Motion of an Elastic Capsule in a Trapezoidal Microchannel under Stokes Flow Conditions

Even though the research interest in the last decades has been mainly focused on the capsule dynamics in cylindrical or rectangular ducts, channels with asymmetric cross-sections may also be desirable especially for capsule migration and sorting. Therefore, in the present study we investigate computationally the motion of an elastic spherical capsule in an isosceles trapezoidal microchannel at low and moderate flow rates under the Stokes regime. The steady-state capsule location is quite close to the location where the single-phase velocity of the surrounding fluid is maximized. Owing to the asymmetry of the trapezoidal channel, the capsule’s steady-state shape is asymmetric while its membrane slowly tank-treads. In addition, our investigation reveals that tall trapezoidal channels with low base ratios produce significant off-center migration for large capsules compared to that for smaller capsules for a given channel length. Thus, we propose a microdevice for the sorting of artificial and physiological capsules based on their size, by utilizing tall trapezoidal microchannels with low base ratios. The proposed sorting microdevice can be readily produced via glass fabrication or as a microfluidic device via micromilling, while the required flow conditions do not cause membrane rupture.

Influence of membrane viscosity on capsule dynamics in shear flow

Most previous numerical studies on capsule dynamics in shear flow have ignored the role of membrane viscosity. Here we present a numerical method for large deformation of capsules using a Kelvin–Voigt viscoelastic model for the membrane. After introducing the model and the related numerical implementation, we present a comprehensive analysis of the influence of the membrane viscosity on buckling, deformation and dynamics. We observe that the membrane viscosity leads to buckling in the range of shear rate in which no buckling is observed for capsules with purely elastic membrane. For moderate to large shear rates, the wrinkles on the capsule surface appear in the same range of the membrane viscosity that was reported earlier for artificial capsules and red blood cells based on experimental measurements. In order to obtain stable shapes, it is necessary to introduce the bending stiffness. It is observed that the range of the bending stiffness required is also in the same range as that reported for the red blood cells, but considerably higher than that estimated for artificial capsules. Using the stable shapes obtained in the presence of bending stiffness, we analyse the influence of membrane viscosity on deformation, inclination and tank-treading frequency of initially spherical capsules. Membrane viscosity is observed to reduce the capsule deformation, and introduce a damped oscillation in time-dependent deformation and inclination. The time-averaged inclination angle shows a non-monotonic trend with an initial decrease reaching a minimum and a subsequent increase with increasing membrane viscosity. A similar non-monotonic trend is also observed in the tank-treading frequency. We then consider the influence of the membrane viscosity on the unsteady dynamics of an initially oblate capsule. The dynamics is observed to change from a swinging motion to a tumbling motion with increasing membrane viscosity. Further, a transient dynamics is also observed in which a capsule starts with one type of dynamics, but settles with a different dynamics over a long time.

Modeling, Analysis, and Optimal Design of the Automotive Transmission Ball Capsule System

Clutch shift control is critical for the performance and fuel economy of automotive transmissions, including both automatic and hybrid transmissions. Among all the factors that influence clutch shift control, clutch fill and clutch engagement are crucial to realize a fast and smooth clutch shift. When the clutch is not engaged, the fluid held by the centrifugal force inside of the clutch chamber, which introduces additional pressure that will affect the subsequent clutch fill and engagement processes, should be released. To realize this function, a ball capsule system is introduced and mounted on the clutch chamber. When the clutch chamber is ready to be filled for engagement, the ball capsule needs to close quickly and remain closed until the clutch is disengaged. It is also desirable to have an appropriate closing velocity for the ball capsule to minimize noise and wear. In this paper, the ball capsule dynamics is modeled, in which the derivation of the ball capsule throttling area is considered novel and critical because of its asymmetrical nature. Through this, the ball capsule’s intrinsic positive feedback structure is also revealed, which is considered to be the key to realize a fast response. Moreover, through the system dynamics analysis, the slope angle of the capsule is found to be an effective control parameter for system performance and robustness. To this end, the optimal shape of the capsule is designed using dynamic programming to achieve the desired performance.