop that falls from the capillary should be given by ρgVideal=2πRσ, where g is the gravitational acceleration. Since Tate’s law is only an approximation and the actual drop volume Vf<Videal, in practice the surface tension of the liquid-air interface is determined from the experimental master curve due to Harkins and Brown (HB). The master curve is a plot of the fraction of the ideal drop volume, Ψ≡Vf∕Videal, as a function of the dimensionless tube radius, Φ≡R∕Vf1∕3. Thus, once the actual drop volume Vf, and hence Φ, is known, σ is readily calculated upon determining the value of Ψ from the master curve and that Ψ=ρgVf∕2πRσ. Alth...

Analysis of the drop weight method

Continuous emission of drops of an incompressible Newtonian liquid from a tube–dripping–is a much studied problem because it is important in applications as diverse as inkjet printing, microarraying, and microencapsulation, and recognized as the prototypical nonlinear dynamical system, viz., the leaky faucet. The faucet’s dynamics are studied in this paper by a combination of experiment, using high-speed imaging, and computation, in which the one-dimensional slender-jet equations are solved numerically by finite element analysis, over ranges of the governing parameters that have heretofore been unexplored. Previous studies when the Bond number G that measures the relative importance of gravitational to surface tension force is moderate, G≈0.5, and the Ohnesorge number Oh that measures the relative importance of viscous to surface tension force is low, Oh≈0.1, have shown that the dynamics changes from (a) simple dripping, i.e., period-1 dripping with or without satellites, to (b) complex dripping, where the system exhibits period doubling bifurcations and hysteresis, to (c) jetting, as the Weber number We that measures the relative importance of inertial to surface tension force increases. New experiments and computations reveal that lowering the Bond number to G≈0.3 while holding Oh fixed results in profound simplification of the behavior of the faucet. At the lower value of G, the faucet exhibits simply period-1 dripping, period-2 dripping, and jetting as We increases. Experimental and computational bifurcation diagrams when G≈0.3 and Oh≈0.1 that depict the variation of drop length or volume at breakup with We are reported and shown to agree well with each other. The range of We over which the faucet exhibits complex dripping when G≈0.3 is shown by both experiment and computation to shrink as Oh increases. Computations are also used to develop a comprehensive phase diagram when G≈0.3 that shows transitions between simple dripping and complex dripping, and those between dripping and jetting in (We,Oh) space. Similar to the case of G≈0.5, dripping faucets of high viscosity (Oh) liquids are shown to transition directly from simple dripping to jetting without exhibiting complex dripping when G≈0.3. When G≈0.3, computed values of We that signal transition from dripping to jetting are further shown to accord well with estimates obtained from scaling analyses. By contrast, new computations in which the Bond number is increased to G≈1, while Oh is held fixed at Oh≈0.1, reveal that the faucet’s response becomes quite complex for large G. In such situations, the computations predict theoretical occurrence of (a) rare period-3 dripping and period-3 intermittence, which have previously been surmised solely by the use of ad hoc spring-mass models of dripping, and (b) chaotic attractors. Therefore, by combining insights from earlier studies and the detailed response of dripping which has been obtained here by varying (i) Oh as 0.01⩽Oh⩽2, a range that is typical of most practical applications, (ii) We from virtually zero to a value just exceeding that at which the system transitions from dripping to jetting, and (iii) G from a small value to a value approaching that beyond which controlled formation of drops is prohibited, this paper provides a comprehensive understanding of the effect of the governing parameters on the nonlinear dynamics of dripping.

Simplicity and complexity in a dripping faucet

Surfactants lower surface tension and are used to facilitate breakup and spreading. How much surfactant remains where a filament of initial radius R breaks is set by the ratio of convection, which sweeps surfactant away, to diffusion, which replenishes it, or Peclet number Pe proportional, variantR. Thus, as is well known, surfactant concentration Gamma-->0 when a macroscale filament breaks. Here theory and simulation are used to investigate pinch-off of microscopic filaments. At breakup, Gamma is shown to be nonzero but uniform on a filament of negligible Pe. Since R must be finite, the zero-Pe limit is transitory and yields to a final regime. Two such regimes with distinct dynamics characterized by different scaling exponents are reported.

Qi Xu

Papers

\textbf{Surfactant effects in dynamics and breakup of a contracting liquid filament}

Computational analysis of drop-on-demand drop formation

Analysis of the drop weight method

Simplicity and complexity in a dripping faucet

Can surfactant be present at pinch-off of a liquid filament?