Glossary

4.2 Liquid-liquid flow regimes

6 min read•august 20, 2024

Liquid-liquid flow regimes are crucial in multiphase systems, involving two immiscible liquids flowing together. These flows are characterized by density differences, contrasts, and effects, which influence the resulting flow patterns and behavior.

Understanding liquid-liquid flow is essential for various applications, from to emulsion formation. Key concepts include stratified vs. , droplet dynamics, pressure drop prediction, and modeling approaches like the two-fluid model and CFD methods.

Liquid-liquid flow characteristics

Density differences

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  • Density differences between two immiscible liquids drive buoyancy forces
  • Lighter liquid tends to rise while heavier liquid tends to sink, leading to stratification
  • Density ratio (ρ1/ρ2\rho_1/\rho_2) influences the stability and mixing of liquid-liquid flows
  • Higher density differences promote segregation of liquids (oil and water)

Viscosity differences

  • Viscosity ratio (μ1/μ2\mu_1/\mu_2) affects the flow behavior and droplet dynamics
  • Higher viscosity liquids exhibit more resistance to deformation and mixing
  • Viscosity differences influence the formation and stability of dispersions
  • Liquids with similar viscosities tend to mix more easily (ethanol and water)

Interfacial tension effects

  • Interfacial tension acts at the boundary between two immiscible liquids
  • Higher interfacial tension promotes droplet formation and hinders mixing
  • Interfacial tension affects droplet size, shape, and coalescence behavior
  • Surfactants can modify interfacial tension and stabilize dispersions (emulsifiers in food products)

Liquid-liquid flow patterns

Stratified vs dispersed flow

  • occurs when immiscible liquids flow separately with a distinct interface
  • Dispersed flow involves one liquid being dispersed as droplets within the other continuous phase
  • Flow pattern depends on fluid properties, flow rates, and pipe geometry
  • Transition between stratified and dispersed flow can occur by changing flow conditions (increasing mixture velocity)

Factors affecting flow pattern

  • Liquid flow rates and volume fractions determine the dominant flow pattern
  • Pipe diameter and inclination angle influence the gravity effects on flow patterns
  • Fluid properties (density, viscosity, interfacial tension) affect the stability of flow patterns
  • Surface wettability and roughness can influence the liquid-wall interactions and flow behavior

Flow pattern maps

  • Flow pattern maps represent the boundaries between different flow regimes
  • Maps are constructed based on experimental data or theoretical models
  • Common parameters used in flow pattern maps include superficial velocities, volume fractions, and dimensionless numbers (, Weber number)
  • Flow pattern maps aid in predicting and designing liquid-liquid flow systems (oil-water pipelines)

Stratified liquid-liquid flow

Smooth stratified flow

  • Occurs at low flow rates when gravity forces dominate over interfacial forces
  • Liquids flow separately with a smooth, undisturbed interface
  • Velocity profile in each layer is determined by its properties and flow rate
  • Analytical models can predict the flow characteristics and pressure drop (two-fluid model)

Stratified wavy flow

  • Develops at higher flow rates when interfacial waves form due to shear instabilities
  • Waves can grow and lead to droplet formation and entrainment
  • Wave characteristics (amplitude, wavelength) depend on fluid properties and flow conditions
  • Wavy interface enhances mixing and between the liquid layers

Onset of entrainment

  • Represents the transition from stratified to dispersed flow
  • Occurs when interfacial waves become unstable and break, forming droplets
  • Entrainment is influenced by liquid velocities, density differences, and interfacial tension
  • Models and criteria exist to predict the onset of entrainment (Kelvin-Helmholtz instability)

Dispersed liquid-liquid flow

Droplet size distribution

  • Dispersed flows exhibit a range of droplet sizes, characterized by a size distribution
  • Droplet size distribution affects the interfacial area, mass transfer, and separation efficiency
  • Mean droplet size depends on fluid properties, flow conditions, and turbulence levels
  • Mathematical models (log-normal, Rosin-Rammler) are used to represent droplet size distributions

Droplet breakup and coalescence

  • Droplet breakup occurs when disruptive forces exceed the stabilizing interfacial tension forces
  • Coalescence happens when two droplets collide and merge into a larger droplet
  • Breakup and coalescence mechanisms govern the evolution of droplet size distribution
  • Models for breakup and coalescence rates consider turbulence, droplet interactions, and fluid properties

Phase inversion

  • Phase inversion refers to the switch of continuous and dispersed phases in a liquid-liquid mixture
  • Occurs when the dispersed phase volume fraction exceeds a critical value
  • Inversion point depends on fluid properties, mixing conditions, and surface chemistry
  • Phase inversion can be triggered by changes in flow rates, temperature, or surfactant addition (oil-water emulsions)

Liquid-liquid flow in pipes

Pressure drop prediction

  • Pressure drop is a key parameter in designing and operating liquid-liquid flow systems
  • Depends on flow pattern, fluid properties, pipe geometry, and flow rates
  • Different models are used for stratified and dispersed flows (homogeneous model, two-fluid model)
  • Empirical correlations and mechanistic models are available for pressure drop estimation (Lockhart-Martinelli correlation)

Holdup and slip velocity

  • Holdup refers to the fraction of pipe volume occupied by each liquid phase
  • Slip velocity represents the relative velocity between the two liquid phases
  • Holdup and slip velocity are interrelated and affect the pressure drop and flow behavior
  • Models and correlations are used to predict holdup and slip velocity based on flow conditions (drift-flux model)

Pipe inclination effects

  • Pipe inclination influences the gravity forces acting on the liquid-liquid flow
  • Upward inclination promotes mixing and dispersion, while downward inclination enhances stratification
  • Inclination affects the flow pattern transitions, pressure drop, and phase distribution
  • Models and flow pattern maps incorporate the effect of pipe inclination (Beggs and Brill correlation)

Liquid-liquid flow in porous media

Relative permeability concepts

  • Relative permeability describes the ability of each liquid phase to flow in the presence of the other
  • Depends on the saturation of each phase and the pore structure of the medium
  • Relative permeability curves relate the phase saturation to the effective permeability
  • Experimental methods (steady-state, unsteady-state) are used to measure relative permeability (core flooding experiments)

Capillary pressure effects

  • Capillary pressure arises from the interfacial tension between the liquid phases and the porous medium
  • Represents the pressure difference across the fluid-fluid interface in pores
  • Capillary pressure affects the fluid distribution, saturation, and flow behavior in porous media
  • Capillary pressure curves relate the phase saturation to the capillary pressure (mercury injection, porous plate method)

Wettability and contact angle

  • Wettability refers to the preference of a solid surface to be in contact with one liquid phase over the other
  • Contact angle quantifies the wettability by measuring the angle between the liquid-liquid interface and the solid surface
  • Wettability influences the fluid distribution, capillary pressure, and relative permeability in porous media
  • Wettability can be altered by surface chemistry, temperature, and fluid composition (surfactants, nanoparticles)

Modeling liquid-liquid flow

Two-fluid model approach

  • Two-fluid model treats each liquid phase separately with its own set of conservation equations
  • Captures the velocity, pressure, and volume fraction of each phase
  • Accounts for the interfacial interactions and momentum transfer between the phases
  • Requires closure relations for interfacial forces, turbulence, and phase interactions

Homogeneous model simplifications

  • Homogeneous model assumes the liquid phases have the same velocity and are well-mixed
  • Treats the liquid-liquid mixture as a single fluid with average properties
  • Simplifies the governing equations and reduces computational complexity
  • Suitable for dispersed flows with small droplet sizes and strong coupling between phases

Computational fluid dynamics (CFD) methods

  • CFD techniques solve the governing equations of liquid-liquid flow numerically
  • Discretize the flow domain into small elements or volumes (finite difference, finite volume, finite element)
  • Employ various turbulence models (k-epsilon, k-omega) to capture the turbulent mixing
  • Enable detailed simulations of complex geometries, flow patterns, and phase interactions (droplet breakup and coalescence)

Applications of liquid-liquid flow

Oil-water separation processes

  • Liquid-liquid flow principles are applied in oil-water separation equipment (gravity separators, hydrocyclones)
  • Density difference and droplet size distribution govern the separation efficiency
  • Design and operation of separators rely on understanding the flow patterns and phase interactions
  • Optimization of separation processes involves controlling the flow rates, residence time, and fluid properties

Liquid-liquid extraction columns

  • Extraction columns are used for mass transfer between immiscible liquids (solvent extraction)
  • Flow patterns and mixing characteristics affect the mass transfer efficiency and column performance
  • Different column designs (spray columns, packed columns, pulsed columns) exploit specific flow regimes
  • Modeling and simulation of extraction columns require knowledge of liquid-liquid flow behavior and mass transfer mechanisms

Emulsion formation and stability

  • Emulsions are dispersions of one liquid phase within another (oil-in-water, water-in-oil)
  • Formation and stability of emulsions depend on liquid-liquid flow conditions and surface-active agents (emulsifiers)
  • Droplet size distribution, rheology, and phase inversion are key aspects of emulsion behavior
  • Understanding liquid-liquid flow is crucial for designing and controlling emulsification processes (homogenizers, colloid mills)

Key Terms to Review (18)

Bond Number: The Bond number is a dimensionless number used in fluid dynamics to describe the relative importance of gravitational forces to surface tension forces in a liquid-liquid system. It helps in understanding how these two forces interact to affect the flow behavior and stability of different liquid-liquid flow regimes.
Chemical Reactors: Chemical reactors are vessels designed to facilitate chemical reactions by providing the necessary conditions for reactants to interact. These reactors play a crucial role in various processes, including multiphase flow systems, where they manage the interaction of multiple phases like gas, liquid, and solid, impacting efficiency and product yield. Understanding how different flow regimes and modeling approaches affect reactor performance is vital for optimizing reaction outcomes.
Dispersed Flow: Dispersed flow refers to a flow regime where small droplets, bubbles, or particles are distributed within a continuous phase, typically liquid or gas. In this type of flow, the dispersed phase occupies a smaller volume fraction compared to the continuous phase, leading to unique interactions between the phases that can significantly influence transport phenomena and energy transfer. Understanding dispersed flow is crucial for analyzing various multiphase systems, such as plumes and liquid-liquid mixtures.
Emulsified Flow: Emulsified flow refers to a specific type of liquid-liquid flow regime where two immiscible liquids are dispersed into each other, creating a stable mixture or emulsion. This phenomenon occurs when the shear forces in the flow are strong enough to overcome the interfacial tension between the two liquids, leading to the formation of tiny droplets of one liquid suspended within another. Emulsified flow is important in various industrial processes, such as chemical engineering and oil recovery, as it affects the transport properties and separation processes of different liquids.
Eulerian-Eulerian Model: The Eulerian-Eulerian model is a mathematical framework used to describe multiphase flow systems, treating each phase as a continuous medium. This approach allows for the simulation of complex interactions between different phases, such as momentum, mass, and energy transfer, by employing averaged quantities instead of tracking individual particles. It plays a critical role in understanding flow behaviors in various systems including liquid-liquid interactions, reactor dynamics, and flow regime transitions.
High-speed imaging: High-speed imaging is a technique used to capture rapid events in detail by recording at significantly higher frame rates than standard video. This method allows for the observation and analysis of fast phenomena, making it essential for studying complex behaviors in multiphase flows, including interfacial instabilities, coalescence and breakup processes, flow patterns, and transitions in regimes.
Interfacial Tension: Interfacial tension is the force that exists at the interface between two immiscible fluids, which acts to minimize the surface area and create a stable boundary between the fluids. This phenomenon plays a crucial role in various multiphase flow dynamics, affecting how different phases interact, disperse, and behave under various conditions.
Mass transfer: Mass transfer refers to the movement of mass from one location to another, often involving the exchange of particles, molecules, or energy between phases or within a single phase. It is a fundamental process that is crucial for understanding how substances interact and distribute in different systems, such as gases and liquids, which are particularly important in multiphase flow scenarios, enhancing processes like cooling, separation, and chemical reactions.
Oil-water separation: Oil-water separation refers to the process of separating oil from water, which is essential in various industrial applications, especially in the petroleum and environmental sectors. This separation is crucial for recovering valuable oil resources, preventing environmental pollution, and ensuring efficient processing in multiphase flow systems. Understanding the principles of volume fraction and phase fraction, as well as the technologies like gamma-ray densitometry and the characteristics of liquid-liquid flow regimes, enhances the effectiveness of this separation process.
Particle image velocimetry (PIV): Particle image velocimetry (PIV) is an optical method used to measure the velocity of fluid flow by capturing images of tracer particles suspended in the fluid. This technique allows researchers to visualize flow patterns and obtain quantitative data on velocity fields, making it essential for studying various multiphase flow phenomena and enhancing our understanding of complex interactions between phases.
Phase Separation: Phase separation is the process by which a mixture of different phases, such as liquids or gases, divides into distinct regions with uniform composition. This phenomenon is essential in understanding how different materials interact and separate under varying conditions, impacting various physical processes and applications.
Reynolds Number: Reynolds number is a dimensionless quantity that helps predict flow patterns in different fluid flow situations. It is calculated using the ratio of inertial forces to viscous forces, providing insight into whether the flow will be laminar or turbulent. Understanding Reynolds number is crucial for analyzing fluid behavior in various systems, such as flow pattern maps, drag forces, stirred tank reactors, condensers, distillation columns, and liquid-liquid flow regimes.
Slug Flow: Slug flow is a flow regime characterized by the intermittent movement of large, discrete bubbles or slugs of gas within a liquid, creating a distinct interface between the gas and liquid phases. This type of flow can significantly impact the dynamics of multiphase systems, influencing factors such as volume fraction and interphase interactions.
Stability analysis: Stability analysis is a method used to determine the behavior of a system over time, particularly focusing on whether small disturbances will grow or diminish. In the context of computational fluid dynamics and multiphase flow, stability analysis helps ensure that numerical methods produce reliable and accurate solutions. This analysis is essential for understanding how different modeling techniques can affect the reliability of results, especially when simulating complex flow regimes.
Stratified Flow: Stratified flow refers to a type of multiphase flow where two or more immiscible fluids, typically liquid and gas or two liquids, flow in distinct layers or strata without intermingling. This phenomenon is commonly observed in various engineering applications, where the different densities of the fluids lead to a stable separation, creating layers that can be characterized by their individual properties such as velocity and pressure.
Transition Criteria: Transition criteria refer to the specific conditions or thresholds that determine the change in flow patterns between different flow regimes in multiphase systems, particularly in liquid-liquid flows. Understanding these criteria is crucial for predicting and managing the behavior of fluids when transitioning from one flow regime to another, impacting factors like pressure drop, velocity distribution, and phase interaction.
Viscosity: Viscosity is a measure of a fluid's resistance to flow, indicating how thick or thin a fluid is. This property plays a crucial role in determining how fluids behave during phase transitions, flow dynamics, and interactions between different phases, impacting everything from the speed of flow to how well different substances mix.
Volume of Fluid (VOF): The Volume of Fluid (VOF) method is a numerical technique used for tracking and locating the free surface or interface between two immiscible fluids, such as oil and water. This method is particularly useful in multiphase flow modeling, allowing for accurate representation of fluid interfaces in various flow regimes, including liquid-liquid interactions. It leverages a scalar function to define the fraction of each fluid present in a computational cell, which is essential for simulating complex flow behavior.
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