Importance of Angular-Momentum Conservation Couette Flow

8 Importance of Angular-Momentum Conservation Couette Flow 

As an example of a simation in which it is important to use an algorithm which conserves angular momentum, consider a drop of a highly viscous fluid inside a lower-viscosity fluid in circular Couette flow. In order to avoid the complications of phase-separating two-component fluids, the high viscosity fluid is confined to a radius r Ri by an impenetrable boundary with reflecting boundary conditions (i.e., the momentum parallel to the boundary is conserved in collisions). No-slip boundary conditions between the inner and outer fluids are guaranteed because collision cells reach across the boundary. When a torque is applied to the outer circular wall (with no-slip, bounce-back boundary conditions) of radius R2 Ri, a solid-body rotation of both fluids is expected. The results of simulations with both MPC-AT-a 

The origin of this behavior is that the viscous stress tensor in general has symmetric and antisymmetric contributions (see Sect. 4.1.1), 

The anti-symmetric part of the stress tensor implies an additional torque, which becomes relevant when the boundary condition is given by forces. In cylindrical coordinates (r, 6,z), the azimuthal stress is given by [38] 

The first term is the stress of the angular-momentum-conserving fluid, which depends on the derivative of the angular velocity = v /r. The second term is an additional stress caused by the lack of angular momentum conservation it is proportional to il. 

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