ترغب بنشر مسار تعليمي؟ اضغط هنا

Deformation of a flexible fiber in a viscous flow past an obstacle

114   0   0.0 ( 0 )
 نشر من قبل Harold Auradou
 تاريخ النشر 2015
  مجال البحث فيزياء
والبحث باللغة English
 تأليف H.M. Lopez




اسأل ChatGPT حول البحث

We study the deformation and transport of elastic fibers in a viscous Hele-Shaw flow with curved streamlines. The variations of the global velocity and orientation of the fiber follow closely those of the local flow velocity. The ratios of the curvatures of the fibers by the corresponding curvatures of the streamlines reflect a balance between elastic and viscous forces: this ratio is shown experimentally to be determined by a dimensionless {it Sperm number} $Sp$ combining the characteristic parameters of the flow (transverse velocity gradient, viscosity, fiber diameter/cell gap ratio) and those of the fiber (diameter, effective length, Youngs modulus). For short fibers, the effective length is that of the fiber; for long ones, it is equal to the transverse characteristic length of the flow. For $S_p lesssim 250$, the ratio of the curvatures increases linearly with $Sp$; For $S_p gtrsim 250$, the fiber reaches the same curvature as the streamlines.



قيم البحث

اقرأ أيضاً

We examine experimentally the deformation of flexible, microscale helical ribbons with nanoscale thickness subject to viscous flow in a microfluidic channel. Two aspects of flexible microhelices are quantified: the overall shape of the helix and the viscous frictional properties. The frictional coefficients determined by our experiments are consistent with calculated values in the context of resistive force theory. Deformation of helices by viscous flow is well-described by non-linear finite extensibility. Under distributed loading, the pitch distribution is non-uniform and from this, we identify both linear and non-linear behavior along the contour length of a single helix. Moreover, flexible helices are found to display reversible global to local helical transitions at high flow rate.
We investigate superfluid flow around an airfoil accelerated to a finite velocity from rest. Using simulations of the Gross--Pitaevskii equation we find striking similarities to viscous flows: from production of starting vortices to convergence of ai rfoil circulation onto a quantized version of the Kutta-Joukowski circulation. We predict the number of quantized vortices nucleated by a given foil via a phenomenological argument. We further find stall-like behavior governed by airfoil speed, not angle of attack, as in classical flows. Finally we analyze the lift and drag acting on the airfoil.
In this chapter, we analyze the steady-state microscale fluid--structure interaction (FSI) between a generalized Newtonian fluid and a hyperelastic tube. Physiological flows, especially in hemodynamics, serve as primary examples of such FSI phenomena . The small scale of the physical system renders the flow field, under the power-law rheological model, amenable to a closed-form solution using the lubrication approximation. On the other hand, negligible shear stresses on the walls of a long vessel allow the structure to be treated as a pressure vessel. The constitutive equation for the microtube is prescribed via the strain energy functional for an incompressible, isotropic Mooney--Rivlin material. We employ both the thin- and thick-walled formulations of the pressure vessel theory, and derive the static relation between the pressure load and the deformation of the structure. We harness the latter to determine the flow rate--pressure drop relationship for non-Newtonian flow in thin- and thick-walled soft hyperelastic microtubes. Through illustrative examples, we discuss how a hyperelastic tube supports the same pressure load as a linearly elastic tube with smaller deformation, thus requiring a higher pressure drop across itself to maintain a fixed flow rate.
We study the deformation and breakup of an axisymmetric electrolyte drop which is freely suspended in an infinite dielectric medium and subjected to an imposed electric field. The electric potential in the drop phase is assumed small, so that its gov erning equation is approximated by a linearized Poisson-Boltzmann or modified Helmholtz equation (the Debye-H{u}ckel regime). An accurate and efficient boundary integral method is developed to solve the low-Reynolds-number flow problem for the time-dependent drop deformation, in the case of arbitrary Debye layer thickness. Extensive numerical results are presented for the case when the viscosity of the drop and surrounding medium are comparable. Qualitative similarities are found between the evolution of a drop with a thick Debye layer (characterized by the parameter $chill 1$, which is an inverse dimensionless Debye layer thickness) and a perfect dielectric drop in an insulating medium. In this limit, a highly elongated steady state is obtained for sufficiently large imposed electric field, and the field inside the drop is found to be well approximated using slender body theory. In the opposite limit $chigg 1$, when the Debye layer is thin, the drop behaves as a highly conducting drop, even for moderate permittivity ratio $Q=epsilon_1/epsilon_2$, where $epsilon_1, epsilon_2$ is the dielectric permittivity of drop interior and exterior, respectively. For parameter values at which steady solutions no longer exist, we find three distinct types of unsteady solution or breakup modes. These are termed conical end formation, end splashing, and open end stretching. The second breakup mode, end splashing, resembles the breakup solution presented in a recent paper [R. B. Karyappa et al., J. Fluid Mech. 754, 550-589 (2014)]. We compute a phase diagram which illustrates the regions in parameter space in which the different breakup modes occur.
We study theoretically and experimentally how a thin layer of liquid flows along a flexible beam. The flow is modelled using lubrication theory and the substrate is modelled as an elastica which deforms according to the Euler-Bernoulli equation. A co nstant flux of liquid is supplied at one end of the beam, which is clamped horizontally, while the other end of the beam is free. As the liquid film spreads, its weight causes the beam deflection to increase, which in turn enhances the spreading rate of the liquid. This feedback mechanism causes the front position ${sigma}$(t) and the deflection angle at the front ${phi}$(t) to go through a number of different power-law behaviours. For early times, the liquid spreads like a horizontal gravity current, with ${sigma}$(t) = $t^{4/5}$ and ${phi}$(t) = $t^{13/5}$. For intermediate times, the deflection of the beam leads to rapid acceleration of the liquid layer, with ${sigma}$(t) = $t^4$ and ${phi}$(t) = $t^9$. Finally, when the beam has sagged to become almost vertical, the liquid film flows downward with ${sigma}$(t) = $t$ and ${phi}$(t) ~ ${pi}$/2. We demonstrate good agreement between these theoretical predictions and experimental results.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا