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Entropy production for the terminal orientation of a half cylinder in a flow
1 , 2 , * 2
1  George Mason University
2  Montclair State University


The terminal orientation of a rigid body is a classic example of a system out of thermodynamic equilibrium and a perfect testing ground for the validity of the maximum entropy production principle(MEPP). A freely falling body in a quiescent fluid generates fluid flow around the body resulting in dissipative losses. Thus far dynamical equations  have been employed in deriving the equilibrium states of such falling bodies, but they are far too complex and become analytically intractable when inertial effects come into play.  At that stage, our only recourse is to rely on numerical techniques which can be computationally expensive.  In our past work, we have realized that the MEPP is a reliable tool to help predict mechanical equilibrium states of free falling, highly symmetric bodies such as cylinders, spheroids and toroidal bodies. We have been able to show that the MEPP correctly helps choose the stable equilibrium in cases when the system is slightly out of thermodynamic equilibrium.  In the current paper, we expand our analysis to examine bodies with fewer symmetries than previously reported, for instance, a half-cylinder. Using two-dimensional numerical studies at Reynolds numbers substantially greater than zero, we examine the validity of the MEPP. Does the principle still hold up when a sedimenting body is no longer isotropic or has three planes of symmetry? In addition, we also examine the relation between entropy production and dynamical quantities such as drag force to find possible qualitative relations between them.

Keywords: maximum entropy production, terminal orientation
Comments on this paper
Vihan Patel
Vortices and disequilibrium
I enjoyed your article very much.
One thing that I had a question about: you mention that wake vortices form around the critical Re ~ 2 mark where your simulation moves from maximum to minimum entropy production, coinciding with a movement away from 'near equilibrium' to 'further from equilibrium'.

Are these vortices modelled for in your simulation and accounted for in the total entropy production? If not, might their inclusion mean that the half-cylinder flow system does in fact follow the MEPP?

What other non-equilibrium situations might fluid dynamicists be able to look at when testing the MEPP? For instance, the mixing of two fluids at different temperatures or different viscosities?

Ashwin Vaidya
Hi Vihan

Our computations do simulate the entire fluid flow dynamics, including the wake vortices. At very low flow speeds (or Reynolds numbers) , below Reynolds numbers of ~ 2, the vortices are insignificant and MEP holds. In the case of flow past a half cylinder, there are 2 local maxima of entropy production corresponding to 2 different angles and the experimentally observed one corresponds to the absolute maximum. When Re>2 (approx), the vortices become significant in magnitude and the entropy production corresponding to the physically observed state is the min of the 2 local maxima. So the switching is not from MaxEP to MinEP, but from ABSOLUTE MaxEP to MIN of LOCAL MaxEP states. The MaxEP still holds but is subtly different. In the case of bodies such as an ellipse or a cylinder, which are the typically studied cases, one does not have the opportunity to observe this switching since the body possess a high degree of symmetry.
Regarding your second question, any pattern selection problem, I think, will be valuable to determine the validity of the MEP principle. There are plenty of such phenomena discussed in the fluid dynamics literature. The ones you describe are certainly valid questions though a bit more complex than the one described here. It would also be valuable to select problems which can be experimentally verified.

Do you think the fluid mixing problem could provide hints for the larger scale cosmological questios you are looking at?

Vihan Patel
Thank you for the clarification.

I confess I'm not entirely sure how closely related the cosmological issues are. Cosmological fluids I believe co-exist in space without interacting, so it's difficult to tell immediately how fluid dynamics might help, but the principles are there.