§1.2 Fluid and modeling

1.2.1 Three states of matter

Matter generally exists in three states:gas, liquid and solid.Liquid and gas are collectively referred to as fluid.The main difference between fluid and solid is that they have different resistance to external forces in terms of mechanical analysis.Solid is characterized by constant shape and volume because the mean distance between the molecules is very small and cohesion between the molecules is great.Solids can bear the pressure, but also can bear the tension and resist tensile deformation.Fluids can bear the pressure.But cannot bear the tension and resist tensile deformation due to large distance and small cohesive force between the molecules.Under any tiny shearing force, fluids are prone to deformation or flow.

Although both liquid and gas are fluid, the two have a certain distinction.Liquid has smaller distance and greater cohesive force between the molecules than gas.As a result, liquids can maintain a relatively constant volume and develop a free surface. Another essential difference between them lies in the greater compressibility of gases.

1.2.2 Fluid particle and continuum model

From the point of view of molecular physics, fluid and other matters comprise of a large number of molecules in random motion, and space exists between molecules.Due to the space between molecules, technically speaking, fluid is not continuous and physical quantities describing fluid (mass density ρ, velocity v, pressure p)are not continuous in space, either.Randomness of fluid molecular motion also leads to discontinuity in time of any physical quantity in space.

Under standard conditions,1 cm3fluid roughly contains 3.3× 1022molecules and mean distance between molecules is 3×10-8cm.The task of fluid mechanics is not to study microscopic motion of molecules, but to study macroscopic properties and macro mechanical motion law of the whole fluid.All characteristic scale and characteristic time employed in flow space and time are larger than molecular distance and collision time. Thus, two concepts of fluid particle and continuum model were introduced in order to study fluid motion laws.

1．Fluid particle

The volume which the cluster of molecules occupies must be small compared to the volume occupied by the whole part of the fluid under consideration.On the other hand, the number of molecules in the cluster must be large.This fluid cluster is called a fluid ·6·particle.

2．Continuum model

Fluid continuum model is that fluid was assumed to be a continuum comprised of fluid particles filled with the whole space occupied and physical properties and physical quantities of fluid are continuous.Thus, physical quantities can be considered as continuous functions of place and time.Continuous function theory in mathematical analysis can be used to analyze fluid motion.This hypothesis is applicable for most fluids.However, when the air density is very low, the fluid should be considered as a discrete body and continuum model is not applicable.