Drops falling, balance force

As long as the drop is still hanging at the end of the capillary, its weight is more than balanced by the surface tension. A drop falls off when the gravitational force mg, determined by the mass m of the drop, is no longer balanced by the surface tension. The surface tensional force is equal to the surface tension multiplied by the circumference. This leads to... 

At t = 0, V = 0 and the drag force is zero. As the particle accelerates, the drag force increases, which decreases the acceleration. This process continues until the acceleration drops to zero, at which time the particle falls at a constant velocity because of the balance of forces due to drag and gravity. This steady-state velocity is called the terminal velocity of the body and is given by the solution of Eq. (11-8) with the acceleration equal to zero ... 

The drop does not immediately fall off the leaf owing to the fact that there are residual forces or force fields around all atoms and molecules. At surfaces, there are unbalanced forces which tend to become balanced by binding the droplet molecules to the leaf. These forces vary in intensity inversely as the cube of the distance between the molecules. Obviously, similarly shaped molecules will approach a more ideal juxta-... 

An unconfined jet of liquid will break up into drops this is observable in the jet leaving a faucet or a garden hose (see Fig. 17.12). Here a cylindrical jet of liquid is leaving a nozzle. As the liquid falls, it speeds up, because it is being accelerated by gravity. This causes the jet to decrease in cross-sectional area to satisfy the material balance. Finally the jet breaks up into liquid droplets. This breakup is caused by surface forces the cylindrical column of fluid can rearrange into a system with less surface area by changing over into spherical droplets. 

While the particle diameter of fixed bed reactors is on the order of 1-5 mm, the particle size used in another type of reactor—fluidized bed reactors—is on the order of 50-200 p,m. Because of the small diameters, the effectiveness factor is close to 1 in most cases. The Ergun equation characterizes the pressure drop across a bed of solids—at low gas velocities (relative to the particle terminal velocity). When the drag force of the upward moving fluid exceeds the weight of the particles, the particles become fluidized—they begin to move up and down and the solids bed itself behaves like a fluid objects that are denser than the bed will fall through the bed while objects that are less dense will be remain at the top. Based on a force balance, the pressure drop across the bed, AF/L, will be equal to the head of solids (neglecting frictional forces) ... 

When a pendant drop forms slowly at the lower end of a capillary tube it ultimately falls and stretches the filament (which remains attached to the drop). For a Newtoiuan flmd the filament qmckly thins and breaks but long filaments can be formed from visco-elastic liqmds [Jones et al., 1990]. The forces acting on the falling drop are determined using a force balance, and the extensional stress determined as a function of time [Jones and Rees, 1982], The falling pendent drop technique is simple to set up and analyse, and provides consistent values of an apparent elongational viscosity. 

The rise or fall of a liquid interface in a capiUaiy can be easily calculated by writing the balance of forces on a cylindrical column of height H (see Fig. 5). The water at the bottom of the tube, leveled with the free surface of the liquid, is at atmospheric pressure. The hydrostatic pressure drop just below the meniscus is balanced by the vertical component of surface tension at the wall. 

---