Inertial force, macroscopic

A thermodynamic system is a part of the physical universe with a specified boundary for observation. A system contains a substance with a large amount of molecules or atoms, and is formed by a geometrical volume of macroscopic dimensions subjected to controlled experimental conditions. An ideal thermodynamic system is a model system with simplifications to represent a real system that can be described by the theoretical thermodynamics approach. A simple system is a single state system with no internal boundaries, and is not subject to external force fields or inertial forces. A composite system, however, has at least two simple systems separated by a barrier restrictive to one form of energy or matter. The boundary of the volume separates the system from its surroundings. A system may be taken through a complete cycle of states, in which its final state is the same as its original state. 

The energy dissipation number is derived from the Kolmogorov theory [289, 290]. This theory is based on the concept, that in the turbulent flow range the kinetic energy is transferred by inertial forces from large to ever smaller eddies, until it is finally dissipated through viscosity forces. The eddies produced by the stirrer have the size of the stirrer head and are responsible for the macroscopic turbulence, the smallest eddies on the other hand are directionless. On the microscale so-called isotropic turbulence exists, see Section 1.4.2. 

Reynolds number) is in general smaller than unity, and the ratio of the inertial force to surface tension (Weber number) is also small, so that accurate microfluidic metering is somewhat more difficult than metering for macroscopic flows. For gas flows, the effect of the Knudsen number, defined as the ratio of the molecular mean free path to the channel size, is high and cannot be ignored for microscale channels, and hence the fluid metering discussed here will be for liquids only. The Reynolds number Re, the Weber number We, and the Knudsen number Kn are expressed as follows ... 

Fluid flow in small devices acts differently from those in macroscopic scale. The Reynolds number (Re) is the most often mentioned dimensionless number in fluid mechanics. The Re number, defined by pf/L/p, represents the ratio of inertial forces to viscous ones. In most circumstances involved in micro- and nanofluidics, the Re number is at least one order of magnitude smaller than unity, ruling out any turbulence flows in micro-/nanochannels. Inertial force plays an insignificant role in microfluidics, and as systems continue to scale down, it will become even less important. For such small Re number flows, the convective term (pu Vu) of Navier-Stokes equations can be dropped. Without this nonlinear convection, simple micro-/ nanofluidic systems have laminar, deterministic flow patterns. They have parabolic velocity... 

The complete dynamics of a deforming body requires including the contact forces, the body (gravitational) forces pf with inertial forces. For a macroscopic mass M... 

An understanding of multiphase microflows is critical for the development and application of microstructured chemical systems in the chemical industry. As one of the most important meso-scientific issues, interfacial science could be a bridge connecting microscopic molecular components and macroscopic fluid behaviors in these systems. Working together with viscous and inertial forces, the interfacial force also dominates complicated multiphase flow patterns and well-controlled droplets and bubbles. In this review, the generation mechanisms of different flow patterns and the break-up rules for droplets and bubbles in microchannels are introduced first. The effects of the adjustable fluid/solid interfaces, or so-called wetting properties, of microchannels on multiphase flow patterns, as well as microchannel surface modification methods, are then discussed. The dynamic fluid/fluid interfaces in multiphase microflows with variable... 

A similarity solution is available for Eqs. 9.93 to 9.95 subject to negligible macroscopic inertial and viscous forces, that is, small permeabilities and constant DL [115,116]. The inertial and viscous forces are included by Kaviany [117] through the regular perturbation of the similarity solution for plain media, that is, the Nusselt solution [113]. The perturbation parameter used is... 

When materials are affected by external forces without inertial movement, their geometrical shapes and dimensions will change, and this change is called strain or deformation. When materials deform macroscopically their internal molecules and atoms relatively displace, which brings an additional force against external forces between molecules and atoms. When a balance is reached, the additional internal force is equal to external forces with opposite directions. The internal force per unit area is defined as strain, and its value is equal to that of the external forces. Materials deform in different ways when stressed differently. For the same material, there are three basic types of deformation simple tension, simple shear, and uniform compression. A material is in simple tension when it is affected by two forces that are perpendicular to the section, equal and opposite in direction, and in the same straight line a material has a sheer reaction when it is affected by two forces that are parallel to the section, in equal and opposite direction, and at different straight lines. Uniform compression occurs when the material is surrounded by stress p and the volume decreases. 

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