A Paradifferential Reduction for the Gravity-capillary Waves System at Low Regularity and Applications

2017 ◽  
Vol 145 (4) ◽  
pp. 643-710 ◽  
Author(s):  
Thibault de Poyferré ◽  
Quang-Huy Nguyen
Keyword(s):  
Capillary Waves ◽  
Low Regularity

Effects of capillary waves on the thickness of wetting layers

1988 ◽  
Vol 49 (4) ◽  
pp. 675-680 ◽  
Author(s):  
S. Chatterjee ◽  
E.S.R. Gopal
Keyword(s):  
Capillary Waves ◽  
Wetting Layers

scholarly journals Universal Stokes’s nanomechanical viscometer

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Komal Chaudhary ◽  
Pooja Munjal ◽  
Kamal P. Singh
Keyword(s):  
Electric Field ◽  
Real Time ◽  
Sample Volume ◽  
Capillary Waves ◽  
Small Sample ◽  
Medical Applications ◽  
Rapid Measurement ◽  
Single Lens ◽  
Universal Applicability ◽  
Small Sample Volume

AbstractAlthough, many conventional approaches have been used to measure viscosity of fluids, most methods do not allow non-contact, rapid measurements on small sample volume and have universal applicability to all fluids. Here, we demonstrate a simple yet universal viscometer, as proposed by Stokes more than a century ago, exploiting damping of capillary waves generated electrically and probed optically with sub-nanoscale precision. Using a low electric field local actuation of fluids we generate quasi-monochromatic propagating capillary waves and employ a pair of single-lens based compact interferometers to measure attenuation of capillary waves in real-time. Our setup allows rapid measurement of viscosity of a wide variety of polar, non-polar, transparent, opaque, thin or thick fluids having viscosity values varying over four orders of magnitude from $$10^{0}{-}10^{4}~\text{mPa} \, \text{s}$$ 10 0 - 10 4 mPa s . Furthermore, we discuss two additional damping mechanisms for nanomechanical capillary waves caused by bottom friction and top nano-layer appearing in micro-litre droplets. Such self-stabilized droplets when coupled with precision interferometers form interesting microscopic platform for picomechanical optofluidics for fundamental, industrial and medical applications.

scholarly journals Finite-dimensional boundary uniform stabilization of the Boussinesq system in Besov spaces by critical use of Carleman estimate-based inverse theory

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Irena Lasiecka ◽  
Buddhika Priyasad ◽  
Roberto Triggiani
Keyword(s):  
Besov Space ◽  
Internal Control ◽  
Initial Conditions ◽  
Fluid Velocity ◽  
Critical Role ◽  
Boussinesq System ◽  
Heat Equations ◽  
Fluid Equation ◽  
Low Regularity ◽  
Finite Dimensional

Abstract We consider the 𝑑-dimensional Boussinesq system defined on a sufficiently smooth bounded domain and subject to a pair { v , u } \{v,\boldsymbol{u}\} of controls localized on { Γ ~ , ω } \{\widetilde{\Gamma},\omega\} . Here, 𝑣 is a scalar Dirichlet boundary control for the thermal equation, acting on an arbitrarily small connected portion Γ ~ \widetilde{\Gamma} of the boundary Γ = ∂ ⁡ Ω \Gamma=\partial\Omega . Instead, 𝒖 is a 𝑑-dimensional internal control for the fluid equation acting on an arbitrarily small collar 𝜔 supported by Γ ~ \widetilde{\Gamma} . The initial conditions for both fluid and heat equations are taken of low regularity. We then seek to uniformly stabilize such Boussinesq system in the vicinity of an unstable equilibrium pair, in the critical setting of correspondingly low regularity spaces, by means of an explicitly constructed, finite-dimensional feedback control pair { v , u } \{v,\boldsymbol{u}\} localized on { Γ ~ , ω } \{\widetilde{\Gamma},\omega\} . In addition, they will be minimal in number and of reduced dimension; more precisely, 𝒖 will be of dimension ( d - 1 ) (d-1) , to include necessarily its 𝑑-th component, and 𝑣 will be of dimension 1. The resulting space of well-posedness and stabilization is a suitable, tight Besov space for the fluid velocity component (close to L 3 ⁢ ( Ω ) \boldsymbol{L}^{3}(\Omega) for d = 3 d=3 ) and a corresponding Besov space for the thermal component, q > d q>d . Unique continuation inverse theorems for suitably over-determined adjoint static problems play a critical role in the constructive solution. Their proof rests on Carleman-type estimates, a topic pioneered by M. V. Klibanov since the early 80s.

CAPILLARY WAVES FORMING DURING THE COLLISION OF THE DROP WITH THE SURFACE OF LIQUID

2001 ◽  
Vol 32 ◽  
pp. 701-702
Author(s):  
S.L. ZHBANKOVA ◽  
A.V. KOLPAKOV ◽  
L.V. MALIAROVA
Keyword(s):  
Capillary Waves

scholarly journals Capillary waves on a falling film

2020 ◽  
Vol 5 (11) ◽  
Author(s):  
Guangzhao Zhou ◽  
Andrea Prosperetti
Keyword(s):  
Capillary Waves ◽  
Falling Film

A new method for calculating eigenvalues with applications to gravity-capillary waves with edge constraints

1983 ◽  
Vol 94 (3) ◽  
pp. 553-564 ◽  
Author(s):  
James Graham-Eagle
Keyword(s):  
Boundary Value Problems ◽  
Variational Formulation ◽  
Boundary Value ◽  
Capillary Waves ◽  
Original Study ◽  
New Method ◽  
Linear Boundary ◽  
Hydrodynamic Problem ◽  
Alternative Means ◽  
Standard Linear

The method to be described provides an alternative means of dealing with certain non-standard linear boundary-value problems. It is developed in several applications to the theory of gravity-capillary waves. The analysis is based on a variational formulation of the hydrodynamic problem, being motivated by and extending the original study by Benjamin and Scott [3].

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