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Chapter 2

[2.7]


л = (42,-л22)1/2

Here Дц and A22 correspond to the constants of the two materials.

From Eq. [2.7], Hamakerconstants are always positive, which means the van
der Waals interaction between similar materials in a liquid would be always be
attractive.

Most emulsions in aqueous media are charged due to various reasons, such
as the ionization of surface groups, specific adsorption of ions, and so forth [1]. In
an electrolyte solution, the distribution of ions around a charged sphere is not
uniform and gives an
electrical double layer.

When two charged spheres approach each other in an electrolyte solution,
their diffuse layers will overlap and repulsion develops between them. For two
identical spheres, the repulsion energy is[15]:

= 64πRc0Nkτx20 ехр(_А/г)                            [2.8]

к

Here C0 is the bulk concentration of the ionic specie, Λ∕λ is the Avogadro’s
number (6.02 ×1023 moΓ1), K =
tanh (zeoψc∕4kt) with z being the magnitude of the
ion valence, e0 the electronic charge (1.60 × 10'19 C), κ^1 the so-called Debye
length, which is used to characterize electrical double layer thickness, and
ψo the
electrical potential at the interfaces.

13



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