Spatially resolved simulations of the non-equilibrium cavitation bubble dynamics including vapor and air transport

Der Hauptzweck dieser Studie ist es, ein profundes Wissen über die Wechselwirkung zwischen Kavitation und Luftfreisetzung zu erlangen, indem das komplexe Feld der Blasendynamik und die damit verbundenen Dampf- und Luftflüsse unter Nichtgleichgewichtsbedingungen untersucht werden. Um dieses Ziel zu erreichen, werden die maßgeblichen Differentialgleichungen numerisch gelöst, einschließlich der Erhaltung von Masse, Impuls und Energie innerhalb und außerhalb der Blase. Die gesamte Thermodynamik wurde auf der Grundlage validierter experimenteller Datensätze in das Modell implementiert, sodass das Modell für verschiedene Flüssigkeiten und Flüssigkeitsgemische verwendet werden kann. Dieses Modell mit detaillierter Erklärung der Transportprozesse und der hohen Genauigkeit kann auf die CFD-Codes angewendet und als geeignetes Kavitationsmodell verwendet werden.The main purpose of this study is to gain a profound knowledge of the interaction between cavitation and air release by investigating the complex field of bubble dynamics and its associated vapor and air fluxes under non-equilibrium conditions. For achieving this goal, the governing differential equations are solved numerically, including conservation of mass, momentum, and energy both within and outside the bubble. In contrast to existing models, the whole complete thermodynamics has been implemented into the model based on validated experimental data sets, allowing to utilize the model for different liquids and liquid mixtures. This model, with detailed explanation of transport processes, with the least simplifying assumptions, and the high level of accuracy can be applied into the CFD codes and can be utilized as a proper cavitation model

A free-boundary model of a motile cell explains turning behavior - Fig 8

<p>Steady-state cell shapes, myosin distributions (pseudo-colors), actin velocities (arrows), and motility types from solutions of the ZS (<i>a</i>) and ZV (<i>b</i>) models obtained for specified parameter values (<i>v</i>₀, μ_tot). Gridlines are spaced uniformly with <i>h</i> = 1.</p

Mechanical states of ZV and ZS models for varying sets (<i>v</i>₀, μ_tot) and α = 0.5 and 1.

<p>Mechanical states of ZV and ZS models for varying sets (<i>v</i>₀, μ_tot) and α = 0.5 and 1.</p

Onset of steady rotations in ZV model, (<i>v</i>₀, μ_tot, α) = (12.5, 2π, 1).

<p>(<i>a</i>) Entire cell trajectory and cell centroid track (red dashed curve). (<i>b</i>) Snapshots of transient myosin distributions with individual color scales during a transient, and with white arrows representing actin velocities (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005862#pcbi.1005862.s004" target="_blank">S3 Movie</a>).</p

Steady rotations in ZS model, (<i>v</i>₀, μ_tot, α) = (2.5, 0.75π, 0.5) (see also S4 Movie).

<p>(<i>a</i>) Transient distributions of myosin (pseudo-colors) and actin velocities (arrows): <i>t</i> = 2, an initially symmetric cell with centroid at (<i>x</i>, <i>y</i>) = (0,0) self-polarizes and assumes fast unidirectional motility, myosin accumulates in a semi-circular band, pulling the rear inwards to form a ‘dip’; <i>t</i> = 7, the cell slows down and becomes unstable, as myosin is now close enough to cell front to be able to pull it in as well; <i>t</i> = 9, loss of axial symmetry, as the lower part of the cell with steeper myosin gradients is pulled inwards faster than the upper one; <i>t</i> = 23.5: emergence of stable asymmetric myosin distribution and cell shape, as the cell locks in rotations (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005862#pcbi.1005862.g001" target="_blank">Fig 1<i>C</i></a>). (<i>b</i>) Cell shape and boundary velocities in steady rotations. Positions of the cell boundary and centroid at <i>t</i> = 23.5, 23.6, and 24 (solid, dashed, and dotted-dashed contours, respectively, and filled circles with larger size corresponding to later time). Faster boundary velocities (arrows) in the high curvature region, consistent with the location of steep myosin gradients (panel (<i>a</i>)), ensure rotational motility with a circular trajectory of the centroid (dotted arc), see also <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005862#pcbi.1005862.g001" target="_blank">Fig 1<i>C</i></a>.</p

Aspect ratios and translational or linear rotational speeds of steadily moving cells.

<p>(<i>a</i>) Aspect ratio as a function of viscosity-adhesion length α; the results were obtained with (<i>v</i>₀, μ_tot) = (2.5, 1.5π) for ZS model, and with (<i>v</i>₀, μ_tot) = (5, 1.5π) for ZV model; aspect ratios were computed as ratios of the longest to shortest distances between cell boundary and cell centroid. (<i>b</i>) Dimensionless translational or linear rotational speed of a cell centroid as a function of viscosity-adhesion length α; model parameters are as in panel (<i>a</i>). (<i>c</i>) Aspect ratio as a function of <i>v</i>₀ and μ_tot; the results were obtained with α = 1 for ZV model and with α = 0.5 for ZS model. (<i>d</i>) Radius of rotation of a cell centroid as a function of <i>v</i>₀ and μ_tot, with values of α as in (c). (<i>e</i>) Dimensionless angular velocity of a cell centroid as a function of <i>v</i>₀ and μ_tot, with values of α as in (c).</p

Symmetry breaking in a fixed circle and in a free-boundary problem.

<p>(<i>a</i>) Instability of a symmetric steady state of ZV model in a fixed circle: snapshots of dimensionless myosin density (pseudo-color) and actin velocities (arrows) at specified times <i>t</i> after myosin was slightly shifted left of center; computations were done for μ_tot = 1.5π and α = 0.5. (<i>b</i>) Transition to unidirectional motility in ZS model; dimensionless myosin concentration (pseudo-colors) and boundary velocities (arrows) are shown for the solution obtained with α = 1, <i>v</i>₀ = 5, and μ_tot = 1.5π; the cell assumes steady unidirectional motility after <i>t</i> = 14 (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1005862#pcbi.1005862.s003" target="_blank">S2 Movie</a>).</p