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So this step confuses me. Why is it true that the disturbance force is the total force in stokes flow? Any advice or guidance would be great!

From Pozrikidis' book:enter image description here

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Steady Stokes flow is described by $\nabla\cdot\mathbf{T}=0$, where $\mathbf{T}=-p\boldsymbol{\delta}+\boldsymbol{\sigma}$ is the total stress tensor. $\mathbf{T}$ is the stress exerted on each other by adjoining fluid particles at their contact area. $\nabla\cdot\mathbf{T}$ is the net surface force acting on a fluid particle due to its surrounding fluid, which is zero for Stokes flow (by definition). Thus the base flow velocity field (that in the absence of particle) doesn't give rise to net force.

When a moving particle is present, an external force is needed to drive its motion. In steady flow the particle doesn't accelerate, therefore external force driving the particle is balanced by force due to the surrounding fluid on the particle. Since disturbance flow is entirely due to presence of the particle, the force exerted by the fluid on the particle must be a function of the disturbance velocity field only (this force is called "disturbance force" by Pozrikidis), and this must be the entire force on the particle.

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