Understanding pore heterogeneity can enable us to obtain a deeper insight into the flow and transport processes in any porous medium. In this study, multifractal analysis was employed to analyze gas adsorption isotherms (CO2 and N2) for pore structure characterization in both a source (Upper-Lower Bakken) and a reservoir rock (Middle Bakken). For this purpose, detected micropores from CO2 adsorption isotherms and meso-macropores from N2 adsorption isotherms were analyzed separately. The results showed that the generalized dimensions derived from CO2 and the N2 adsorption isotherms decrease as q increases, demonstrating a multifractal behavior followed by f(α) curves of all pores exhibiting a very strong asymmetry shape. Samples from the Middle Bakken demonstrated the smallest average H value and largest average α10-α10+ for micropores while samples from the Upper Bakken depicted the highest average α10-α10+ for the meso-macropores. This indicated that the Middle Bakken and the Upper Bakken have the largest micropore and meso-macropore heterogeneity, respectively. The impact of rock composition on pore structures showed that organic matter could increase the micropore connectivity and reduce micropore heterogeneity. Also, organic matter will reduce meso-macropore connectivity and increase mesomacropore heterogeneity. We were not able to establish a robust relationship between maturity and pore heterogeneity of the source rock samples from the Bakken.

We report measurements of the Casimir force between a gold sphere and a silicon surface with an array of nanoscale, rectangular corrugations using a micromechanical torsional oscillator. At distances between 150 and 500 nm, the measured force shows significant deviations from the pairwise additive formulism, demonstrating the strong dependence of the Casimir force on the shape of the interacting bodies. The observed deviation, however, is smaller than the calculated values for perfectly conducting surfaces, possibly due to the interplay between finite conductivity and geometry effects. DOI: 10.1103/PhysRevLett.101.030401 PACS numbers: 03.70.+k, 12.20.Fv, 12.20.Ds, 42.50.Lc The Casimir force is the interaction between neutral conductors that can be understood as resulting from the alteration of the zero point energy of the electromagnetic field in the presence of boundaries [1]. For two perfect metallic planar surfaces, the force is attractive and is given by F c 2 @cA=240z4 , where c is the speed of light, @ is the Planck's constant=2, z is the separation between the plates, and A is the area of the plates. There exists a close connection between the Casimir force between conductors and the van der Waals (vdW) force between molecules. For the former, the quantum fluctuations are often associated with the vacuum electromagnetic field, while the latter commonly refers to the interaction between fluctuating dipoles. In simple geometries such as two parallel planes, the Casimir force can be interpreted as an extension of the vdW force in the retarded limit. The interaction between molecules in the two plates is summed to yield the total force. However, such summation of the vdW force is not always valid for extended bodies because the vdW force is not pairwise additive. The interaction between two molecules is affected by the presence of a third molecule. One important characteristic of the Casimir force is its strong dependence on geometry [2]. The Casimir energy for a conducting spherical shell [3] or a rectangular box [4,5] has been calculated to have opposite sign to parallel plates. Whether such geometries exhibit repulsive Casimir forces remains a topic of current interest [6].In recent years, there have been a number of precision measurements of the Casimir force [7][8][9][10][11][12][13][14][15]. These experiments yield agreement with the theoretical calculations to accuracies of better than 1% when nonideal behavior of the metallic surfaces [16][17][18] are taken into account. The vast majority of force measurements were performed between a sphere and a flat plate, two flat plates, or two cylinders. For these simple geometries, the Casimir force is not expected to show significant deviations from the pairwise additive approximation (PAA) at small separations. There has only been one experiment that involved surfaces of other geometries, where the Casimir force is measured between a sphere and a plate with small sinusoidal corrugations [19]. While this measurement shows deviations from PAA, the interpret...

Quantum fluctuations give rise to van der Waals and Casimir forces that dominate the interaction between electrically neutral objects at sub-micron separations. Under the trend of miniaturization, such quantum electrodynamical effects are expected to play an important role in micro-and nano-mechanical devices. Nevertheless, utilization of Casimir forces on the chip level remains a major challenge because all experiments so far require an external object to be manually positioned close to the mechanical element. Here by integrating a forcesensing micromechanical beam and an electrostatic actuator on a single chip, we demonstrate the Casimir effect between two micromachined silicon components on the same substrate. A high degree of parallelism between the two near-planar interacting surfaces can be achieved because they are defined in a single lithographic step. Apart from providing a compact platform for Casimir force measurements, this scheme also opens the possibility of tailoring the Casimir force using lithographically defined components of non-conventional shapes.