Recent studies, have successfully measured surface forces using atomic force microscope (AFM) and modeled surface deformations using the Stokes-Reynolds-Young-Laplace (SRYL) equations for particle-droplet, particle-bubble, droplet-droplet, and bubble-bubble systems in various solutions, The-Current work focuses on interactions between spherical silica particles and,a viscoelastic interface of water droplets in crude oil. The self-assembly of surface active natural polyaromatic molecules (NPAMs) at the oil-water interface has previously been shown to change a viscous dominant oil-water interface to an elastic dominant interface upon aging, due to gradual formation of rigid interfacial networks: AFM was used to measure the interactions between a small silica sphere (D approximate to 8 mu m) and a deformable water droplet (D approximate to 70 mu m), which exhibits time-dependent interfacial viscoelasticity in NPAM solutions. Unlike the systems studied previously, the measured deformation shown as a repulsive force over the region of constant compliance could not be modeled adequately by the conventional SRYL equations which are applicable only to purely Laplacian interfaces. As the water droplet ages in NPAM solutions, a rigid "skin" forms at the oil-water interface, with the interface exhibiting increased elasticity. Over a short aging period (up to 15 min in NPAM-in-toluene solution), interfacial deformation is well predicted by the SRYL model. However, upon further exposure to the NPAM solution, droplet deformation is overpredicted by the model. Physical properties of this mechanical barrier as a function of interfacial, aging were further, investigated by measuring interfacial tension, dilatational rheology, and interfacial "crumpling" (non-smooth, non-Laplacian interface) upon droplet volume reduction. By introducing a viscoelasticity parameter to account for interfacial stiffening and using experimentally determined elasticity, we are able to correct this discrepancy and predict droplet deformation under AFM cantilever compression. This parameter appears to be important for modeling non-Laplacian systems of significant viscoelastic contributions, such as biological cell membranes or polymer blends.