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Stokes flow (named after George Gabriel Stokes), also named creeping flow or creeping motion, [1] is a type of fluid flow where advective inertial forces are small compared with viscous forces. [2] The Reynolds number is low, i.e. R e ≪ 1 {\displaystyle \mathrm {Re} \ll 1} .
Fig. 1 Creeping flow over a sphere: the viscous stress components at the surface and the pressure distribution in an axial plane. Consider creeping motion of a stream of speed U about a solid sphere of radius a. It is convenient to use spherical polar coordinates ( r , θ ) with θ = 0 in the direction of U.
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Physically, the presssure gradient drives the flow by overcoming viscous resistence, but does. affect the fluid inertia significantly. Refering to Figure 2.5 for the spherical coordinate system (r, θ, φ). Let the ambient velocity be upward and along the polar (z) axis: (u, v, w) = (0, 0, W ).
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Creeping flow past a falling sphere in a fluid (e.g., a droplet of fog falling through the air): streamlines, drag force F d and force by gravity F g. At terminal (or settling) velocity , the excess force F e due to the difference between the weight and buoyancy of the sphere (both caused by gravity [ 7 ] ) is given by:
May 24, 2020 · Stokes’ law of friction for laminar flows around spherical bodies states that the drag force is proportional to the viscosity of the fluid, the flow velocity and the radius of the sphere!
III. STOKES FLOWS AROUND A SINGLE SPHERE A. Rotation Consider a sphere of radius arotating with angular velocity Ω in unbounded fluid. We want to solve µ∇2u = ∇p, ∇·u = 0, subject to the boundary conditions u = Ω×x on r= a, and u,p→ 0 as r→ ∞.
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Schematics of creeping flow over a sphere. The equations governing a fluid creeping motion is given as . or E4 ψ = 0 , ∂. 2. (1) θ∂ . 2 r ∂ + r. 2 ∂ θ sin. ∂ ψ= 0 . sin. θ∂θ . (2) For flow around the sphere shown in the figure, the boundary conditions are: = ∂ ψ. v = 0. r. 2 sin. 1. θ∂θ ∂ ψ. v = −. θ. = 0. r sin θ ∂ r.
