Cold granular targets slow the bulk freezing of an impacting droplet.

When making contact with an undercooled target, a drop freezes. The colder the target is, the more rapid the freezing is supposed to be. In this research, we explore the impact of droplets on cold granular material. As the undercooling degree increases, the bulk freezing of the droplet is delayed by at least an order of magnitude. The postponement of the overall solidification is accompanied by substantial changes in dynamics, including the spreading-retraction process, satellite drop generation, and cratering in the target. The solidification of the wetted pores in the granular target primarily causes these effects. The freezing process over the pore dimension occurs rapidly enough to match the characteristic timescales of impact dynamics at moderate undercooling degrees. As a result, the hydrophilic impact appears "hydrophobic," and the dimension of the solidified droplet shrinks. A monolayer of cold grains on a surface can reproduce these consequences. Our research presents a potential approach to regulate solidified morphology for subfreezing drop impacts. It additionally sheds light on the impact scenario of strong coupling between the dynamics and solidification.

Freezing Delay of a Drop Impacting on a Monolayer of Cold Grains.

We investigate a subfreezing droplet impact scenario in a low-humidity environment, where the target is a cold granular monolayer. When the undercooling degree of targets passes a threshold, such a granular layer effectively postpones the bulk freezing time of the droplet in comparison with the impact on the bare substrate underneath. In this case, the retraction of the droplet after impact reduces the contact area with the cold substrate, even though both the grains and the substrate are wettable to the liquid. We find that the significant changes in the dynamic behavior are triggered by freezing the liquid that wets the pores. Owing to the small dimension of the pores, the freezing process is rapid enough to match the dynamics over the droplet dimension. In certain circumstances, the rapid freezing may even stop liquid penetration and shed icing from the surface underneath.

Impact cratering in sand: comparing solid and liquid intruders.

How does the impact of a deformable droplet on a granular bed differ from that caused by a solid impactor of similar size and density? Here, we experimentally study this question and focus on the effect of intruder deformability on the crater shape. For comparable impact energies, we show that the crater diameter is larger for droplets than for solid intruders but that the impact of the latter results in deeper craters. Interestingly, for initially dense beds of packing fractions larger than 0.58, we find that the resultant excavated crater volume is independent of the intruder deformability, suggesting an impactor-independent dissipation mechanism within the sand for these dense beds.

Liquid-Grain Mixing Suppresses Droplet Spreading and Splashing during Impact.

Would a raindrop impacting on a coarse beach behave differently from that impacting on a desert of fine sand? We study this question by a series of model experiments, where the packing density of the granular target, the wettability of individual grains, the grain size, the impacting liquid, and the impact speed are varied. We find that by increasing the grain size and/or the wettability of individual grains the maximum droplet spreading undergoes a transition from a capillary regime towards a viscous regime, and splashing is suppressed. The liquid-grain mixing is discovered to be the underlying mechanism. An effective viscosity is defined accordingly to quantitatively explain the observations.

Upper bound on the Edwards entropy in frictional monodisperse hard-sphere packings.

We extend the Widom particle insertion method [B. Widom, J. Chem. Phys., 1963, 39, 2808-2812] to determine an upper bound sub on the Edwards entropy in frictional hard-sphere packings. sub corresponds to the logarithm of the number of mechanically stable configurations for a given volume fraction and boundary conditions. To accomplish this, we extend the method for estimating the particle insertion probability through the pore-size distribution in frictionless packings [V. Baranau, et al., Soft Matter, 2013, 9, 3361-3372] to the case of frictional particles. We use computer-generated and experimentally obtained three-dimensional sphere packings with volume fractions φ in the range 0.551-0.65. We find that sub has a maximum in the vicinity of the Random Loose Packing Limit φRLP = 0.55 and decreases then monotonically with increasing φ to reach a minimum at φ = 0.65. Further on, sub does not distinguish between real mechanical stability and packings in close proximity to mechanical stable configurations. The probability to find a given number of contacts for a particle inserted in a large enough pore does not depend on φ, but it decreases strongly with the contact number.

Raindrop impact on sand: a dynamic explanation of crater morphologies.

As a droplet impacts upon a granular substrate, both the intruder and the target undergo deformation, during which the liquid may penetrate into the substrate. These three aspects together distinguish it from other impact phenomena in the literature. We perform high-speed, double-laser profilometry measurements and disentangle the dynamics into three aspects: the deformation of the substrate during the impact, the maximum spreading diameter of the droplet, and the penetration of the liquid into the substrate. By systematically varying the impact speed and the packing fraction of the substrate, (i) the substrate deformation indicates a critical packing fraction ϕ* ≈ 0.585; (ii) the maximum droplet spreading diameter is found to scale with a Weber number corrected by the substrate deformation; and (iii) a model of the liquid penetration is established and is used to explain the observed crater morphology transition.

Measuring the configurational temperature of a binary disc packing.

Jammed packings of granular materials differ from systems normally described by statistical mechanics in that they are athermal. In recent years a statistical mechanics of static granular media has emerged where the thermodynamic temperature is replaced by a configurational temperature X which describes how the number of mechanically stable configurations depends on the volume. Four different methods have been suggested to measure X. Three of them are computed from properties of the Voronoi volume distribution, the fourth takes into account the contact number and the global volume fraction. This paper answers two questions using experimental binary disc packings: first we test if the four methods to measure compactivity provide identical results when applied to the same dataset. We find that only two of the methods agree quantitatively. This implies that at least two of the four methods are wrong. Secondly, we test if X is indeed an intensive variable; this becomes true only for samples larger than roughly 200 particles. This result is shown to be due to recently measured correlations between the particle volumes [Zhao et al., Europhys. Lett., 2012, 97, 34004].

Collective motion of granular matter subjected to swirling excitation.

A two-dimensional granular packing under horizontally circular shaking exhibits various collective motion modes where nonuniform density distribution and correlated dynamics are present. For intermediate packing density and oscillation amplitude, a condensed phase travels around the container's side wall in the clockwise direction, while the oscillation itself is set anticlockwise. Further increasing the packing density towards that of hexagonal packing, the whole packing rotates collectively in the clockwise direction. The core of the packing rotates as a solid and is separated from the boundary by a fluid-like layer. Both motion modes are associated with the asymmetric motion of particles close to the side wall in one oscillation cycle, where the dependence of particle velocity on the local density plays a key role.

Crater formation during raindrop impact on sand.

After a raindrop impacts on a granular bed, a crater is formed as both drop and target deform. After an initial, transient, phase in which the maximum crater depth is reached, the crater broadens outwards until a final steady shape is attained. By varying the impact velocity of the drop and the packing density of the bed, we find that avalanches of grains are important in the second phase and hence affect the final crater shape. In a previous paper, we introduced an estimate of the impact energy going solely into sand deformation and here we show that both the transient and final crater diameter collapse with this quantity for various packing densities. The aspect ratio of the transient crater is however altered by changes in the packing fraction.

Posterior C1-C2 screw-rod fixation and autograft fusion for the treatment of os odontoideum with C1-C2 instability.

OBJECTIVE: To report our experience treating os odontoideum with C1-C2 instability via C1-C2 screw-rod fixation and autograft fusion and to explore the clinical efficacy of such a treatment strategy. PATIENTS AND METHODS: We retrospectively reviewed the medical records of patients who were diagnosed with os odontoideum with C1-C2 instability and treated by posterior C1-C2 screw-rod fixation and fusion. Neurological deficits were measured with the Japanese Orthopedic Association (JOA) scoring system and neck pain was assessed using the Visual Analogue Scale (VAS) score. Fusion was determined based on the presence of bridging bone in computed tomography (CT) imaging, whereas stability was determined based on the lack of movement in dynamic radiographs. RESULTS: Thirty-two patients (18 males) were included in the study. The surgery was successfully accomplished in all patients. Thirty (93.8%) patients had confirmed C1-C2 bony fusion in CT images and all patients (100%) were stable in dynamic radiographs. The mean preoperative JOA score was 14.3±1.4 (range 11-16); at the final visit, it increased to 16.2±0.8 (range 14-17) (p<0.001). The mean preoperative VAS score was 3.8±0.7 (range 3-5) and decreased at the final visit to 1.0±0.6 (range 0-2) (p<0.001). CONCLUSION: Our treatment strategy (C1-C2 screw-rod fixation and autograft fusion) can achieve excellent clinical results with minor complications for patients with os odontoideum with C1-C2 instability.

A morphometric study of the middle and lower cervical vertebral endplates and their components.

Cervical disc arthroplasty is a common method of treating cervical degenerative disease. However, the footprints of most prosthesis dimensions are obtained from data of Caucasian individuals. Besides, there is a large discrepancy between footprints of currently available cervical disc prostheses and anatomic dimensions of cervical endplates. We aimed to detail the three-dimensional (3D) anatomic morphology of the subaxial cervical vertebral endplate, utilizing high-precision, high-resolution scanning equipment, and provide a theoretical basis for designing appropriate disc prostheses for Chinese patients.A total of 138 cervical vertebral endplates were studied. Each endplate was digitized using a non-contact optical 3D range scanning system and then reconstructed to quantify diameters and surface area for the whole endplate and its components (central endplate and epiphyseal rim). The whole endplate and mid-plane concavity depth were measured.There is marked morphologic asymmetry, in that the cranial endplate is more concave than the corresponding caudal endplate, with endplate concavity depths of 2.04 and 0.69 mm, respectively. For the caudal endplates, the endplate concavity apex locations were always located in the posterior portion (81.42%), while in cranial endplates relatively even. The central endplate was approximately 60% of the area of the whole endplate and the anterior section of the ring was the widest. From C3/4 down to C6/7 discs, the vertebral endplate gradually became more elliptical. Chinese cervical endplate anatomic sizes are generally smaller than that of Caucasians. Although Korean and Chinese individuals both belong to the Asian population subgroup, the majority of anatomic dimensions differ. Singaporean cervical endplate morphology is very similar to that of Chinese patients.We performed a comprehensive and accurate quantitative description of the cervical endplate, which provide references to shape and profile an artificial cervical disc without sacrificing valuable bone stock. To design a device with footprint as large as possible to distribute the axial load, we suggest that additional attention should be paid to the marginal rim. It is essential to specifically design appropriate disc prosthesis for Chinese patients. To fit the morphologic and biomechanical variations, we also propose that the disc prostheses for different vertebral segments should be separately designed.

Biomechanical Analysis of a Novel Prosthesis Based on the Physiological Curvature of Endplate for Cervical Disc Replacement.

STUDY DESIGN: Biomechanical analysis of a novel prosthesis based on the physiological curvature of endplate was performed. OBJECTIVE: To compare the biomechanical differences between a novel prosthesis based on the physiological curvature of the endplate and the Prestige LP prosthesis after cervical disc replacement (CDR). SUMMARY OF BACKGROUND DATA: Artificial disc prostheses have been widely used to preserve the physiological function of treated and adjacent motion segments in CDR, while most of those present a flat surface instead of an arcuate surface which approximately similar to anatomic structures in vivo. We first reported a well-designed artificial disc prosthesis based on the physiological curvature of the endplate. METHODS: Three motion segments of 24 ovine cervical spines (C2-5) were evaluated in a robotic spine system with axial compressive loads of 50N. Testing conditions were as follows: 1) intact, 2) C3-4 CDR with artificial disc prosthesis based on the physiological curvature of the endplate, and 3) C3-4 CDR with the Prestige LP prosthesis. The range of motion (ROM) and the pressures on the inferior surface of the two prostheses were recorded and analyzed. RESULTS: As compared to the intact state, the ROM of all three segments had no significant difference in the replacement group. Additionally, there was no significant difference in ROM between the two prostheses. The mean pressure on the novel prosthesis was significantly less than the Prestige LP prosthesis. CONCLUSION: ROM in 3 groups (intact group, CDR group with novel prosthesis and CDR group with Prestige LP) showed no significant difference. The mean pressure on the inferior surface of the novel prosthesis was significantly lower than the Prestige LP prosthesis. Therefore, the novel artificial disc prosthesis is feasible and effective, and can reduce the implant-bone interface pressure on the endplate, which may be one possible reason of prosthesis subsidence.