Heat conduction from irregular surfaces

The effect of irregularities on the rate of heat conduction from a two-dimensional isothermal surface into a semi infinite medium is considered. The effect of protrusions, depressions, and surface roughness is quantified in terms of the displacement of the linear temperature profile prevailing far from the surface. This shift, coined the displacement length, is designated as an appropriate global measure of the effect of the surface indentations incorporating the particular details of the possibly intricate geometry. To compute the displacement length, Laplace's equation describing the temperature distribution in the semi-infinite space above the surface is solved numerically by a modified Schwarz-Christoffel transformation whose computation requires solving a system of highly non-linear algebraic equations by iterative methods, and an integral equation method originating from the single-layer integral representation of a harmonic function involving the periodic Green's function. The conformal mapping method is superior in that it is capable of handling with high accuracy a large number of vertices and intricate wall geometries. On the other hand, the boundary integral method yields the displacement length as part of the solution. Families of polygonal wall shapes composed of segments in regular, irregular, and random arrangement are considered, and pre-fractal geometries consisting of large numbers of vertices are analyzed. The results illustrate the effect of wall geometry on the flux distribution and on the overall enhancement in the rate of transport for regular and complex wall shapes

Nuclear kinetic energy spectra of D_2^+ in intense laser field: Beyond Born Oppenheimer approximation

Simultaneously, the vibrational nuclear dynamics and full dimensional electronic dynamics of the deuterium molecular ion exposed to the linear polarized intense laser field are studied. The time dependent Schr\"odinger equation of the aligned D2+ with the electric laser field is solved for the simulation of the complicated dissociative ionization processes and compared with the recent related experimental results. In this work, the R-dependent ionization rate and the enhanced ionization phenomenon beyond the Born-Oppenheimer approximation (BOA) are introduced and calculated. The substructure of the nuclear kinetic energy release spectra are revealed as the Coulomb explosion energy spectra and dissociation energy spectra in the dissociation-ionization channel. The significant and trace of these distinct sub-spectra in the total spectra comparatively are displayed and discussed.Comment: 17 pages, 4 figure

New analytical progress in the theory of vesicles under linear flow

Vesicles are becoming a quite popular model for the study of red blood cells (RBCs). This is a free boundary problem which is rather difficult to handle theoretically. Quantitative computational approaches constitute also a challenge. In addition, with numerical studies, it is not easy to scan within a reasonable time the whole parameter space. Therefore, having quantitative analytical results is an essential advance that provides deeper understanding of observed features and can be used to accompany and possibly guide further numerical development. In this paper shape evolution equations for a vesicle in a shear flow are derived analytically with precision being cubic (which is quadratic in previous theories) with regard to the deformation of the vesicle relative to a spherical shape. The phase diagram distinguishing regions of parameters where different types of motion (tank-treading, tumbling and vacillating-breathing) are manifested is presented. This theory reveals unsuspected features: including higher order terms and harmonics (even if they are not directly excited by the shear flow) is necessary, whatever the shape is close to a sphere. Not only does this theory cure a quite large quantitative discrepancy between previous theories and recent experiments and numerical studies, but also it reveals a new phenomenon: the VB mode band in parameter space, which is believed to saturate after a moderate shear rate, exhibits a striking widening beyond a critical shear rate. The widening results from excitation of fourth order harmonic. The obtained phase diagram is in a remarkably good agreement with recent three dimensional numerical simulations based on the boundary integral formulation. Comparison of our results with experiments is systematically made.Comment: a tex file and 6 figure

Segregation by membrane rigidity in flowing binary suspensions of elastic capsules

Spatial segregation in the wall normal direction is investigated in suspensions containing a binary mixture of Neo-Hookean capsules subjected to pressure driven flow in a planar slit. The two components of the binary mixture have unequal membrane rigidities. The problem is studied numerically using an accelerated implementation of the boundary integral method. The effect of a variety of parameters was investigated, including the capillary number, rigidity ratio between the two species, volume fraction, confinement ratio, and the number fraction of the more floppy particle $X_f$ in the mixture. It was observed that in suspensions of pure species, the mean wall normal positions of the stiff and the floppy particles are comparable. In mixtures, however, the stiff particles were found to be increasingly displaced towards the walls with increasing $X_f$, while the floppy particles were found to increasingly accumulate near the centerline with decreasing $X_f$. The origins of this segregation is traced to the effect of the number fraction $X_f$ on the localization of the stiff and the floppy particles in the near wall region -- the probability of escape of a stiff particle from the near wall region to the interior is greatly reduced with increasing $X_f$, while the exact opposite trend is observed for a floppy particle with decreasing $X_f$. Simple model studies on heterogeneous pair collisions involving a stiff and a floppy particle mechanistically explain this observation. The key result in these studies is that the stiff particle experiences much larger cross-stream displacement in heterogeneous collisions than the floppy particle. A unified mechanism incorporating the wall-induced migration of deformable particles and the particle fluxes associated with heterogeneous and homogeneous pair collisions is presented.Comment: 19 Pages, 16 Figure

Wrinkling of microcapsules in shear flow

Elastic capsules can exhibit short wavelength wrinkling in external shear flow. We analyse this instability of the capsule shape and use the length scale separation between the capsule radius and the wrinkling wavelength to derive analytical results both for the threshold value of the shear rate and for the critical wave-length of the wrinkling. These results can be used to deduce elastic parameters from experiments.Comment: 4 pages, 2 figures, submitted to PR

Two-dimensional Vesicle dynamics under shear flow: effect of confinement

Dynamics of a single vesicle under shear flow between two parallel plates is studied using two-dimensional lattice-Boltzmann simulations. We first present how we adapted the lattice-Boltzmann method to simulate vesicle dynamics, using an approach known from the immersed boundary method. The fluid flow is computed on an Eulerian regular fixed mesh while the location of the vesicle membrane is tracked by a Lagrangian moving mesh. As benchmarking tests, the known vesicle equilibrium shapes in a fluid at rest are found and the dynamical behavior of a vesicle under simple shear flow is being reproduced. Further, we focus on investigating the effect of the confinement on the dynamics, a question that has received little attention so far. In particular, we study how the vesicle steady inclination angle in the tank-treading regime depends on the degree of confinement. The influence of the confinement on the effective viscosity of the composite fluid is also analyzed. At a given reduced volume (the swelling degree) of a vesicle we find that both the inclination angle, and the membrane tank-treading velocity decrease with increasing confinement. At sufficiently large degree of confinement the tank-treading velocity exhibits a non-monotonous dependence on the reduced volume and the effective viscosity shows a nonlinear behavior.Comment: 12 pages, 8 figure

Dynamical regimes and hydrodynamic lift of viscous vesicles under shear

The dynamics of two-dimensional viscous vesicles in shear flow, with different fluid viscosities $\eta_{\rm in}$ and $\eta_{\rm out}$ inside and outside, respectively, is studied using mesoscale simulation techniques. Besides the well-known tank-treading and tumbling motions, an oscillatory swinging motion is observed in the simulations for large shear rate. The existence of this swinging motion requires the excitation of higher-order undulation modes (beyond elliptical deformations) in two dimensions. Keller-Skalak theory is extended to deformable two-dimensional vesicles, such that a dynamical phase diagram can be predicted for the reduced shear rate and the viscosity contrast $\eta_{\rm in}/\eta_{\rm out}$. The simulation results are found to be in good agreement with the theoretical predictions, when thermal fluctuations are incorporated in the theory. Moreover, the hydrodynamic lift force, acting on vesicles under shear close to a wall, is determined from simulations for various viscosity contrasts. For comparison, the lift force is calculated numerically in the absence of thermal fluctuations using the boundary-integral method for equal inside and outside viscosities. Both methods show that the dependence of the lift force on the distance $y_{\rm {cm}}$ of the vesicle center of mass from the wall is well described by an effective power law $y_{\rm {cm}}^{-2}$ for intermediate distances $0.8 R_{\rm p} \lesssim y_{\rm {cm}} \lesssim 3 R_{\rm p}$ with vesicle radius $R_{\rm p}$. The boundary-integral calculation indicates that the lift force decays asymptotically as $1/[y_{\rm {cm}}\ln(y_{\rm {cm}})]$ far from the wall.Comment: 13 pages, 13 figure

Underwater bubble pinch-off: transient stretching flow

At the point of pinch-off of an underwater air bubble, the speed of water rushing in diverges. Previous studies that assumed radial flow throughout showed that the local axial shape is two smoothly connected, slender cones that transition very slowly (logarithmically) to a cylindrical segment. Our simulations show that even with initially radial flow, a transient vertical flow develops with comparable speeds. Bernoulli pressure draws water into the singularity region while incompressibility forces it away from the neck minimum, generating significant vertical flows that rapidly slenderize and symmetrize the collapse region. This transition is due to a different mechanism, occurring much faster than previously expected. Vertical flows dictate the neck shape evolution.Comment: 5 pages, 6 figure