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November 22, 2001, 13:15 
Particles in slow dense fluid

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I'm trying to simulate the motion of small particles of carbon in a slow moving diluted fluid. There is an obstacle in which the moving particles will eventually impact. So far the results for liquid superficial velocities of about 1 to 0.1 m/s show the particles following approximately the streamlines of the fluid. But when I go to 0.05 or less the particles begin to follow erratic almost random paths. I don't know if this is physically meaningful ( is it a kind of sedimentation? )or if I'm obtaining numerical instabilities or something else. Can anybody please give me some advice. Thanks Newbie. 

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November 24, 2001, 00:35 
Re: Particles in slow dense fluid

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We need to know what kind of model/continuum theory you are using the LagrangianEulerian or EulerianEulerian (mixture theory or twofluid) approach. You need to be much more specific about your setup as many outcomes are possible in multiphase flow. What is the Reynolds number of the carrier phase?
Relative motion between particles and fluid is generally controlled by the Stokes number, or the ratio of the Stokes to the Froude number squared. These are the *particle* numbers, Many outcomes are possible. What is the viscosity of your fluid? True collision is less likley with viscous fluids as a result of "lubrication" et., etc., etc. 

November 24, 2001, 01:31 
Re: Particles in slow dense fluid

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Thanks for your answer. The simulations are lagrangian. The liquid has density close to water and the solid is less than 10% in concentration so collissions are not likely to exists. There are only one fluid phase that contains the solid particles. The liquid has Reynolds numbers less than 0.1
Hope this diminishes the outcomes Thanks again Newbie 

November 27, 2001, 11:09 
Re: Particles in slow dense fluid

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Hi Newbie,
If I understood correctly you are solving the fluid equations for the liquid and are solving additional equations for the particles as solid bodies (point masses). The main force acting on the solid particles is the drag force which is proportional to the drag parameter (say gamma) and the velocity difference (between the velocity of the particles and of the liquid). For different values of the drag parameter you can have different PHYSICAL behaviours. The drag parameter itself can take different analytical expression depending on the density of the liquid, the density of the particles, their radius and the sound speed in the liquid, etc... The drag parameter has units of 1/time, so it is convenient to look at the inverse of it: 1/gamma. 1/gamma has units of time and can be denoted (say) tau. tau is actually the time it takes for the particles to be at rest in the local flow (i.e. moving together with the flow like a tracer). Sometimes tau is called the 'stopping' time, since it is the time it takes to stop the particle in the flow, but since the flow itself moves, it does not really mean the particles stop in the inertial frame of reference. Now for small values of tau (large values of gamma), the particles are quickly dragged by the flow and they act like tracers. Their motions is the same as the motion of the fluid elements in the flow. For large values of tau (small values of gamma), the particles moves freely and are not affected by the liquid (gas, flow or whatever fluid you have). The interesting (physical) behaviour is when tau is in between these two values, so that the particles are slightly dragged by the flow but they also can move rather freely. I guess the situation that you described in your first message, where particles seem as if they were moving randomly is probalbly when the drag parameter gamma is indeed very small (unless your flow is kind of turbulent and the particles follow the turbulent motion of the flow?  which is probably not the case since you mentioned that the flow is 'slow'). I hope this help. Patrick 

November 27, 2001, 22:58 
Re: Particles in slow dense fluid

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It surprises me that this problem that seemed of little difficult could have such a complicacy. I will investigate what you mention.
Thanks Newbie 

November 28, 2001, 11:02 
Re: Particles in slow dense fluid

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I suggest that you look at the substantial literature on this subject. My favorite is:
Raju & Meiburg, 1995, The accumulation and dispersion of heavy particles in forced twodimensional mixing layers. Part 2: The effect of gravity, Physics of Fluids, v. 7, no. 6, p. 12411264. 

December 6, 2001, 10:43 
Re: Particles in slow dense fluid

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Thank you. Your contribution has been very helpfull.
Newbie 

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