Computer Simulation of the Pre-Heating, Gelation, and Rheology of Acid Skim Milk Systems - Food Colloids: Self-Assembly and Material Science - page 270

other and the casein micelles. Depending on the physical circumstances,
different complexes of whey proteins and casein micelles are formed, influenc-
ing the properties of the products after further processing. 3,4 We consider here
the subsequent gelation of the pre-heated samples, and also the properties of
the resulting binary gels, specifically their break-up under shear.

18.2 Simulation Model
We model the colloidal skim milk solution as a bidisperse distribution of soft
spherical particles in a homogeneous solvent. The larger particles correspond to
the casein micelles, and the smaller ones to the whey proteins. The particles move
through the solute by Brownian motion. There are two distinct mutual particle
interactions: a medium-range reversible attraction or repulsion and an irrevers-
ible short-range bonding interaction. During the shearing stage, we allow this
bond to break beyond a certain maximal stretching length, in order to study
rupture. But during the gelation stage, the bonds once formed are permanent.
The Brownian dynamics (BD) simulation model is based on the Langevin
equation, the dynamical equation of motion for a system of diffusing particles.
The total force is the sum of the net force of interaction between particles, the
random fluctuating Brownian force, and the hydrodynamic interactions. The
solvent is regarded as continuous and the Brownian force mimics thermal
collisions between the solvent and the dispersed particles. The total force on
particle i is given by

dt 2 ¼ S i þ H i þ X
neighbours

P ij þ X
bonds

F ¼ m d 2 r i

B ij ; ð 1 Þ

where S i is the stochastic (Brownian) force, H i the force modelling hydrody-
namic interactions, r i the position of particle i, and t the time. We approximate
the hydrodynamic force H i by simple Stokesian friction, neglecting hydrody-
namic interactions between particles. The liquid drag force on a single particle,
H i , is proportional to the particle velocity, i.e.,

dr i
dt

H i ¼ g a ð 2 Þ

;

where g a ¼ 6 pZ R a is the Stokes drag, Z the solvent shear viscosity, and R a the
particle radius with the index a referring to the large (l) or small (s) particles.
The physical interactions P ij between the neighbouring particles are a constant
repulsive or attractive force when two particles are within a cut-off distance, but
not overlapping. When the soft elastic particles overlap there is a Hookean
restoring force between small and/or large particles. The chemical or binding
interaction is governed by a binding probability, a binding distance, and a
binding strength. There can be only one direct bond between any two particles.
Once a bond is formed it produces a force

B ij ¼ k ab (b j b i ), (3)