Translational and Shear Flows

Translational flow. For uniform translational flow with velocity Uj around a finite body, the boundary condition remote from the body has the form 

Let us consider more complicated situations, which are typical of gradient flows of inhomogeneous structure. 

Shear flows. An arbitrary stationary velocity field V(R) in an incompressible medium can be approximated near the point R = 0 by two terms of the Taylor 

Here V and Gkm are the fluid velocity and the shear tensor components in the Cartesian coordinates X, X2, A3. The sum is taken over the repeated index m since the fluid is incompressible, it follows that the sum of the diagonal entries Gmm is zero. 

For viscous flows around particles whose size is much less than the characteristic size of flow inhomogeneities, the velocity distribution (1.1.15) can be viewed as the velocity field remote from the particle. The special case Gkm = 0 corresponds to uniform translational flow. For Vj.(0) = 0, Eq. (1.1.15) describes the velocity field in an arbitrary linear shear flow. 

---

Transient Mass Transfer in Steady-State Translational and Shear Flows... 

In Chapters 1 and 2 we study fluid flows, which underlie numerous processes of chemical engineering science. We present up-to-date results about translational and shear flows past particles, drops, and bubbles of various shapes at a wide range of Reynolds numbers. Single particles and systems of particles are considered. Film and jet flows, fluid flows through tubes and channels of various shapes, and flow past plates, cylinders, and disks are examined. 

---