Xiaolin Chu

Transverse and longitudinal waves induced and sustained by surfactant gradients at liquid-liquid interfaces

Abstract Dispersion relations are derived for transverse and longitudinal modes of oscillation appearing as a result of transfer, adsorption and eventual accumulation of a surfactant at the interface of two liquids. Also provided here are the values of the Marangoni number sufficient to sustain these waves and a comparison between theoretical predictions and available experimental data.

Transverse and longitudinal waves at the air-liquid interface in the presence of an adsorption barrier

Abstract Analytical and computer results are provided here for the onset of oscillatory convective motions induced at the free surface of a liquid open to air, when there is transfer of a surfactant from one to the other phase. Special attention is paid to the role of a potential barrier, the interfacial deformability of the surface, and the competition between sorption and solute diffusion processes.

Oblique and head‐on collisions of solitary waves in Marangoni–Bénard convection

In Marangoni–Benard convection with mass transfer from gas phase to liquid phase, it is found that solitary waves, excited and sustained by Marangoni stresses, are very stable during interactions with others, keeping their original shapes and celerities after interactions, thus experiencing at most a phase shift. Both positive and negative phase shifts have been observed for different types of oblique interaction. A ‘‘critical’’ angle, at which zero phase shift occurs as a result of the interaction, has been defined to delineate regions of negative and positive phase shifts.

Onset of possible solitons in surface tension-driven convection

For a shallow liquid layer open to air, and subjected to a thermal gradient, threshold conditions are given for the onset of Korteweg-de Vries soliton excitation as the result of an instability triggered by the Marangoni effect, i.e., by the variation of the interfacial tension with temperature or, equivalently, concentration of a surfactant.

The relation of fluxes and forces to work in nonequilibrium systems

Prior work has shown that an excess work is necessary to displace a chemical or physical system from a stationary state, and this excess work determines the stationary distribution of a stochastic birth–death master equation. We derive the augmentation of this master equation for a one‐variable system in the presence of external noise. When this noise is much larger than internal noise, but still small compared to macroscopic averages, then the stationary distribution reduces to a form suggested by Landau and Schlogl, which is the integral of the flux of the deterministic kinetic equation. A similar result was obtained on the basis of an assumed Fokker–Planck equation. Hence, in the presence of external forces exceeding in intensity the internal fluctuations, fluxes are proportional to forces without linearization in concentrations.

Complex kinetics of systems with multiple stationary states at equilibrium

We consider chemical reactions which at equilibrium have multiple stationary states due to nonidealities of chemical species. When such reactions are included in a simple reaction mechanism open to mass flow, without autocatalysis or feedback steps, there may occur complex dynamics such as relaxation oscillations, as reported earlier for regular solutions. Here we consider both regular solution and ionic species (Debye–Huckel nonideality), show that chemical oscillations may occur arbitrarily close to chemical equilibrium, and trace the topological structure of the complex dynamics of relaxation oscillations, sustained oscillations, stable focus, and stable nodes to the multiplicity of equilibrium states, for stated constraints. Relaxation oscillations occur around an unstable stationary state which, on approach to equilibrium, connects to an unstable equilibrium state. Thus, there is no bifurcation to oscillations on removing the systems from equilibrium. Neither is there a region where linear irreversib...

Toward a thermodynamic theory of hydrodynamics: The Lorenz equations

Earlier work on the thermodynamics of nonlinear systems is extended to the Lorenz model in a first attempt to apply the theory to hydrodynamics. An excess work, Φ, related to the work necessary for displacement of the system from stationary states is defined. The excess work Φ is shown to have the following properties: (1) The differential of Φ is expressed in terms of thermodynamic functions: the energy for viscous flow and the entropy for thermal conduction when taken separately; (2) Φ is an extremum at all stationary states, a minimum (maximum) at stable (unstable) stationary states, and thus yields necessary and sufficient criteria for stability; (3) Φ describes the bifurcation from homogeneous to inhomogeneous stationary states; (4) Φ is a Lyapunov function with physical significance parallel to that of the Gibbs free energy change (maximum work) on relaxation to an equilibrium state; (5) Φ is the thermodynamic ‘‘driving force’’ (potential) toward stable stationary states; (6) Φ is a component of th...

Bénard-Marangoni convection in liquid layers with a deformable open surface: Note on the role of solute accumulation at the air-liquid interface

Abstract Adsorption and subsequent surface accumulation at the air-liquid interface in a two-component Benard-Marangoni layer heated from the liquid side is shown to play a stabilizing role relative to the adsorption-free case. Moreover, we also show that cellular convection tends to form with a longer wavelength than in the other case and a physical explanation is given of this prediction.

Thermodynamic and stochastic theory for nonideal systems far from equilibrium

The thermodynamic and stochastic theory of nonlinear chemical kinetics systems, possibly with multiple stable stationary states, is extended to nonideal species, either nonideal gases or nonideal solutions. The Bronsted theory of the kinetics of nonideal species is chosen for explicit formulation of this extension, but the development is similar for other choices.

Solitary waves driven by Marangoni stresses

Abstract Evidence is provided of solitary waves in Marangoni-Benard convection with mass transfer from gas-phase to liquid-phase. It has been found that solitary waves, excited and sustained by Marangoni stresses, are very stable during interactions with others, keeping their original shapes and celerities after interactions, thus experiencing at most a phase shift. Both positive and negative phase shifts appear according to the interaction angle.