Flow past a droplet

The fluid mechanical problem of solving for the flow around a droplet is a standard one and has formed the starting point of many of the methods and theories on how interfacial effects influence fluid flow. A droplet of matmal A is immersed in an inflnite medium B. The latter flows upward past the droplet and exrats a drag force on the droplet. This drag force is balanced by gravity, so that the droplet stays in place and steady state is reached. Far from the droplet, the velocity in phase B assumes a constant (upward) value U. 

FIGURE 7.2 The spherical coordinate system is employed with the origin at the center of the drop of phase A. Far away from the drop the velocity field is Ue in phase B. 

FIGURE 7.3 The arrangement of the dip coating experiment is shown. The plate is being withdrawn at a constant velocity V The film profile h reaches a constant value in the region far from the meniscus. 

Bird et al. (2002) discuss the biharmonic operator E and show how Equation 7.20 can be solved for flow around a solid sphere and how quantities like the drag force on the sphere can be evaluated. The solution for the case of a fluid sphere is given in Levich (1%2) using a somewhat different method of attack. Following the lines of development pursued here, Equations 7.20 through 7.22 apply in both the iimer and outer fluids, but the boimdary conditions are different. We first list the boundary conditions 

The drag force F is the quantity of interest and is equal to the net gravitational force 

---

Hinze8 and others have observed that as the vapor flowing past a droplet... 

Keywords Drag coefficient Drag of deformed drops ing droplets Flow past a droplet Interacting drops... 

---