The total electrical double layer due to the formation of the counterion layers results in electrostatic screening of the wall charge and minimizes the Gibbs free energy of EDL formation. The thickness of the diffuse electric double layer is known as the Debye screening length . At a distance of two Debye screening lengths the electrical potential energy is reduced to 2 percent of the value at the surface wall. with unit of m−1, where is the number density of ion i in the bulk solution, z is the valency of the ion (for example, H+ has a valency of +1, and Ca2+ has a valency of +2), is the vacuum permittivity, is the relative static permittivity, kB is the Boltzmann constant. The repulsive free energy per unit area between two planar surfaces is shown as where is the reduced surface potential, , is the potential on the surface. The interaction free energy between two spheres of radius R is Combining the van der Waals interaction energy and the double layer interaction energy, the interaction between two particles or two surfaces in a liquid can be expressed as where W(D)R is the repulsive interaction energy due to electric repulsion, and W(D)A is the attractive interaction energy due to van der Waals interaction. Effect of shear flows The DLVO theory of colloidal stability has been extended to take into account the effect of shear flow in fluid dynamic systems, which is relevant for many applications e.g. microfluidics, chemical reactors, atmospheric and environmental flows, in the work of Alessio Zaccone and collaborators. In this extended DLVO theory for sheared systems, the DLVO energy barrier for aggregation gets reduced by a negative contribution which is proportional to the Péclet number of the particles, i.e. proportional to the shear rate, to the viscosity of the medium, and to the cube of the colloidal particle size, while the proportionality coefficient depends on the flow geometry. This result is obtained from an approximate solution to the governing Smoluchowski convection-diffusion equation obtained via the method of matched asymptotic expansions. The theory explains a characteristic lag-time in the shear-induced aggregation of the particles, which decreases exponentially with the shear rate. It also explains the subsequent runaway (autocatalytic) regime of aggregation kinetics after the lag-time, as well as the characteristic bimodal cluster size distribution of aggregates found typically in shear-induced aggregating and self-assembling systems. Furthermore, the theory has been