Dear Oualid imène,

   particle motion in a fluid flow it is not a trivial phenomenon, specially if we are dealing with numerical simulations. Basically the simulation can take in to account the interaction between the fluid flow and point-size particles in these ways:

0-way coupling: particles are simply tracers, and they follow the fluid motion without exchanging momentum or energy with the fluid flow;

1-way coupling: particles are influenced by the fluid, but not the other way round, see the paper suggested by prof. Filippo Maria Denaro or more easily https://en.wikipedia.org/wiki/Basset%E2%80%93Boussinesq%E2%80%93Oseen_equation;

2-way coupling: particles can also influence the fluid motion by means of a coupling term in the navier-stokes equations.

I don't know how comsol models the particles, but I guess it uses a point size model with either 0-way coupling or a 1-way coupling.

So, I guess that when you add the drag in comsol you are switching from a 0-way coupling to a 1-way coupling. When you do so, particles are not forced to follow the fluid motion but they have their own equation of motion: the fluid acts on them with a certain drag force and they move with a certain inertia.

Generally you should consider the particle Stokes number (https://en.wikipedia.org/wiki/Stokes_number) to decide with approach to use. If particles stokes number is very low, particles tend to follow the motion of the fluid so it is reasonable to adopt a 0-way coupling approach, if this is not true, you must consider also the drag force, or if relevant also the other forces in the Basset–Boussinesq–Oseen equation.

Visually, If particles are heavy they tend to deviate from the fluid flow trying to "escape" from the fluid vortex as a consequence their inertia.

Cheers,

Francesco

I think you can start with the paper

Maxey, M. R.; J. J. Riley (1983). Phys. Fluids. 26: 883–889.

Then, you can find a lot of recent published papers that describe this issue

Thank you both  Mr. Filippo and Vitalii for recommanding me this books and articles but at the same time I want to know if there is chance to simulating it the correct way in COMSOL 5.2 since I am using it, I have already tried to creat a model if any one could take a look just for this part with and without the drag force how it should change the particle's trajectory in a laminar flow ?

Best regards.

Imène Oualid.

Dear Oualid imène,

   particle motion in a fluid flow it is not a trivial phenomenon, specially if we are dealing with numerical simulations. Basically the simulation can take in to account the interaction between the fluid flow and point-size particles in these ways:

0-way coupling: particles are simply tracers, and they follow the fluid motion without exchanging momentum or energy with the fluid flow;

1-way coupling: particles are influenced by the fluid, but not the other way round, see the paper suggested by prof. Filippo Maria Denaro or more easily https://en.wikipedia.org/wiki/Basset%E2%80%93Boussinesq%E2%80%93Oseen_equation;

2-way coupling: particles can also influence the fluid motion by means of a coupling term in the navier-stokes equations.

I don't know how comsol models the particles, but I guess it uses a point size model with either 0-way coupling or a 1-way coupling.

So, I guess that when you add the drag in comsol you are switching from a 0-way coupling to a 1-way coupling. When you do so, particles are not forced to follow the fluid motion but they have their own equation of motion: the fluid acts on them with a certain drag force and they move with a certain inertia.

Generally you should consider the particle Stokes number (https://en.wikipedia.org/wiki/Stokes_number) to decide with approach to use. If particles stokes number is very low, particles tend to follow the motion of the fluid so it is reasonable to adopt a 0-way coupling approach, if this is not true, you must consider also the drag force, or if relevant also the other forces in the Basset–Boussinesq–Oseen equation.

Visually, If particles are heavy they tend to deviate from the fluid flow trying to "escape" from the fluid vortex as a consequence their inertia.

Cheers,

Francesco

Dealing with a particle suspended in a fluid pressure gradient(net force exerted on particle surface) leads to particles motion , Brownian motion (random movement of particles) also should be considered. 

in a flow stream at the surface of particle which is the interaction boundary between particle and fluid difference between  particle velocity and its surrounding fluid  velocity leads to net force acting on particle :

1. if particle is slower than fluid (particle lags the flow)then fluid push it forward 

2. if particle is faster than fluid(particle lead the flow) then fluid resist and slow it down 

3. if they have same velocity then there is no net force acting on  particle.

in general, the magnitude of the force is proportional to the velocity difference.

so, with drag force particle should follow fluid streamlines and without drag force there should be some kind of Brownian motion.  

I think Imene has to explain her problem in more detail to get more meaningful answers.

The answers so far are very diverse. The size of the particle and the speed of the particle in relation to the air flow is critical.

Most of the time, engineers analyse solid bodies that are a lot bigger than the air molecules, and we talk of relative motion of the air particles such that the ramdom motion of the particles does not matter any more, i.e. the flow is fast enough to worry about the random motion of the particles.

So, Imene, I hope you will be able to articulate your problems better.

Wan Zaidi

Thank you everybody for helping me it is so kind of you, I read all the papers and the books that you proposed to me.

But since I am using Comsol Mutliphysics for this task I wanted someone to help me in simulating theses cases:

Case 1: Where the velocity of the particule is reduced compared to the velocity of the air.

Case 2: Where The velocity of the particle is greater than the velocity of the air.

Case 3: Where the particle and the flow of air have the same velocity.

In order to see how the drag force reacts on this latter one and to obtain results similar to the theory.

Thank you again for your help.

Yours faithfully !

imène Oualid.