The colloidal interactions of solid particles with deformable fluid interfaces are not well understood fundamentally and are only accessible for study in very limited configurations under restrictive and ideal environments, most often through some indirect means.  The increasing interest in solid-fluid interactions is attested to by the scientific literature, but it is driven by the need to describe accurately various “soft” colloidal behavior for process design.  Air flotation—used for years in mineral separation and printed-paper recycling—and oil-assisted agglomeration, may be optimized for applications such as soil remediation, plastics recycling, or semiconductor polishing.  The ability to predict the stability of mixed colloidal systems is equally valuable when considering the quality of paints, cosmetics, and foods, for instance, or strictly as a scientific endeavor for understanding the world that surrounds us.
    The present work seeks to develop a quantitative method for measuring interaction forces between a single particle of the micron-scale or less and a fluid-fluid interface, specifically an oil droplet submerged in water.  The atomic force microscope (AFM) is the ideal candidate for such a task.  AFM is well suited for detecting forces directly between a microsphere and another particle or extended surface with sensitivity to the level of an individual covalent bond rupture.  Many different designs of AFM are commercially available, but they all have the same basic operating principles for imaging and force profiling.
    The adjacent drawing (Fig. 1.1) depicts an AFM using a three-dimensional piezo-electric scanner to provide sample-probe positioning from microns to Ångstroms.  Any force acting on the probe, e.g. sharp conical or pyramidal tip or attached microsphere, deflects the flexible cantilever being monitored by a reflecting laser and intercepting photodector (PSPD).  For small equilibrium deflections, the displacement registered by the PSPD is directly proportional to the interaction force.  These deflections also correspond to the topography for simple contact imaging, where the probe is lightly dragged over a substrate to follow the contour, in some cases with sub-Ångstrom resolution.
    Aside from imaging, the AFM is also used to measure the interaction force as a function of vertical sample displacement.  It is from these force-distance data that force-separation profiles are constructed for comparison with other systems and with theoretical force curves.  A very simplistic force diagram (Fig. 1.2) shows the typical characteristics of a rigid surface in air:  attractive snap-in to contact due mostly to capillary and van der Waals forces, linear compliance for an undeforming substrate, and large pull-off force related to adhesion.  The picture quickly gets complicated for real systems in fluid media, when electrostatics and hydrodynamics become important, or for softer samples that deform from contact.
    There are a number of critical deficiencies with commercial AFM and current methodologies for measuring force profiles that must be addressed in order to investigate oil-particle behavior.  The more important aspects are as follows:

    1. Determining the separation between sphere and oil droplet.
    2. Qualifying the role of the hydrophobic interaction in oil-particle aggregation.
    3. Understanding the mechanism, strength, and range of the hydrophobic interaction.
    4. Quantifying surface forces between attracting bodies from transient interactions.

The aspiration is that all of these may be suitably addressed and answered; however, there are several fundamental and technical limitations that will restrict the ultimate success of these investigations.
    First, the AFM is incapable of measuring the oil-particle separation, so it must be inferred.  Careful mathematical description of the deformation of the oil-water interface caused by an impinging sphere allows separation to be determined through model fitting.  This is also crucial for determining the equilibrium forces from dynamic or transient interactions precipitated by attractive forces rapidly deforming the interface.  The most common culprit is the attractive hydrophobic interaction which may be stronger and longer-range than DLVO forces, i.e van der Waals and electrostatic double-layer interactions.  While the following chapters will illuminate the role of the hydrophobic force and add to the body of knowledge, a truly fundamental understanding of its mechanism is likely far off and awaits further study by the scientific community.