Multiplicity, Dispersity, and Polydispersity of Foams

Multiplicity. One of the most important quantitative characteristics of foam is the multiplicity K. This is a conventional name for the dimensionless reciprocal of the volume fraction of fluid in the foam [38,125,280,480]. If is the volume fraction of gas in the foam, then 

This quantity is sufficiently large (usually, of the order of 102 to 103) and more convenient than the moisture content, which, accordingly, is 10 2 to 10-3. In terms of multiplicity, the conventional range of cellular foam is 4 K 170 [214]. 

Dispersity. Foam cells usually have the shape of rounded polyhedra. Therefore, it is convenient to choose the radius a of the volume-equivalent bubble, that is, of a spherical bubble of the same volume as the cell as the single linear dimension characterizing the interior scale of foam. Foam consisting of cells of the same size is said to be monodisperse. This kind of foam is extremely rare. Usually, there exists a spectrum of radii ai. a in this case, the foam dispersity characterizes the mean linear dimension of the cell [214]  

Sometimes the foam dispersity is characterized by the specific interfacial area e equal to the total surface of gaseous bubbles per unit volume of foam, 

Polydispersity. If a liquid is injected into polydisperse cellular foam (a process which decreases the foam multiplicity) until the foam becomes spherical with the same size distribution of bubbles, then the obtained spherical foam is said to be equivalent. The equivalent foam is characterized by the multiplicity called the minimum multiplicity Kmjn. Obviously, the minimum multiplicity of polydisperse foam is larger than that of monodisperse foam, since in gaps between densely packed spheres of the same largest size, spheres of smaller sizes can be located. Thus the value K a can be used as a quantitative measure of polydispersity [214], While K a = 3.86 for monodisperse foam, for actual polydisperse foam we have 10 to 15 in practice Kma never exceeds 20 [480], 

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