Intuitive Considerations Clarifying the Origin and Applicability of the Benford Law

The diverse applications of the Benford law attract investigators working in various fields of physics, biology and sociology. At the same time, the groundings of the Benford law remain obscure. Our paper demonstrates that the Benford law arises from the positional (place-value) notation accepted for representing various sets of data. An alternative to Benford formulae to predict the distribution of digits in statistical data are derived. Application of these formulae to the statistical analysis of infrared spectra of polymers is presented. Violations of the Benford Law are discussed.Comment: 12 pages, 2 Tables, 3 Figure

Mapping outcomes of liquid marble collisions

© 2019 The Royal Society of Chemistry. Liquid marbles (LMs) have many promising roles in the ongoing development of microfluidics, microreactors, bioreactors, and unconventional computing. In many of these applications, the coalescence of two LMs is either required or actively discouraged, therefore it is important to study liquid marble collisions and establish parameters which enable the desired collision outcome. Recent reports on LM coalescence have focused on either two mobile LMs colliding, or an accelerating LM hitting a sessile LM with a backstop. A further possible scenario is the impact of a mobile LM against a non-supported static LM. This paper investigates such a collision, using high-speed videography for single-frame analysis. Multiple collisions were undertaken whilst varying the modified Weber number (We∗) and offset ratios (X∗). Parameter ranges of 1.0 0.25, and We∗ 1.55 resulted in 100% non-coalescence. Additionally, observations of LMs moving above a threshold velocity of 0.6 m s -1 have revealed a new and unusual deformation. Comparisons of the outcome of collisions whilst varying both the LM volume and the powder grain size have also been made, revealing a strong link. The results of this work provide a deeper understanding of LM coalescence, allowing improved control when designing future collision experiments

Mechanical sequential counting with liquid marbles

© 2018, Springer International Publishing AG, part of Springer Nature. Here we demonstrate the first working example of a liquid marble-operated sequential binary counting device. We have designed a lightweight gate that can be actuated by the low mass and momentum of a liquid marble. By linking a number of these gates in series, we are able to digitally count up to binary 1111 (upper limit only by our requirements). Using liquid marbles in such a system opens up new avenues of research and design, by way of modifying the coating and/or core of the liquid marbles, and thereby giving extra dimensions for calculation (e.g. a calculation that takes into consideration the progress of a chemical reaction inside a liquid marble). In addition, the new gate design has multiple uses in liquid marble rerouting

Particles at oil–air surfaces : powdered oil, liquid oil marbles, and oil foam

The type of material stabilized by four kinds of fluorinated particles (sericite and bentonite platelet clays and spherical zinc oxide) in air–oil mixtures has been investigated. It depends on the particle wettability and the degree of shear. Upon vigorous agitation, oil dispersions are formed in all the oils containing relatively large bentonite particles and in oils of relatively low surface tension (γla < 26 mN m⁻¹) like dodecane, 20 cS silicone, and cyclomethicone containing the other fluorinated particles. Particle-stabilized oil foams were obtained in oils having γla > 26 mN m⁻¹ where the advancing air–oil–solid contact angle θ lies between ca. 90° and 120°. Gentle shaking, however, gives oil-in-air liquid marbles with all the oil–particle systems except for cases where θ is <60°. For oils of tension >24 mN m⁻¹ with omniphobic zinc oxide and sericite particles for which advancing θ ≥ 90°, dry oil powders consisting of oil drops in air which do not leak oil could be made upon gentle agitation up to a critical oil:particle ratio (COPR). Above the COPR, catastrophic phase inversion of the dry oil powders to air-in-oil foams was observed. When sheared on a substrate, the dry oil powders containing at least 60 wt % of oil release the encapsulated oil, making these materials attractive formulations in the cosmetic and food industries

Liquid Marble Actuator for Microfluidic Logic Systems

© 2018, The Author(s). A mechanical flip-flop actuator has been developed that allows for the facile re-routing and distribution of liquid marbles (LMs) in digital microfluidic devices. Shaped loosely like a triangle, the actuating switch pivots from one bistable position to another, being actuated by the very low mass and momentum of a LM rolling under gravity (~4 × 10 −6 kg ms −1 ). The actuator was laser-cut from cast acrylic, held on a PTFE coated pivot, and used a PTFE washer. Due to the rocking motion of the switch, sequential LMs are distributed along different channels, allowing for sequential LMs to traverse parallel paths. This distributing effect can be easily cascaded, for example to evenly divide sequential LMs down four different paths. This lightweight, cheap and versatile actuator has been demonstrated in the design and construction of a LM-operated mechanical multiplication device — establishing its effectiveness. The actuator can be operated solely by gravity, giving it potential use in point-of-care devices in low resource areas

Numerical study of wetting transitions on biomimetic surfaces using a lattice Boltzmann approach with large density ratio

The hydrophobicity of natural surfaces have drawn much attention of scientific communities in recent years. By mimicking natural surfaces, the manufactured biomimetic hydrophobic surfaces have been widely applied to green technologies such as self-cleaning surfaces. Although the theories for wetting and hydrophobicity have been developed, the mechanism of wetting transitions between heterogeneous wetting state and homogeneous wetting state is still not fully clarified. As understanding of wetting transitions is crucial for manufacturing a biomimetic superhydrophobic surface, more fundamental discussions in this area should be carried out. In the present work the wetting transitions are numerically studied using a phase field lattice Boltzmann approach with large density ratio, which should be helpful in understanding the mechanism of wetting transitions. The dynamic wetting transition processes between Cassie-Baxter state and Wenzel state are presented, and the energy barrier and the gravity effect on transition are discussed. It is found that the two wetting transition processes are irreversible for specific inherent contact angles and have different transition routes, the energy barrier exists on an ideally patterned surface and the gravity can be crucial to overcome the energy barrier and trigger the transition

Bioactive Hydrogel Marbles

Liquid marbles represented a signifcant advance in the manipulation of fuids as they used particle flms to confne liquid drops, creating a robust and durable soft solid. We exploit this technology to engineering a bioactive hydrogel marble (BHM). Specifcally, pristine bioactive glass nanoparticles were chemically tuned to produce biocompatible hydrophobic bioactive glass nanoparticles (H-BGNPs) that shielded a gelatin-based bead. The designed BHM shell promoted the growth of a bone-like apatite layer upon immersion in a physiological environment. The fabrication process allowed the efcient incorporation of drugs and cells into the engineered structure. The BHM provided a simultaneously controlled release of distinct encapsulated therapeutic model molecules. Moreover, the BHM sustained cell encapsulation in a 3D environment as demonstrated by an excellent in vitro stability and cytocompatibility. The engineered structures also showed potential to regulate a pre-osteoblastic cell line into osteogenic commitment. Overall, these hierarchical nanostructured and functional marbles revealed a high potential for future applications in bone tissue engineering.Portuguese Foundation for Science and Technology − FCT (Grant Nos SFRH/BD/73174/2010 and SFRH/BD/73172/2010, respectively), from the program POPH/FSE from QREN. The authors would like to acknowledge the support of the European Research Council grant agreement ERC-2014-ADG-669858 for project ATLASinfo:eu-repo/semantics/publishedVersio