Determining interfacial tension for fluid-fluid-solid environments

A system comprising:

• a processing circuit configured to operate an atomic force microscope (AFM), the AFM comprising a first AFM tip having first radius, a second AFM tip having a second radius, and a third AFM tip having a third radius;
• wherein the processing circuit is further configured to:
• determine, by operation the first AFM tip, a first snap-off force of a solid surface immersed in a first fluid;
• determine, by operation of the second AFM tip, a second snap-off force of the solid surface immersed in the first fluid;
• determine by operation of the third AFM tip, a third snap-off force of the solid surface immersed in the first fluid;
• determine, by operation of the first AFM tip, a fourth snap-off force of a first droplet of the first fluid deposited on the solid surface, wherein the first droplet, the first AFM tip, and the solid surface are immersed in a second fluid;
• determine, by operation of the second AFM tip, a fifth snap-off force of the first droplet of the first fluid deposited on the solid surface, wherein the first droplet, the second AFM tip, and the solid surface are immersed in the second fluid;
• determine, by operation of the third AFM tip, a sixth snap-off force of the first droplet of the first fluid deposited on the solid surface, wherein the first droplet, the third AFM tip, and the solid surface are immersed in the second fluid;
• determine a first capillary force for the first AFM tip radius and the first droplet of the first fluid immersed in the second fluid based on the first snap-off force and the fourth snap-off force;
• determine a second capillary force for the second AFM tip radius and the first droplet of the first fluid immersed in the second fluid based on the second snap-off force and the fifth snap-off force;
• determining a third capillary force for the third AFM tip radius and the first droplet of the first fluid immersed in the second fluid based on the third snap-off force and the sixth snap-off force;
• and
• determine an interfacial tension between the first fluid and the second fluid based at least in part on the first capillary force, the second capillary force, and the third capillary force.

A computer-implemented method comprising:

• using a processor to control an atomic force microscope (AFM) to make determinations, wherein the AFM comprises a planar AFM cantilever;
• and
• wherein the determinations include:
• determining, by a processor operating the planar AFM cantilever, a first snap-off force of a first spherical protrusion from a solid surface, wherein the AFM cantilever and the first spherical protrusion are immersed in a first fluid, and wherein the first spherical protrusion comprises a first radius;
• determining, by the processor operating the planar AFM cantilever, a second snap-off force of a second spherical protrusion from a solid surface, wherein the AFM cantilever and the second spherical protrusion are immersed in a first fluid, and wherein the second spherical protrusion comprises a second radius;
• determining, by the processor operating the planar AFM cantilever, a third snap-off force of a third spherical protrusion from a solid surface, wherein the AFM cantilever and the third spherical protrusion are immersed in a first fluid, and wherein the third spherical protrusion comprises a third radius;
• determining, by the processor operating the planar AFM cantilever, a fourth snap-off force of a droplet of the first fluid deposited on the first spherical protrusion from the solid surface, wherein the droplet, the AFM cantilever, and the first spherical protrusion are immersed in a second fluid;
• determining, by the processor operating the planar AFM cantilever, a fifth snap-off force of a droplet of a first fluid deposited on the second spherical protrusion from the solid surface, wherein the droplet, the AFM cantilever, and the second spherical protrusion are immersed in a second fluid;
• determining, by the processor operating the planar AFM cantilever, a sixth snap-off force of a droplet of a first fluid deposited on the third spherical protrusion from the solid surface, wherein the droplet, the AFM cantilever, and the third spherical protrusion are immersed in a second fluid;
• determining, by the processor, a first capillary force for the first spherical protrusion radius and the droplet of the first fluid immersed in the second fluid based on the first snap-off force and the fourth snap-off force;
• determining, by the processor, a second capillary force for the second spherical protrusion radius and the droplet of the first fluid immersed in the second fluid based on the second snap-off force and the fifth snap-off force;
• determining, by the processor, a third capillary force for the third spherical protrusion radius and the droplet of the first fluid immersed in the second fluid based on the third snap-off force and the sixth snap-off force;
• and
• determining, by the processor, an interfacial tension between the first fluid and second fluid based at least in part on the first capillary force, the second capillary force and the third capillary force.