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2024 | Book

Tip Streaming of Simple and Complex Fluids

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About this book

This book comprehensively describes the tip streaming in simple fluids and those containing surfactants and polymeric molecules. It summarizes the theoretical models and approximations commonly adopted to analyze this phenomenon. It provides relevant experimental results and presents the scaling laws for rationalizing those results. The stability of the flows leading to tip streaming is analyzed theoretically and experimentally. Attention is paid to the effects of surfactant monolayers and viscoelasticity, including solutocapillarity, interfacial elasticity, surface viscosity, and extensional thickening caused by the polymer coil-stretch transition.

It also offers an overall perspective of the numerous technological applications of the tip-streaming phenomenon. Remarkable examples are the production of microemulsions and microencapsulation of active agents for the food and pharmacy industries, the atomization of charged liquids for analytical chemistry, and the ejection of ultra-fast and ultra-thin jets for crystallography.

Physical mechanisms responsible for the onset of tip streaming driven by hydrodynamic and electrohydrodynamic forces are described. Relevant theoretical and experimental results of the periodic microdripping and continuous microjetting modes of tip streaming produced with microfluidic configurations such as electrospray, flow focusing, coflowing, and selective withdrawal are discussed. The physical mechanisms responsible for the instability of the microjetting mode are studied in detail.

The book collects the scaling laws used to predict the outcome of the microfluidic configurations mentioned above. The author combines state-of-the-art experimental results and linear stability analysis to identify the instability mechanisms limiting the applicability of the above-mentioned microfluidic configurations. In this way, the book connects experimental observations with fundamental aspects of tip streaming,bridging the microfluidic and fluid dynamicist communities. The connection between results obtained from the theoretical and experimental approaches will help experimentalists to understand the fundamental aspects of their practical problems. A useful guide for researchers working on hydrodynamic focusing and electrospray.

Table of Contents

Frontmatter
Chapter 1. Introduction
Abstract
This book’s title requires clarifying two concepts: “tip streaming” and “complex fluid.” In essence, tip streaming is the flow producing tiny drops or jets from the tip of a mother droplet, fluid meniscus, or liquid film. We devote the first part of this chapter to motivating and contextualizing the tip streaming phenomenon. We also introduce the microfluidic configurations commonly used to produce this singular flow. These configurations and their specific applications will be analyzed in more detail throughout the text.
The term “complex fluids” has been coined to refer to substances involving the coexistence of several phases, such as foams, suspensions, and emulsions. It also refers to fluids containing colloids and macromolecules, as well as liquid crystals and quantum fluids, among others. Here, we use this term to refer only to liquids containing surfactant molecules or polymer chains, which produce interfacial and bulk viscoelastic effects, respectively. As explained in other chapters, surfactants and polymers substantially alter the tip streaming flow in many technologically relevant applications. In the last part of this chapter, we briefly describe these two elements. We also introduce the effect of externally applied electric fields, which drive the flow in many tip streaming realizations.
José María Montanero
Chapter 2. Governing Equations
Abstract
This chapter presents the equations framing the tip streaming phenomenon. These equations provide the theoretical framework to analyze the microfluidic applications studied in other chapters. We consider simple models for describing the effects of viscoelasticity, surfactants, and externally applied electric fields. In this latter case, we introduce the frequently used charge-conservative approximation and leaky-dielectric model, which allow for examining electrohydrodynamic processes in a relatively simple way. The relationship between these approaches and the full electrokinetic model is discussed.
We introduce some rheological models to obtain the polymer stress in dilute viscoelastic liquids. We present the equations describing the transport and conservation of surfactants in the hydrodynamic bulk and interface, simple kinetic models to account for the adsorption-desorption processes, and commonly used equations of state to calculate the interfacial tension as a function of the surfactant surface density. The surface viscous stresses caused by a Newtonian surfactant monolayer are considered as well. The chapter closes with the one-dimensional (1D) approximation for slender configurations, such as jets with relatively small spatial accelerations.
José María Montanero
Chapter 3. Theoretical Methods
Abstract
This chapter briefly describes the theoretical approaches commonly used to gain insight into the tip streaming phenomenon. These approaches allow one to solve or at least obtain information from the governing equations presented in the previous chapter.
We discuss the main characteristics of direct numerical simulations and global and local stability analyses. The differences between these two last approaches are explained to emphasize the importance of the global stability analysis for tip streaming. Concepts such as global modes, asymptotic stability, and short-term response are also discussed.
The temporal and spatiotemporal local stability analyses provide information on the behavior of the jets emitted in the microjetting mode of the tip streaming configurations. This chapter closes with some results obtained from those analyses and directly related to those configurations, including the effects of electric fields, surfactants, and viscoelasticity.
José María Montanero
Chapter 4. Experimental Methods
Abstract
The tip streaming of simple fluids is affected by the densities and viscosities of the phases involved in the phenomenon, as well as by the surface tensions of the interfaces formed between them. In addition, electrical conductivities and permittivities are essential when electrohydrodynamic forces drive this phenomenon. As explained in Chap. 1, complex fluids are referred to as those including surfactant molecules and polymer chains. The tip streaming of these fluids involves additional physical properties that must be known to analyze the phenomenon. The first section of this chapter describes the experimental techniques commonly used to characterize complex fluids for studying tip streaming.
The analysis of the tip streaming flow relies on visualization techniques in practically all the experiments. The method most frequently used for this purpose is the observation of the interface contour, in many cases using high-speed imaging. The last section of this chapter reviews the most relevant aspects of this methodology. We also briefly describe some specific characteristics of particle image velocimetry.
José María Montanero
Chapter 5. Electrohydrodynamic Transient Tip Streaming
Abstract
Tip streaming can be classified into two fundamentally different categories: transient tip streaming and periodic microdripping/steady microjetting. We devote this chapter and Chap. 6 to analyzing the first category.
Electrohydrodynamic and hydrodynamic forces can power transient tip streaming. This chapter presents some results for transient tip streaming driven by electrohydrodynamic forces. Special attention will be paid to a low-conductivity droplet subject to a strong electric field. We will consider the mechanism leading to the onset of tip streaming, examining the role of charge relaxation. The scaling laws for the size and charge of the first-emitted droplet are reviewed.
José María Montanero
Chapter 6. Hydrodynamic Transient Tip Streaming
Abstract
As mentioned in the previous chapter, tip streaming can be categorized into two different classes: transient tip streaming and microdripping/microjetting. This chapter reviews some transient tip streaming flows produced by hydrodynamics means. Specifically, we consider a surfactant-loaded droplet in a linear extensional flow, the viscous entrainment of selective withdrawal, and bubble bursting. The chapter closes by mentioning other examples that have received less attention.
We consider both the subcritical steady flow and the onset of tip streaming in a droplet submerged in a linear extensional flow, paying attention to the effect of a surfactant monolayer. We present the same analysis for the viscous entrainment of selective withdrawal. With respect to bubble bursting, we review the major results for simple liquids and summarize recent studies for liquids containing polymers and surfactants.
José María Montanero
Chapter 7. Microfluidic Configurations for Producing Tip Streaming
Abstract
As described in the previous chapter, tip streaming can be produced by accelerating the fluid in the tip of a mother drop. Stresses of hydrodynamic or electrohydrodynamic nature drive this acceleration to the extent of overcoming the resistance offered by the capillary and viscous forces. This phenomenon has modest practical (technological) applications due to the intrinsic unsteady character of the process. Besides, the experimenter has limited control over the flow outcome (for instance, the size of the emitted droplets), which can be achieved only by fixing the flow rate at which the dispersed phase is ejected.
When the droplet is attached to a capillary and fed at the appropriate flow rate, the system eventually adopts either the microdripping or microjetting mode. Microdripping periodically emits tiny droplets of almost equal size from the droplet tip, while microjetting steadily ejects a thin, long, fluid thread. Microdripping and microjetting can produce droplets with the desired morphology, size, and electrical charge.
This chapter describes the axisymmetric microfluidic configurations used to produce microdripping and microjetting. Specifically, we consider the cone-jet mode of electrospray and the coflowing, flow focusing, and confined selective withdrawal configurations. The characteristics of the selective withdrawal and electrified films are also discussed. We introduce and explain the meaning of the dimensionless numbers characterizing the corresponding flows. The numerical and experimental results will be discussed in the following chapters.
José María Montanero
Chapter 8. Electrospray
Abstract
This chapter focuses on some fundamental results of the classical steady cone-jet mode of electrospray. Specifically, we review the scaling laws that allow one to estimate the droplet diameter, electric current, breakup length, and minimum flow rate stability limit. The numerical solution of the leaky-dielectric model enables us to describe the electrospray phenomenon for flow rates relatively close to the minimum value. We present the results of the global stability analysis, paying attention to charge relaxation. The characteristics of coaxial Taylor cone-jets and AC electrospray are also briefly reviewed. Little attention is paid to the electrospinning configuration, which has been nicely reviewed in several works [1, 2].
José María Montanero
Chapter 9. Coflowing and Hydrodynamic Focusing
Abstract
One of the most salient applications of the tip streaming phenomenon is the production of monodisperse emulsions of micrometer droplets. The microdripping and microjetting modes can be realized in different microfluidic devices for this purpose. These devices can be grouped into three main classes [1]: crossflowing systems, coflowing streams, and hydrodynamic focusing. Only the last two classes correspond to an axisymmetric configuration.
In this chapter, we review some relevant results obtained in this field. Specifically, we describe the coflowing, flow focusing, confined selective withdrawal, and selective withdrawal techniques. We present results for liquid-liquid and liquid-gas systems. We do not consider here the gaseous flow-focusing configuration (a liquid stream focused by a gaseous current), to which we devote two specific chapters.
Two significant aspects of each configuration mentioned above are examined: the stability of the tip streaming flow and the scaling laws predicting the size of the jets and droplets. We present some preliminary numerical results on the effect of a soluble surfactant in liquid-liquid flow focusing. The chapter closes with some results about viscous entrainment and microjetting in a uniaxial extensional flow. This microjetting mode may lead to the stable production of arbitrarily thin fluid jets.
José María Montanero
Chapter 10. Gaseous Flow Focusing I
Abstract
We describe the geometries that produce the flow focusing effect and their applications. The forces, flow patterns, and instability mechanisms in the low-viscosity and viscous cases are discussed. We show results on the popular gas dynamic virtual nozzle (GDVN) geometry. Global stability analysis is used to gain insight into the axisymmetric and whipping instabilities limiting the applicability of this technique. Results of the microdripping mode are also presented.
José María Montanero
Chapter 11. Gaseous Flow Focusing II
Abstract
Serial femtosecond crystallography (SFX) is the most remarkable application of gaseous flow focusing. In this application, the gaseous stream driving the jet is normally discharged into a vacuum chamber, which makes the gas current reach the sound velocity in the nozzle orifice. We devote the first part of this chapter to analyzing this transonic version of flow focusing.
Gaseous flow focusing can be employed to produce fibers and films when the liquid phase is a viscoelastic fluid. The second part of this chapter describes these interesting applications of flow focusing.
The large strain rates produced in the tip of the tapering meniscus of flow focusing can trigger the coil-stretch transition of the polymers dissolved in the liquid, which leads to the building of large axial viscoelastic stresses. This can fundamentally change the behavior of weakly viscoelastic flow focusing, increasing the stability of both the tapering meniscus and the emitted jet. This chapter closes by analyzing this novel and interesting phenomenon. Attention is paid to this viscoelastic transition and the superstability of the jets emitted when that transition occurs.
José María Montanero
Metadata
Title
Tip Streaming of Simple and Complex Fluids
Author
José María Montanero
Copyright Year
2024
Electronic ISBN
978-3-031-52768-5
Print ISBN
978-3-031-52767-8
DOI
https://doi.org/10.1007/978-3-031-52768-5

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