Fluid Mechanics at Interfaces 1

Methods and Diversity

Roger Prudhomme, Stephane Vincent, Roger Prud'homme

• Publisher: Wiley-ISTE
• Year: 2022
• Print ISBN:
  9781786308160
• eBook ISBN:
  9781119902966
• Edition: 1
• Topic: Physical Sciences
• Subtopic: Fluid Mechanics

Interfaces are present in most fluid mechanics problems. They not only denote phase separations and boundary conditions, but also thin flames and discontinuity waves. Fluid Mechanics at Interfaces 1 focuses on the science of interfaces, in particular, using various scientific methods of analysis relating to space, speed and time. Our investigation takes us from the microscopic or small scale (starting with molecular and nanoscopic scales) to the macroscopic (including meso and interstellar scales), and also explores the laws of interfaces (classical mechanics, quantum mechanics and relativistic mechanics).

Chapter 1 examines the questions raised by modeling interfaces in the presence of one or more fluid phases. Chapter 2 discusses the action of turbulence in liquid–vapor flows that contain both small, dispersed bubbles as well as large bubbles, with heat exchanges at the interfaces. In addition, a new model is presented, using large eddy simulation (LES). Chapter 3 studies an original method for calculating the drag force and thermal transfers in flows around networks of spherical particles, while Chapter 4 focuses on the relationships between interfaces and critical fluids.

Chapter 5 examines shearing, which causes anomalies in the Brownian motion of particles in strongly fluctuating near-critical mixtures, and Chapter 6 introduces basic concepts related to combustion interfaces, raising the question of the combustion of solids, before ending with a brief presentation of the Rankine–Hugoniot theory and a historical overview of the research carried out in the field of combustion.

1
Modeling Interfaces with Fluid Phase

It seemed necessary to reflect on interface models with at least one fluid phase. The concept and the thermodynamic and mechanical modeling of interfaces are partially revisited. The balance laws and constitutive relations are recalled, and various examples are given to support the remarks. Some questions and perspectives are also proposed.

List of symbols

1.1. The concept of an interface

The general concept of an interface assumes contact or separation between material objects. While the concept of an interface in physics may refer to situations of a very different nature, there are also commonalities between these. Among these commonalities, we will study surface quantities and balance laws in particular, i.e. equations with partial derivatives that connect these quantities, in interaction with those in the media in contact.

Under certain conditions, using simplifying hypotheses, it is possible to establish balance laws for interfaces using physico-chemical quantities – constituent mass, total mass, momentum, energy, entropy – in a unique form, as is done for continuous 3D media (whether fluid or solid). We will see that this requires a small-scale internal exploration of the interface throughout its thickness, and an integration of the results obtained in the normal direction.

1.1.1. Interface in physics and geometric surfaces

The term “interface” refers to a separation surface. However, while the term “surface” has a precise meaning in mathematics, being a 2D manifold endowed with geometric properties, the definition of discontinuity surfaces must be refined by mechanics, more generally, in physics or chemistry.

Figure 1.1. Interfacial layer and interface. a) Gray rectangular zone obtained by dilating the X-axis of the gray part of the figure, b) the sudden growth is replaced by continuous growth between f^– and f⁺

Thus, as soon as this interface presents internal physical properties such as surface tension, or when it modifies the exchanges between the media that it separates, or again, when it is the site of production of different natures, it is no longer a simple separation surface.

On the contrary, there is the question of the scale of observation. The interface appears as a discontinuity surface on a macroscopic scale, but may become a continuous medium on a smaller scale. Moreover, if we observe it on an even smaller scale, the continuity gives way to atomic and molecular discontinuities and their constituents, the elementary particles (Rocard 1933; Roussel 2016).

For a mechanical physicist, the macroscopic description is required to model a problem. However, the mechanical physicist must sometimes go down to a very small scale within the objects to understand their behavior.

This is true for both interfaces and bulks. The mechanical physicist and thermodynamician willingly explore the molecular level to understand the behavior of gases, liquids or solids. The application of the laws of mechanics to objects at a molecular level makes it possible to establish macroscopic constitutive laws of mechanics for continuous media through the statistical theories that use approximations. These scientists commonly use Boltzmann’s equation, Fermi’s theory and the BBGKY hierarchy. The experimental measurements provide the data that allows them ...

Table of contents

• Cover
• Table of Contents
• Title Page
• Copyright
• Preface
• 1 Modeling Interfaces with Fluid Phase
• 2 Simulations of Turbulent Two-Phase Flows with Phase Change Using a Multifield Approach Combined with LES
• 3 An Original Approach to Extract Momentum and Heat Transfers from Particle-Resolved Simulations of Particulate Flows
• 4 Interfaces and Critical Fluids
• 5 Shear-Induced Anomalies in the Brownian Motion of Particles in Strongly Fluctuating Near-Critical Mixtures
• 6 Basics on Interfaces in Combustion
• List of Authors
• Index
• Summary of Volume 2
• End User License Agreement