= Surface independence of Stokes force and torque integrals
{title2=$\int_S\boldsymbol\sigma\mathbf n\,dS,\quad\int_S\mathbf x\times\boldsymbol\sigma\mathbf n\,dS$}
For <Stokes flow> without body forces, $\nabla\cdot\boldsymbol\sigma=0$. Symmetry of the <Newtonian fluid stress tensor> also gives $\nabla\cdot(\mathbf x\times\boldsymbol\sigma)=0$, interpreted componentwise as the angular-momentum flux. The <divergence theorem> makes the resultant <force> and <torque> the same on any two homologous enclosing surfaces lying in a nonsingular fluid region. In a <boundary perturbation of a nearly spherical particle>, evaluating each perturbation field on a fixed enclosing surface avoids spurious geometric force terms: the geometric terms from changing the surface normal and area cancel those from evaluating the base stress at the displaced surface.
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