A magnetically controlled spiral capsule robot is designed. When the robot is running in a pipe filled with mucus, computational fluid dynamics is used to analyze the fluid field (velocity, streamlines, and vorticity) in the pipe, and particle image velocimetry is used to measure the above fluid field surrounding the robot. The measured fluid field is basically similar to the numerical result. The relationship between the operating parameters of the robot and the performance of the robot is further calculated and analyzed. The results show that the resistance to the robot in the forward direction, average turbulent intensity of the fluid surrounding the robot, and maximum fluid pressure to the pipe wall are proportional to the robotic translational speed. The resisting moment of the robot in the forward direction, average turbulent intensity of the fluid surrounding the robot, and maximum fluid pressure to the pipe wall are proportional to the robotic rotational speed.

For the measurement of flow-induced microrotations in flows utilizing the depolarization of phosphorescence anisotropy, suitable luminophores are crucial. The present work examines dyes of the xanthene family, namely Rhodamine B, Eosin Y and Erythrosine B. Both in solution and incorporated in particles, the dyes are examined regarding their luminescent lifetimes and their quantum yield. In an oxygen-rich environment at room temperature, all dyes exhibit lifetimes in the sub-microsecond range and a low intensity signal, making them suitable for sensing fast rotations with sensitive acquisition systems.

Vortex and vorticity are two correlated but fundamentally different concepts which have been the central issues in fluid mechanics research. Vorticity has rigorous mathematical definition (curl of velocity), but no clear physical meaning. Vortex has clear physical meaning (rotation) but no rigorous mathematical definition. For a long time, many people treat them as a same thing. However, based on our high-order direct numerical simulation (DNS), we found that first, “vortex” is not “vorticity tube” or “vortex tube” which is widely defined as a bundle of vorticity lines without any vorticity line leak. Actually, vortex is an open area for vorticity line penetration. Second, vortex is not necessarily congregation of vorticity lines, but dispersion in many 3-dimensional cases. Some textbooks say that vortex cannot end inside the flow field but must end on the solid wall (and/or boundaries). Our DNS observation and many other numerical results show almost all vortices are ended inside the flow field. Finally, a more theoretical study shows that neither vortex nor vorticity line can attach to the solid wall and they must be detached from the wall.

The Zagros hinterland fold-and-thrust belt is located in the central portion of the Zagros Thrust System and consists of the exhumed basement windows associated with NW-striking and NE-dipping flexural duplex structures that contain in-sequence thrusting and related folds. Mylonitic nappes of the basement were exhumed along deep-seated sole thrusts of the Zagros Thrust System. Lattice preferred orientation (LPO) c-axes of quartz show asymmetric type-1 crossed girdles that demonstrate a non-coaxial deformation under plane strain conditions. Based on the opening angles of quartz c-axis fabric skeletons, deformation temperatures vary from 425±50°C to 540±50°C, indicating amphibolite facies conditions. The estimated mean kinematic vorticity evaluated from quartz c-axis of the quartzo-feldspathic mylonites (Wm = 0.55±0.06) indicates the degree of non-coaxiality during mylonite exhumation. The estimated angle θ between the maximum instantaneous strain axis (ISA1) and the transpressional zone boundary is 17°, and the angle of oblique convergence is 57° in the M2 nappe of the basement involved. This indicates that the mylonitic nappe was formed by a combination of 62% pure shear and 38% simple shear during oblique convergence.

This paper presents a new approach to verify the accuracy of computational simulations. We develop mathematical theorems which can serve as robust a posteriori error estimation techniques to identify numerical pollution, check the performance of adaptive meshes, and verify numerical solutions. We demonstrate performance of this methodology on problems from flow thorough porous media. However, one can extend it to other models. We construct mathematical properties such that the solutions to Darcy and Darcy-Brinkman equations satisfy them. The mathematical properties include the total minimum mechanical power, minimum dissipation theorem, reciprocal relation, and maximum principle for the vorticity. All the developed theorems have firm mechanical bases and are independent of numerical methods. So, these can be utilized for solution verification of finite element, finite volume, finite difference, lattice Boltzmann methods and so forth. In particular, we show that, for a given set of boundary conditions, Darcy velocity has the minimum total mechanical power of all the kinematically admissible vector fields. We also show that a similar result holds for Darcy-Brinkman velocity. We then show for a conservative body force, the Darcy and Darcy-Brinkman velocities have the minimum total dissipation among their respective kinematically admissible vector fields. Using numerical examples, we show that the minimum dissipation and total mechanical power theorems can be utilized to identify pollution errors in numerical solutions. The solutions to Darcy and Darcy-Brinkman equations are shown to satisfy a reciprocal relation, which has the potential to identify errors in the numerical implementation of boundary conditions. It is also shown that the vorticity under both steady and transient Darcy-Brinkman equations satisfy maximum principles if the body force is conservative and the permeability is homogeneous and isotropic. A discussion on the nature of vorticity under steady and transient Darcy equations is also presented. Using several numerical examples, we will demonstrate the predictive capabilities of the proposed a posteriori techniques in assessing the accuracy of numerical solutions for a general class of problems, which could involve complex domains and general computational grids.

We present an existence and stability theory for gravity–capillary solitary waves with constant vorticity on the surface of a body of water of finite depth. Exploiting a rotational version of the classical variational principle, we prove the existence of a minimizer of the wave energy 𝓗 subject to the constraint 𝓘 = 2µ, where 𝓘 is the wave momentum and 0 < µ ≪ 1. Since 𝓗 and 𝓘 are both conserved quantities, a standard argument asserts the stability of the set Dµ of minimizers: solutions starting near Dµ remain close to Dµ in a suitably defined energy space over their interval of existence. In the applied mathematics literature solitary water waves of the present kind are described by solutions of a Korteweg–de Vries equation (for strong surface tension) or a nonlinear Schrödinger equation (for weak surface tension). We show that the waves detected by our variational method converge (after an appropriate rescaling) to solutions of the appropriate model equation as µ ↓ 0.

This paper studies outflow of a light fluid from a point source, starting from an initially spherical bubble. This region of light fluid is embedded in a heavy fluid, from which it is separated by a thin interface. A gravitational force directed radially inward toward the mass source is permitted. Because the light inner fluid is pushing the heavy outer fluid, the interface between them may be unstable to small perturbations, in the Rayleigh–Taylor sense. An inviscid model of this two-layer flow is presented, and a linearized solution is developed for early times. It is argued that the inviscid solution develops a point of infinite curvature at the interface within finite time, after which the solution fails to exist. A Boussinesq viscous model is then presented as a means of quantifying the precise effects of viscosity. The interface is represented as a narrow region of large density gradient. The viscous results agree well with the inviscid theory at early times, but the curvature singularity of the inviscid theory is instead replaced by jet formation in the viscous case. This may be of relevance to underwater explosions and stellar evolution.

This paper presents quantitative data on the finite strain, quartz crystal fabric, geometry of flow and deformation temperatures in deformed quartzite samples to characterize the ductile deformation along the thrust sheets constituting the Sanandaj–Sirjan Metamorphic Belt within the Zagros Mountains of Iran. The results of this study emphasize the heterogeneous nature of deformation in this belt, showing a spatial variation in strain magnitude and in degree of non-coaxiality. A dominant top-to-the-SE sense of shear is indicated by the asymmetry of microstructures and quartz c-axis fabrics. Quartz c-axis opening angles suggest deformation temperatures range between 435° ± 50°C and 510° ± 50°C, which yield greenschist to amphibolite facies conditions during the ductile deformation. Mean kinematic vorticity number (Wm) measured in the quartzite samples ranges between 0.6 and 0.9 with an average of 0.76, which indicates that extrusion of the metamorphic rocks of the region was facilitated by a significant component of pure shear strain. Traced towards the basal thrust of the Zagros Thrust System from northeast to southwest, the quartz grain fabrics change from asymmetric cross-girdle fabrics in the internal part of the deformation zone to an asymmetric single-girdle fabric at distances close to the basal thrust. This variation may depend on the structural depth and on the geometry of the ductile deformation zone. The observed increase in strain and vorticity within the study area is comparable with patterns recorded within metamorphic rock extrusions within other orogens in the world.