Snapshot 1: a stability map for a biopolymer having a molecular radius of 20 nm and
of 200 kDa ("medium") coating lipid droplets with a radius of 250 nm at a surface load of
Snapshot 2: stability map for a biopolymer having a molecular radius of 40 nm and
of 400 kDa ("large") coating lipid droplets with a radius of 300 nm at a surface load of
Snapshot 3: stability map for a small surface active biopolymer with a molecular radius of 15 nm and
of 150 kDa ("small") covering lipid droplets with a radius of 500 nm at a surface load of
This Demonstration combines three equations to create the stability map. They calculate:
1. the characteristic saturation concentration,
, which is the minimum biopolymer concentration required to fully saturate all the droplet surfaces.
is calculated as
is the lipid droplets’ volume fraction,
is the surface load, and
is the droplets’ mean radius.
2. the characteristic adsorption concentration,
, which is the minimum biopolymer concentration needed to ensure that its adsorption will occur faster than the droplets’ collisions.
is calculated as
is the biopolymer’s mean hydrodynamic radius.
3. the characteristic depletion concentration,
, which is the smallest biopolymer concentration where depletion flocculation is observed.
is calculated through a series of nested equations as described and explained in  and .
For a stable multilayered emulsion to be formed, the biopolymer concentration ought to be in a range whose lower bound is
, shown as a red curve, and upper bound is
, shown as a green curve. The light blue area between those curves defines the entire range of stable emulsions. The red, green, and blue dots mark the three function values for a particular volume, which you can enter with the
The values of the three functions’ parameters,
, are entered with sliders and so are the upper limits of the chart’s
The equations to calculate and plot the chart are based on the assumption that any repulsive interactions between the biopolymer molecules and the emulsifier are negligible. They are used only for parameter ranges where the solutions have physical meaning.
 Y. H. Cho and D. J. McClements, "Theoretical Stability Maps for Guiding Preparation of Emulsions Stabilized by Protein-Polysaccharide Interfacial Complexes," Langmuir
(12), 2009 pp. 6649–6657.
 D. Guzey and D. J. McClements, "Formation, Stability and Properties of Multilayer Emulsions for Application in the Food Industry," Advances in Colloid and Interface Science
, 2006 pp. 227–248.
 D. J. McClements, "Design of Nano-Laminated Coatings to Control Bioavailability of Lipophilic Food Components," Journal of Food Science
(1), 2010 pp. R30–R42.