A new approach for exploring effects of interfaces on polar liquids is presented. Their impact on the polar liquid film motor(PLFM) – a novel micro-fluidic device – is studied. We account for the interface's imp...A new approach for exploring effects of interfaces on polar liquids is presented. Their impact on the polar liquid film motor(PLFM) – a novel micro-fluidic device – is studied. We account for the interface's impact by modeling slip boundary effects on the PLFM's electro-hydro-dynamical rotations. Our analytical results show as k = l_s/R increases(with ls denoting the slip length resulting from the interface's impact on the film's properties, k >-1 and R denoting the film's radius):(a) PLFMs subsequently exhibit rotation characteristics under "negative-", "no-", "partial-" and"perfect-" slip boundary conditions;(b) The maximum value of the linear velocity of the steady rotating film increases linearly and its location approaches the film's border;(c) The decay of the angular velocities' dependency on the distance from the center of the film slows down, resulting in a macroscopic flow near the boundary. With our calculated rotation speed distributions consistent with the existing experimental ones, research aiming at fitting computed to measured distributions promises identifying the factors affecting ls, e.g., solid-fluid potential interactions and surface roughness.The consistency also is advantageous for optimizing PLFM's applications as micro-washers, centrifuges, mixers in the lab-on-a-chip.展开更多
In this paper,a basic estimate for the conditional Riemannian Brownian motion on a complete manifold with non-negative Ricci curvature is established.Applying it to the heat kernel estimate of the operator 1/2△+b,we ...In this paper,a basic estimate for the conditional Riemannian Brownian motion on a complete manifold with non-negative Ricci curvature is established.Applying it to the heat kernel estimate of the operator 1/2△+b,we obtain the Aronson′s estimate for the operator 1/2△+b,which can be regarded as an extension of Peter Li and S.T.Yau's heat kernel estimate for the Laplace-Beltrami operator.展开更多
基金Supported by National Natural Science Foundation of China under Grant Nos.11302118,11275112Natural Science Foundation of Shandong Province under Grant No.ZR2013AQ015
文摘A new approach for exploring effects of interfaces on polar liquids is presented. Their impact on the polar liquid film motor(PLFM) – a novel micro-fluidic device – is studied. We account for the interface's impact by modeling slip boundary effects on the PLFM's electro-hydro-dynamical rotations. Our analytical results show as k = l_s/R increases(with ls denoting the slip length resulting from the interface's impact on the film's properties, k >-1 and R denoting the film's radius):(a) PLFMs subsequently exhibit rotation characteristics under "negative-", "no-", "partial-" and"perfect-" slip boundary conditions;(b) The maximum value of the linear velocity of the steady rotating film increases linearly and its location approaches the film's border;(c) The decay of the angular velocities' dependency on the distance from the center of the film slows down, resulting in a macroscopic flow near the boundary. With our calculated rotation speed distributions consistent with the existing experimental ones, research aiming at fitting computed to measured distributions promises identifying the factors affecting ls, e.g., solid-fluid potential interactions and surface roughness.The consistency also is advantageous for optimizing PLFM's applications as micro-washers, centrifuges, mixers in the lab-on-a-chip.
文摘In this paper,a basic estimate for the conditional Riemannian Brownian motion on a complete manifold with non-negative Ricci curvature is established.Applying it to the heat kernel estimate of the operator 1/2△+b,we obtain the Aronson′s estimate for the operator 1/2△+b,which can be regarded as an extension of Peter Li and S.T.Yau's heat kernel estimate for the Laplace-Beltrami operator.
