Diffusion through a Fluid

object and its length, divided by the fluid’s coefficient of viscosity. If this number is about one, the flow will be laminar, especially if a smooth shape exists for the object. If this number is between one and ten, there is a transition to turbulent flow. If this number is greater than ten, the flow will transition to turbulent around the object. For very large numbers, greater than 106, the flow will be turbulent.

One of the consequences of viscosity is a resistance force called the viscous drag force exerted on a moving object. This force depends on the object’s speed and will be proportional to speed at low speeds and proportional to the speed squared at high speeds (high Reynolds numbers). This explains why cyclists travel in packs because there will be decreased drag force on the secondary riders and the rider in the front will take turns with the others so that the headwind is traded off between cyclists.

A consequence of this is that the drag force will mean that, with an object falling, its acceleration will cause it to have a greater drag force as it falls, which slows its acceleration until it reaches a critical speed, referred to as its terminal velocity or terminal speed, with zero acceleration. The object will fall at the same terminal velocity until it reaches the bottom. This is the case for particles of sand falling in the ocean and for sky divers. Terminal speed will be the greatest for low-viscosity fluids and with objects that have high densities and small sizes. This means that sky divers will fall faster with hands near their side than they will with their arms spread out.

DIFFUSION THROUGH A FLUID

Atoms and molecules will have a “random walk” through a fluid, resulting in diffusion due to random thermal molecular motion. Odors can even diffuse through solids like the ice in your freezer. It is a slow process that eventually has macroscopic influences. The average distance of random molecular motion is proportional to the square root of time. In fact, the root-mean-square distance is equal to the square root of 2 times the diffusion constant for a molecule in a medium and time.

The units for the diffusion constant are meters squared per second. The larger the molecule, the smaller is the diffusion constant because molecular speed is inversely proportional to molecular mass. Diffusion constants will increase with temperature,

decrease with molecular mass, and will be related to the kinetic energy of the molecule in the liquid. Diffusion proceeds from an area of higher concentration to an area of lower concentration. Cohesive and adhesive forces will all affect the values of the diffusion constant.

Osmosis involves the transport of water through a semipermeable membrane from a region of high concentration to an area of low concentration. It is driven by the imbalance in water concentration from one side to another. Water is more concentrated in dilute solutions and is less concentrated in concentrated solutions (the opposite of the concentration of the solute in solution).

Osmosis can create a substantial difference in pressure across a membrane. The pressure will rise until there is a back pressure that stops the osmosis, which is also called the “relative osmotic pressure”. This is the pressure reached when a solution is equal in concentration of water on both sides of the membrane and the net transfer of water is zero. This osmotic pressure is described in figure 71.

Figure 71.

On the other hand, dialysis is the transport of any other molecule through a semipermeable membrane due to differences in their relative concentration difference. Both osmosis and dialysis can be reversed by the back pressure on one side of the membrane. Active transport involves the transport across a membrane using energy from the cell in biological systems.