Incompressible flow doesn't certainly implies that density is constant..!

Hi Guys , this time I have something very interesting to share with you all ..........Do you know incompressibility of fluid it doesn't  mean that  its density  is constant , are u guys shocked ?
When we talk about incompressibility its about the flow we are referring to and when we say that the flow is incompressible it means that , if we will going to follow a packet of fluid inside the domain of the flow its density will not change.

Let me explain you with an example , consider the fully developed laminar flow in a pipe shown above; now the shear rate is more at the wall and its zero at the center, as a result energy will dissipate in the form of heat which will increase the wall temperature  while the  temperature at the center will be less . So , density will be higher at the center and low at the walls but the flow will be incompressible if we are following a certain packet of fluid and its density doesn't change through out the path it travels.

Viscosity of liquids and suspensions

Hi Everyone !

We are so used to the term viscosity that we never try to imagine the phenomena at molecular  level. At molecular level in a liquid at rest continuous rearrangement of molecules takes place within a confined volume due to closed packing,this random motion of molecules is the cause of viscosity ,thus at a molecular level viscosity is a function of the attractive forces of the molecules of the liquid.The fluids which obey linear relationship between stress (momentum flux) and velocity gradient are Newtonian fluids but as the rearrangements of molecules increases with existence of velocity gradient and applied shear the relationship no longer remains linear and Non-Newtonian liquids cones into picture.

 

 Now lets discuss about the viscosity of suspensions, they consists of solid and liquid phase and the viscosity mainly depends on inter particle forces which plays a crucial role specially in case of concentrated suspensions. Einstein was the first one to propose the relation for viscosity of dilute suspensions assuming that the solid phase is in the form of rigid spherical particles. This was done by solving equations for flow around a single sphere ,avoiding inter particle interaction thus making the suspension as single  phase entity.He gave the effective viscosity as a function of volume fraction of solid spheres. Thus dilute suspensions can be treated as Newtonian-fluid but for concentrated suspensions the viscosity depends on velocity gradient which makes them Non-Newtonian in nature.

A lot of research prevails in the field of determinig exact viscosity for concentrated suspension and Stoesian Dynamics is one of the tool to study such rheological properties but for Stokes flow regime (Re << 1).

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My work in stokesian Dynamics

Hi everyone ! I like to explain that what I have to do with Stokesian Dynamics. After working in this field for a year I came to know about the various places where this can be applied for example biofluidics (to know the stress on the blood vessels, cell transfer), carbonnanotubes etc. The most interesting thing about this tool is that it can be easily scaled for a nano as well as a macro system as the equations solved here are dimensionless in nature. What is important here is that we are mainly concerned with particle motion rather then that of  fluid, present inside the fluid (remember we are dealing with suspensions which constitutes of fluid and solid rigid spherical particles). This kind of modeling is discrete in nature.

Relating the force and velocity of particles through constants depending on the configuration of system forms the heart of Stokesian Dynamics. Brady, Bossis, Durlosky mainly used this to simulate suspension with great precision and accuracy. Anyways what I am trying to do is to simulate dilute suspension inside the rotating horizontal cylinder made of spherical particles.

Introduction: Stokesian Dynamics

Stokesian Dynamics is an important tool developed by Brady and Bossis to carry out numerical simulations for suspensions of particles interacting through hydrodynamic, Brownian, inter particle and external forces. Stokesian dynamics is capable of handling both hydrodynamic and non-hydrodynamic forces in a simple way. There are numerous application of this method in examining suspension rheology and its properties. As the name suggests this method is applicable only for  low reynolds number simulation. The method has been verified for bounded suspensions simulatios but still needs to be developed for multilayer simulation. My present work focus on multilayer simulation of suspension inside a rotating cylider.