Cell Models for Non-Newtonian Fluid Past a Semipermeable Sphere

This paper is focused on investigating the boundary effects of the steady translational motion of a semipermeable sphere located at the center of a spherical envelope filled with an incompressible micropolar fluid. Stokes equations of micropolar fluid are employed inside the spherical envelope and Darcy’s law governs in semipermeable region. On the surface of semipermeable sphere, the boundary conditions used are continuity of normal velocity, vanishing of tangential velocity of micropolar fluid, and continuity of pressure. On the surface of the spherical envelope, the Happel’s, Kuwabara’s, Kvashnin’s, and Cunningham’s boundary conditions, are used along with no spin boundary condition. The expression for the hydrodynamic normalized drag force acting on the semipermeable sphere is obtained. The limiting cases of drag expression exerted on the semipermeable sphere and impermeable solid sphere in cell models filled with Newtonian fluid are obtained. Also, in absence of envelope, the drag expression for the micropolar fluid past a semipermeable sphere is obtained.

Imaging the water snowline in a protostellar envelope with H13CO+

Context. Snowlines are key ingredients for planet formation. Providing observational constraints on the locations of the major snowlines is therefore crucial for fully connecting planet compositions to their formation mechanism. Unfortunately, the most important snowline, that of water, is very difficult to observe directly in protoplanetary disks because of the close proximity of this snowline to the central star. Aims. Based on chemical considerations, HCO+ is predicted to be a good chemical tracer of the water snowline because it is particularly abundant in dense clouds when water is frozen out. This work aims to map the optically thin isotopolog H13CO+ toward the envelope of the low-mass protostar NGC 1333-IRAS2A, where the snowline is at a greater distance from the star than in disks. Comparison with previous observations of H218O show whether H13CO+ is indeed a good tracer of the water snowline. Methods. NGC 1333-IRAS2A was observed using the NOrthern Extended Millimeter Array (NOEMA) at ~0.′′9 resolution, targeting the H13CO+ J = 3 − 2 transition at 260.255 GHz. The integrated emission profile was analyzed using 1D radiative transfer modeling of a spherical envelope with a parametrized abundance profile for H13CO+. This profile was validated with a full chemical model. Results. The H13CO+ emission peaks ~ 2′′ northeast of the continuum peak, whereas H218O shows compact emission on source. Quantitative modeling shows that a decrease in H13CO+ abundance by at least a factor of six is needed in the inner ~360 AU to reproduce the observed emission profile. Chemical modeling indeed predicts a steep increase in HCO+ just outside the water snowline; the 50% decrease in gaseous H2O at the snowline is not enough to allow HCO+ to be abundant. This places the water snowline at 225 AU, further away from the star than expected based on the 1D envelope temperature structure for NGC 1333-IRAS2A. In contrast, DCO+ observations show that the CO snowline is at the expected location, making an outburst scenario unlikely. Conclusions. The spatial anticorrelation of H13CO+ and H218O emission provide proof of concept that H13CO+ can be used as a tracer of the water snowline.

Compensation system design of disturbing torques for a magnetically suspended sensitive gyroscope with double spherical envelope surfaces

Magnetically suspended sensitive gyroscopes (MSSGs) provide an interesting alternative for achieving precious attitude angular measurement. But the high accuracy is sensitive to various disturbing torques acting on the rotor. In order to compensate for the drift errors produced by disturbing torques, this paper proposes a compensation system of Lorentz force magnetic bearings. Based on the geometric construction and running regularity of the compensation system, the analytical expression of the compensation torque has been deduced, and the generation mechanism of the compensation torque is revealed, which laid the foundation for the design of high-precision MSSGs. The common issues caused by disturbing torques can be effectively resolved by the proposed method in gyroscopes with a levitating rotor. To verify the feasibility and superiority of this compensation method, comparative simulations are carried out before and after the disturbing torques were compensated.

MOTION OF A SLIP SPHERE IN A NONCONCENTRIC FICTITIOUS SPHERICAL ENVELOPE OF MICROPOLAR FLUID

Stokes’ axisymmetrical translational motion of a slip sphere, located anywhere on the diameter of a virtual spherical fluid ‘cell’, is investigated. The fluid is micropolar and flows are parallel to the line connecting the two centres. An infinite-series solution is presented for the stream function, pressure field, vorticity, microrotation component, shear stress and couple stress of the flow. Basset-type slip boundary conditions on the sphere surface are used for velocity and microrotation. The Happel and Kuwabara boundary conditions are used on the fictitious surface of the cell model. Numerical results for the normalized drag force acting on the sphere are obtained with excellent convergence for various values of the volume fraction, the relative distance between the centre of the sphere and the virtual envelope, the vortex viscosity parameter and the slip coefficients of the sphere. In the special case when the spherical particle is in the concentric position with the cell surface, the numerical values of the normalized drag force agree with the available values in the literature.