Diffusion-controlled Adsorption Kinetics at Air/Solution Surface Studied by Maximum Bubble Pressure Method

In studying the diffusion-controlled adsorption kinetics of aqueous surfactant solutions at the air/solution surface by means of the maximal bubble pressure method, Fick's diffusion equation for a sphere should be used. In this paper the equation was solved by means of Laplace transformation under different initial and boundary conditions. The dynamic surface adsorption F(t) for a surfactant solution, which was used to describe the diffusion-controlled adsorption kinetics at the solution surface, was derived. Different from the planar surface adsorption, the dynamic surface adsorption F(t) for the short time consists of two terms: one is the same as Ward-Tordai equation and the other reflects the geometric effect caused by the spherical bubble surface. This effect should not be neglected for the very small radius of the capillary. The equilibrium surface tension γeq and the dynamic surface tension γ(t) of aqueous C10E6 [CH3(CH2)9(OCH2CH2)6OH] solution at temperature 25℃ were measuredby means of Wilhelmy plate method and maximal bubble pressure method respectively. As t→ 0, the theoreticalanalysis is in good agreement with experimental results and the dependence of γ(t) on is linear.

Phase field simulation of single bubble behavior under an electric field

Based on the Cahn-Hilliard phase field model, a three-dimensional multiple-field coupling model for simulating the motion characteristics of a rising bubble in a liquid is established in a gas-liquid two-phase flow. The gas-liquid interface motion is simulated by using a phase-field method, and the effect of the electric field intensity on bubble dynamics is studied without electric field, or with vertical electric field or horizontal electric field. Through the coupling effect of electric field and flow field, the deformation of a single rising bubble and the formation of wake vortices under the action of gravity and electric field force are studied in detail. The correctness of the results is verified by mass conservation, and the influences of different electric field directions and different voltages on the movement of bubbles in liquid are considered. The results show that the ratio of the length to axis is proportional to the strength of the electric field when the air bubble is stretched into an ellipsoid along the electric field line under the action of electrostatic gravity and surface tension. In addition, the bubble rising speed is affected by the electric field, the vertical electric field accelerates the bubble rise, and the horizontal direction slows it down.

Effects of T-S wave amplitude on the control of boundary layer transition by streaks

The effects of streaks on boundary layer transition depend on the initial amplitude of T-S waves introduced to excite the transition. This problem was studied in a flat-plate boundary layer in water tunnel by using hydrogen bubble method. Three T-S wave initial amplitudes were tested. The results show that both narrow and wide-spacing streaks depress the transition excited by T-S waves with lower initial amplitude. However, when transition is excited by T-S waves of higher initial amplitude, the narrow-spacing streaks depress the transition, while the wide-spacing streaks promote the transition. Futrther the underlying mechanisms were also analyzed.

Acceleration Strategies Based on an Improved Bubble Packing Method

The bubble packing method can generate high-quality node sets in simple and complex domains.However,its efficiency remains to be improved.This study is a part of an ongoing effort to introduce several acceleration schemes to reduce the cost of simulation.Firstly,allow the viscosity coefficient c in the bubble governing equations to change according the coordinate of the bubble which are defined separately as odd and normal bubbles,and meanwhile with the saw-shape relationship with time or iterations.Then,in order to relieve the over crowded initial bubble placement,two coefficients w1 and w2 are introduced to modify the insertion criterion.The range of those two coefficients are discussed to be w1=1,w2∈[0.5,0.8].Finally,a self-adaptive termination condition is logically set when the stable system equilibrium is achieved.Numerical examples illustrate that the computing cost can significantly decrease by roughly 80%via adopting various combination of proper schemes(except the uniform placement example),and the average qualities of corresponding Delaunay triangulation substantially exceed 0.9.It shows that those strategies are efficient and can generate a node set with high quality.

Diffusion-Controlled Adsorption Kinetics of Triton X-100 at Air/Solution Interface

In this paper, the equilibrium surface tension and the dynamic surface tension of aqueous Triton X-100 solution at temperature 25 ℃ were measured by means of Wilhelmy plate method and maximal bubble pressure method respectively. The determined critical micellar concentration（cmc） of Triton X-100 at 25 ℃ is (2.2×10-4) mol/dm3. The adsorption mechanics of Triton X-100 at air/solution was determined. For the submicellar concentrations it is diffusion-controlled. The diffusion coefficient was calculated from the experimental data in the range of short limit. In the range of long time adsorption, the subsurface concentration is fitted from the measured dynamic surface tensions.

Numerical study of spike characteristics due to the motions of a non-spherical rebounding bubble

The boundary integral method（BIM） is used to simulate the 3-D gas bubble, generated within the two bubble pulsation periods in proximity to a free surface in an inviscid, incompressible and irrotational flow. The present method is well validated by comparing the calculated shapes of the bubble and the free surface with both the experimental results and the numerical ones obtained by the Axisymmetric BIM code. The expansion, the collapse of the gas bubble and the further evolution of the rebounding non-spherical bubble are simulated. The various variation patterns of the free surface spike and the bubble centroid for different standoff distances, the buoyancy parameters and the strength parameters are obtained to reveal the nonlinear interaction between the bubble and the free surface. The amplitude of the second maximum bubble volume and the four typical patterns of the bubble jet and the free surface spike are examined in the context of the standoff distance. The large buoyancy is used to elevate the spray dome rather than the free surface spike.