arXiv subjects

Tomas Bohr

Publications and source records attributed to Tomas Bohr.

17 recordsLinked to original sources

arXiv2020

Viscous energy dissipation in slender channels with porous or semipermeable walls

We study the viscous dissipation in pipe flows in long channels with porous or semipermeable walls, taking into account both the dissipation in the bulk of the channel and in the pores. We give simple closed form expressions for the dissipation in terms of the axially varying flow rate $Q(x)$ and the pressure $p(x)$, generalizing the well known expression $\dot W=Q\,Δp$ for the case of impenetrable walls with constant $Q$ and a pressure difference $Δp$ between the ends of the pipe. When the pressure $p_0$ outside the pipe is constant, the result is the straightforward generalization $\dot W=Δ\left[(p-p_0) \,Q\right]$. Finally, applications to osmotic flows are considered.

physics.flu-dyn↗

arXiv2020

Surface Tension and Energy Conservation in a Moving Fluid

The transport of energy in a moving fluid with a simply connected free surface is analyzed, taking into account the contribution of surface tension. This is done by following a "control volume" with arbitrary, specified velocity, independent of the flow velocity, and determining the rates of energy passing through the boundaries, as well as the energy dissipation in the bulk. In particular, a simple conservation equation for the surface area is written down, which clearly shows the contribution of the Laplace pressure at the free surface and the tangential surface tension forces at its boundary. It emerges as the mechanical conservation law for the surface energy in its general form. For a static control volume, all contributions from surface tension disappear, except that the pressure has to be modified by the Laplace contribution.

physics.flu-dyn↗

arXiv2019

Surface tension and the origin of the circular hydraulic jump in a thin liquid film

It was recently claimed by Bhagat et al. (J. Fluid Mech. vol. 851 (2018), R5) that the scientific literature on the circular hydraulic jump in a thin liquid film is flawed by improper treatment and severe underestimation of the influence of surface tension. Bhagat {\em et al.} use an energy equation with a new surface energy term that is introduced without reference, and they conclude that the location of the hydraulic jump is determined by surface tension alone. We show that this approach is incorrect and derive a corrected energy equation. Proper treatment of surface tension in thin film flows is of general interest beyond hydraulic jumps, and we show that the effect of surface tension is fully contained in the Laplace pressure due to the curvature of the surface. Following the same approach as Bhagat et al., i.e., keeping only the first derivative of the surface velocity, the influence of surface tension is, for thin films, much smaller than claimed by them. We further describe the influence of viscosity in thin film flows, and we conclude by discussing the distinction between time-dependent and stationary hydraulic jumps.

physics.flu-dyn↗

arXiv2018

Imbibition in plant seeds

We describe imbibition in real and artificial plant seeds, using a combination of experiments and theory. In both systems, our experiments demonstrate that liquid permeates the substrate at a rate which decreases gradually over time. Tomographic imaging of soy seeds is used to confirmed this by observation of the permeating liquid using an iodine stain. To rationalize the experimental data, we propose a model based on capillary action which predicts the temporal evolution of the radius of the wet front and the seed mass. The depth of the wetting front initially evolves as $t^{1/2}$ in accord with the Lucas-Washburn law. At later times, when the sphere is almost completely filled, the front radius scales as $(1-t/t_{\text{max}})^{1/2}$ where $t_{\text{max}}$ is the time required to complete imbibition. The data obtained on both natural and artificial seeds collapse onto a single curve that agrees well with our model, suggesting that capillary phenomena contribute to moisture uptake in soy seeds.

physics.bio-ph↗

arXiv2014

Diffusion and bulk flow in phloem loading - a theoretical analysis of the polymer trap mechanism in plants

Plants create sugar in the mesophyll cells of their leaves by photosynthesis. This sugar, mostly sucrose, has to be loaded via the bundle sheath into the phloem vascular system (the sieve elements), where it is distributed to growing parts of the plant. We analyze the feasibility of a particular loading mechanism, active symplasmic loading, also called the polymer trap mechanism, where sucrose is transformed into heavier sugars, such as raffinose and stachyose, in the intermediary-type companion cells bordering the sieve elements in the minor veins of the phloem. Keeping the heavier sugars from diffusing back requires that the plasmodesmata connecting the bundle sheath with the intermediary cell act as extremely precise filters, which are able to distinguish between molecules that differ by less than 20% in size. In our modeling, we take into account the coupled water and sugar movement across the relevant interfaces, without explicitly considering the chemical reactions transforming the sucrose into the heavier sugars. Based on the available data for plasmodesmata geometry, sugar concentrations and flux rates, we conclude that this mechanism can in principle function. We find that the water flow through the plasmodesmata, which has not been quantified before, contributes only 10-20% to the sucrose flux into the intermediary cells, while the main part is transported by diffusion. On the other hand, the subsequent sugar translocation into the sieve elements would very likely be carried predominantly by bulk water flow through the plasmodesmata. Thus, in contrast to apoplasmic loaders, all the necessary water for phloem translocation would be supplied in this way with no need for additional water uptake across the plasma membranes of the phloem.

physics.bio-ph↗

arXiv2014

Comment on Y. Couder and E. Fort: "Single-Particle Diffraction and Interference at a Macroscopic Scale", Phys. Rev. Lett. (2006)

In a paper from 2006, Couder and Fort [1] describe a version of the famous double slit experiment performed with drops bouncing on a vibrated fluid surface, where interference in the particle statistics is found even though it is possible to determine unambiguously which slit the "walking" drop passes. It is one of the first papers in an impressive series, showing that such walking drops closely resemble de Broglie waves and can reproduce typical quantum phenomena like tunneling and quantized states [2-13]. The double slit experiment is, however, a more stringent test of quantum mechanics, because it relies upon superposition and phase coherence. In the present comment we first point out that the experimental data presented in [1] are not convincing, and secondly we argue that it is not possible in general to capture quantum mechanical results in a system, where the trajectory of the particle is well-defined.

physics.flu-dyn↗

arXiv2012

Analytical Solution of the Proprio-Graviceptive equation for shoot gravitropism of plants

We derive the analytical solutions to the second order generalised gravi-proprioceptive equation given in our recent paper [Bastien et al. 2012]. These equations show how plants adjust to the surrounding gravitation field and highlight the fact that the plant must be able to not only sense its local posture with respect to the gravitational field, but also to sense its own local curvature. In [Bastien et al. 2012] we obtained explicit analytical solutions of these equations in terms of (sums of) Bessel functions, and in the present paper we derive these solutions.

q-bio.TO↗

arXiv2012

Model For Polygonal Hydraulic Jumps

We propose a phenomenological model for the polygonal hydraulic jumps discovered by Ellegaard et al., based on the known flow structure for the type II hydraulic jumps with a "roller" (separation eddy) near the free surface in the jump region. The model consists of mass conservation and radial force balance between hydrostatic pressure and viscous stresses on the roller surface. In addition, we consider the azimuthal force balance, primarily between pressure and viscosity, but also including non-hydrostatic pressure contributions from surface tension in light of recent observations by Bush et al. The model can be analyzed by linearization around the circular state, resulting in a parameter relationship for nearly circular polygonal states. A truncated, but fully nonlinear version of the model can be solved analytically. This simpler model gives rise to polygonal shapes that are very similar to those observed in experiments, even though surface tension is neglected, and the condition for the existence of a polygon with N corners depends only on a single dimensionless number ϕ. Finally, we include time-dependent terms in the model and study linear stability of the circular state. Instability occurs for suffciently small Bond number and the most unstable wave length is expected to be roughly proportional to the width of the roller as in the Rayleigh-Plateau instability.

physics.flu-dyn↗

arXiv2008

Osmotically driven flows in microchannels separated by a semipermeable membrane

We perform experimental investigations of osmotically driven flows in artificial microchannels by studying the dynamics and structure of the front of a sugar solution traveling in 200 um wide and 50-200 um deep microchannels. We find that the sugar front travels with constant speed, and that this speed is proportional to the concentration of the sugar solution and inversely proportional to the depth of the channel. We propose a theoretical model, which, in the limit of low axial flow resistance, predicts that the sugar front indeed should travel with a constant velocity. The model also predicts an inverse relationship between the depth of the channel and the speed and a linear relation between the sugar concentration and the speed. We thus find good agreement between the experimental results and the predictions of the model. Our motivation for studying osmotically driven flows is that they are believed to be responsible for the translocation of sugar in plants through the phloem sieve element cells. Also, we suggest that osmotic elements can act as integrated pumps with no movable parts in lab-on-a-chip systems.

physics.flu-dyn↗

arXiv2005

Polygons on a Rotating Fluid Surface

We report a novel and spectacular instability of a fluid surface in a rotating system. In a flow driven by rotating the bottom plate of a partially filled, stationary cylindrical container, the shape of the free surface can spontaneously break the axial symmetry and assume the form of a polygon rotating rigidly with a speed different from that of the plate. With water we have observed polygons with up to 6 corners. It has been known for many years that such flows are prone to symmetry breaking, but apparently the polygonal surface shapes have never been observed. The creation of rotating internal waves in a similar setup was observed for much lower rotation rates, where the free surface remains essentially flat. We speculate that the instability is caused by the strong azimuthal shear due to the stationary walls and that it is triggered by minute wobbling of the rotating plate. The slight asymmetry induces a tendency for mode-locking between the plate and the polygon, where the polygon rotates by one corner for each complete rotation of the plate.

physics.flu-dyn↗

arXiv2004

The Shape and Stability of a Viscous Thread

When a viscous fluid, like oil or syrup, streams from a small orifice and falls freely under gravity, it forms a long slender thread, which can be maintained in a stable, stationary state with lengths up to several meters. We shall discuss the shape of such liquid threads and their surprising stability. It turns out that the strong advection of the falling fluid can almost outrun the Rayleigh-Plateau instability. Even for a very viscous fluid like sirup or silicone oil, the asymptotic shape and stability is independent of viscosity and small perturbations grow with time as $\exp({{\rm C} t^{1/4}})$, where the constant is independent of viscosity. The corresponding spatial growth has the form $\exp({(z/L)^{1/8}})$, where $z$ is the down stream distance and $L \sim Q^2 σ^{-2} g$ and where $σ$ is the surface tension, $g$ is the gravity and $Q$ is the flux. However, the value of viscosity determines the break-up length of a thread $L_ν \sim ν^{1/4}$ and thus the possibility of observing the $\exp({{\rm C} t^{1/4}})$ type asymptotics.

physics.flu-dyn↗

arXiv2002

Universal and non-universal properties of transitions to spatio-temporal chaos in coupled map lattices

We study the transition from laminar to chaotic behavior in deterministic chaotic coupled map lattices and in an extension of the stochastic Domany--Kinzel cellular automaton [DK]. For the deterministic coupled map lattices we find evidence that ``solitons'' can change the {\em nature} of the transition: for short soliton lifetimes it is of second order, while for longer but {\em finite} lifetimes, it is more reminiscent of a first order transition. In the second order regime the deterministic model behaves like Directed Percolation with infinitely many absorbing states; we present evidence obtained from the study of bulk properties and the spreading of chaotic seeds in a laminar background. To study the influence of the solitons more specifically, we introduce a soliton including variant of the stochastic Domany--Kinzel cellular automaton. Similar to the deterministic model, we find a transition from second to first order behavior due to the solitons, both in a mean field analysis and in a numerical study of the statistical properties of this stochastic model. Our study illustrates that under the appropriate mapping some deterministic chaotic systems behave like stochastic models; but it is hard to know precisely which degrees of freedom need to be included in such description.

cond-mat.stat-mech↗

arXiv2001

Breakdown of universality in transitions to spatio-temporal chaos

In this Letter we show that the transition from laminar to active behavior in extended chaotic systems can vary from a continuous transition in the universality class of Directed Percolation with infinitely many absorbing states to what appears as a first order transition. The latter occurs when {\em finite} lifetime non-chaotic structures, called ``solitons'', dominate the dynamics. We illustrate this scenario in an extension of the deterministic Chaté--Manneville coupled map lattice model and in a soliton including variant of the stochastic Domany-Kinzel cellular automaton.

cond-mat.stat-mech↗

arXiv2000

Integral methods for shallow free-surface flows with separation

We study laminar thin film flows with large distortions in the free surface using the method of averaging across the flow. Two concrete problems are studied: the circular hydraulic jump and the flow down an inclined plane. For the circular hydraulic jump our method is able to handle an internal eddy and separated flow. Assuming a variable radial velocity profile like in Karman-Pohlhausen's method, we obtain a system of two ordinary differential equations for stationary states that can smoothly go through the jump where previous studies encountered a singularity. Solutions of the system are in good agreement with experiments. For the flow down an inclined plane we take a similar approach and derive a simple model in which the velocity profile is not restricted to a parabolic or self-similar form. Two types of solutions with large surface distortions are found: solitary, kink-like propagating fronts, obtained when the flow rate is suddenly changed, and stationary jumps, obtained, e.g., behind a sluice gate. We then include time-dependence in the model to study stability of these waves. This allows us to distinguish between sub- and supercritical flows by calculating dispersion relations for wavelengths of the order of the width of the layer.

physics.flu-dyn↗

arXiv1997

Directed Percolation Universality in Asynchronous Evolution of Spatio-Temporal Intermittency

We present strong evidence that a coupled-map-lattice model for spatio-temporal intermittency belongs to the universality class of directed percolation when the updating rules are asynchronous, i.e. when only one randomly chosen site is evolved at each time step. In contrast, when the system is subjected to parallel updating, available numerical evidence suggests that it does not belong to this universality class and that it is not even universal. We argue that in the absence of periodic external forcing, the asynchronous rule is the more physical.

chao-dyn↗

arXiv1997

Fractal tracer distributions in turbulent field theories

We study the motion of passive tracers in a two-dimensional turbulent velocity field generated by the Kuramoto-Sivashinsky equation. By varying the direction of the velocity-vector with respect to the field-gradient we can continuously vary the two Lyapunov exponents for the particle motion and thereby find a regime in which the particle distribution is a strange attractor. We compare the Lyapunov dimension to the information dimension of actual particle distributions and show that there is good agreement with the Kaplan-Yorke conjecture. Similar phenomena have been observed experimentally.

chao-dyn↗

arXiv1997

Averaging theory for the structure of hydraulic jumps and separation in laminar free-surface flows

We present a simple viscous theory of free-surface flows in boundary layers, which can accommodate regions of separated flow. In particular this yields the structure of stationary hydraulic jumps, both in their circular and linear versions, as well as structures moving with a constant speed. Finally we show how the fundamental hydraulic concepts of subcritical and supercritical flow, originating from inviscid theory, emerge at intermediate length scales in our model.

physics.flu-dyn↗