Diffusive therapies rely on several phenomena including ordinary diffusion and forced diffusion. Ordinary (or Fickian) diffusion describes the molecular movement induced by random movements coupled to the non-uniform distribution in space of the species. This is shown in Fig. 14.1b, where eventual uniform distribution of molecular species will be seen within a solution. The rate of this process is defined by the diffusive flux. The flux is defined as the number of molecules that pass through a unit area in a unit time. Clearly the flux is also dependent on any concentration gradient involving the diffusing substance and this process, for any given molecular species A, is described by Fick’s law [3]:
where is the gradient and D is the Fickian diffusivity. Ordinary diffusion effectively scatters molecular species throughout the medium and is dependent on numerous factors including molecular size and properties of the solution. Separation, however, is determined by the introduction of a further element such as a membrane or gel. These will affect diffusion coefficients significantly, allowing molecular separation to occur, which in turn is limited by the available concentration gradients. Forced diffusion describes the application of an external force which acts differently on the molecular species present facilitating separation. Thus in a dialysis machine separation is enhanced not only by the membrane but by concentration gradients (ordinary diffusion) but also by pressure changes through the application of blood pumps (forced diffusion). In practice this results in the passage of a molecular species along a concentration gradient, and this solute transport can be expressed as:
where DTA are the diffusion coefficient (which varies with the cubed root of the molecular weight), temperature and the surface area of the membrane and ∂c is the concentration gradient across the membrane with ∂d being the membrane thickness. This differs from convective based treatments (Fig. 14.2) where clearance of a molecular species is, as indicated, driven by hydrostatic pressures and convection. The hydrostatic pressure driving convection is that pressure generated across the membrane (TMP). This transmembrane pressure is defined as:

where Pb is the hydrostatic pressure in the blood compartment and Pd is the hydrostatic pressure on the ultrafiltrate side of the membrane. The oncotic pressure is given by π. It follows from this equation that convective flux (Jf) of any given molecular species will be given by:
with Kf being the membrane permeability coefficient. The rate at which molecular species cross the membrane depends on the membrane rejection coefficient (σ) which is effectively zero for small species such as urea but approaches 1 for larger molecules such as albumin. The sieving coefficient (Sc) is given by:

This can be determined by measuring the concentration of a given solute in the plasma water and the ultrafiltrate. Thus a simple view of solute clearance (K) in convective treatments is the product of:
where Qf is the ultrafiltration rate. It follows that where Sc = 1, the clearance is equal to Qf. Solute clearance using diffusion-based systems may be calculated from:
with Qdo and Cdo being the dialysate effluent flow and solute concentration in the effluent dialysate (that leaving the dialyser). Cbi is the concentration of the solute of interest entering the dialyser [4]. In summary, diffusion provides the main basis for the separation of molecular species in dialysis aided by convection, whereas in filtration convection is aided by diffusion, and as such the two processes often act simultaneously with any division being somewhat artificial.