Flow Past a Spherical Drop or Bubble

To obtain the velocity and pressure profiles for the fluid in each phase, we shall use the Stokes equations (2.1.1). As previously, the condition that the flow is uniform remote from the drop has the form (2.2.2). 

Let us write out four conditions that must be satisfied on the boundary of a spherical drop. 

The jump of the normal stress across the interface is equal to the pressure increment due to interfacial tension  

We introduce the stream function P(rn) in each of the phases (m = 1,2) according to formulas (2.1.3). Conditions (2.2.6)-(2.2.10) allow us to determine the constants in the general solutions (2.1.5) inside and outside the drop. As a result, we obtain the Hadamard-Rybczynski solution [94, 179] 

By using formulas (2.1.3), we calculate the velocity and the pressure outside the drop  

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