Interdisciplinary Applied Mathematics

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1. The particle motion is dominated by the Brownian motion and interfacial interactions. This becomes significant in submicron scales.

2. Brownian motion is random, and therefore it is very difficult to control.

3. The assembly times of the colloidal particles are too slow for practical technologies. Due to their larger size, the motion of colloidal particles is orders of magnitude slower than that of the atom. This is one of the reasons why molecular self-assembly in nature is common and easier than colloidal self-assembly.

Despite these difficulties, major strides have been made in the construction of self-assembled monolayers (Wasserman et al., 1989). As a result, designing surfaces and structures at the molecular scale has now become a possibility. The current molecular self-assembly techniques are inspired by processes in biological systems that enable proteins and cells to arrange themselves organically in functionally beneficial ways. This involves designing molecules and supramolecular entities that will aggregate into desired structures due to their shape complementarity (Wasserman et al., 1989).

Simulation of particulate microflows could play an important role in the development and active control of dynamically reconfigurable self-assembled structures. Colloidal micropumps and colloidal microvalves are already in existence and have been used for active microfluidic control; see an    example    in Figure    1.6,    and    for    details    (Terray    et    al.,    2002).    Self

assembly of colloidal particles onto the interface of emulsion droplets has been exploited by (Dinsmore et al., 2002) to fabricate solid capsules with precise control of size, permeability, strength, and compatibility. The resultant structures, which are called colloidosomes, are hollow elastic shells; they can be used for cellular immunoisolation.

Electrorheological (ER) and magnetorheological (MR) fluids, that is, suspensions that exhibit sensitivity to external electric and magnetic fields, are fluids    with    more    than    just    viscosity    as    their main    property.    ER and

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