**4. Conclusions**

22 Hydrodynamics

software (Domínguez-García & Rubio (2009)) employs open-sourced algorithms for detecting the centres of mass of the particles by detecting the borders of each object and then obtaining its geometrical properties. As an example, we have tried to evaluate how this border detection can have an influence on the result of the electrostatic potential. A measured apparent displacement Δ(*r*) = *r*� − *r* should affect to the radial distribution function in the following

For obtaining Δ(*r*) we have extracted a typical particle image and we have composed some set of images which consist on separating the two particles a known distance (*r*) in pixels. Next, we apply our methods of image analysis for obtaining the position of those particles

to grow when the particles are very near. In Fig.6, we display the results of our calculations on the possible artefact in the analysis of the position of the particles by image binarization and binary watershed, a method for automatically separating particles that are in contact. The figure reveals that the correction on the electrostatic potential for this cause is basically negligible, because the correction in the potential is zero for distances *r* > 1.2 *μ*m. In the inset of the figure we can see some of the images we have employed for this calculation, showing

Fig. 6. Estimation of a possible artefact in the analysis of the position of the particles. In the

In any case, the possibility of an artifact can be the cause of these observations in the electrostatic potential cannot be descarted. However, the direct or indirect presence and influence of these attractive wells has been detected in many other situations in these experiments. For example, the attractive interaction disappears when we added a salt, in our case KCl, to the suspensions, confirming the electrostatic nature of the phenomena (Domínguez-García, Pastor, Melle & Rubio (2009)). In disaggregation it is observed how the particles move inside the chains without leaving them (Domínguez-García et al. (2011)). The lapse of time that the particles are in this situation depends on the initial morphology of the aggregates, something which has been observed to depend on the ratio *R*1/*R*<sup>0</sup> (Domínguez-García, Melle & Rubio (2009); Domínguez-García & Rubio (2010)). Then, this effective lapse of time depends of how many particles are located near the other in a short distance. In that situation, the attractive interaction should play a role in disaggregation, as it

inset we have included some examples of the images used for this calculation.

(*r*) <sup>−</sup> *<sup>β</sup>U*(*r*) <sup>∼</sup><sup>=</sup> <sup>−</sup>*<sup>β</sup> dU*(*r*)

(*r* + Δ(*r*))(1 + *d*Δ(*r*)/*dr*) (Polin et al. (2007)). From that expression, the

*dr* <sup>Δ</sup>(*r*) + *<sup>d</sup>*Δ(*r*)

). Then, the apparent displacement, Δ(*r*) = *r*� − *r*, is observed

*dr* (48)

form: *g*(*r*) = *g*�

variation in the electrostatic potential is:

and calculate the distances (*r*�

*βU*�

the detected border of the particles among the images themselves.

In this chapter, we have reviewed the main interactions, with focus on hydrodynamics and from a experimental point of view, that can be important in a confined colloidal system at low concentration of microparticles. We have used charged superparamagnetic microparticles dispersed in water in low-confinement conditions by means of a glass cell for the study of irreversible field-induced aggregation and disaggregation, as well as the microstructure of the suspension. Regarding aggregation characteristic times and basic behaviour on the disaggregation of the particles, we have observed significant discrepancies between the experimental results and the theory. Morover, anomalous effects in the electrostatic behaviour have been observed, showing that, in this kind of systems, the electro-hydrodynamics interactions are not well understood at present and deserve more theoretical and experimental investigations.
