Interfacial Tension Gradient Research Articles

The effects of interfacial tension gradients on the motion of drops and bubbles

The motion of a small drop or bubble is examined within the context of a theory which takes account of interfacial tension gradients brought on by composition variations around the periphery of the drop or bubble. Two situations are examined for large Peclet numbers: an almost freely circulating interface and an almost rigid interface. The results indicate a fairly rapid transition between these two states as the radius is decreased, even though the amount of surface-active material is small enough to preclude the formation of a stagnant cap per se. Consequently, the results complement those obtained with Savic's stagnant-cap model.

Film shapes for deformable drops at liquid-liquid interfaces. II. The mechanisms of film drainage

The light interference pattern produced by illuminating the thin liquid film of water trapped between a rising oil drop and the bulk oil/water interface with white light was observed for various sizes of oil drops for four oil/water systems. Various concentrations of a surfactant, sodium lauryl sulfate, were used in the water phase. The interference patterns are presented and are broken into mechanisms to explain the different patterns observed. These mechanisms are based on analyses of the shear stress at the bulk (surfactant-bearing) interface and of the interfacial concentration gradient of the surfactant and consequent interfacial tension gradient that this produces in the interface. The mechanisms are rapid approach of the drop to the interface, dimple formation, even drainage, uneven drainage, and film rupture. Uneven drainage is discussed in detail, with particular reference to toluene and anisole drops at the bulk interface. Measurements gave 300–500 Å as the film thickness at rupture.

The effects of interfacial tension gradients on the motion of drops and bubbles

The motion of a small drop or bubble is examined within the context of a theory which takes account of interfacial tension gradients brought on by comp

Adsorption of polyvinyl alcohol on the paraffin—water interface. III. Emulsification of paraffin in aqueous solutions of polyvinyl alcohol and the properties of paraffin-in-water emulsions stabilized by polyvinyl alcohol

A study has been made of the emulsification of paraffin in water with polyvinyl alcohol (PVA) as the emulsifier. Attention was paid to the influence of the composition of the mixture and the molecular weight and acetate group content of the polymer on the properties of the emulsions formed. For each emulsion, the specific area and the amount of PVA adsorbed were determined. The most remarkable result is that for relatively hydrophobic PVA samples (acetate content > 10%) the specific area of the emulsion does not increase indefinitely with increasing polymer concentration c p but passes through a maximum. The polymer concentration where this maximum is reached increases with decreasing molecular weight. No such irregularity was observed with relatively hydrophilic PVA samples (acetate content <10%). An explanation is presented in terms of the various phenomena occurring during the emulsification process. Important quantities are interfacial tension gradients, the rate of adsorption of polymers by diffusion and reconformation, and the rate of coalescence, all during emulsification. The obtained emulsions are generally very stable. At high c p the adsorbed molecules are subjected to considerable lateral constriction, the more so the more hydrophobic the molecule.

The flocculation of aqueous sols of a graphitized carbon black by a potential-determining electrolyte

Recent work on the film thinning behavior during the coalescence of oil drops in water is summarized. In the experimental work, color movies were taken of the light interference patterns produced by the thin film of water trapped between the rising drop and the bulk oil phase. The drops were relatively small (0.2–0.32 cm diam.); sufficient KCl was added to minimize double layer repulsion. Concentrations of 10 −6 –10 −2 g l −1 of sodium lauryl sulfate were used. The oils used were toluene, anisole, cyclohexanol and a mixture of anisole and cyclohexane. Five different patterns of film behavior were observed. The mechanisms to explain these patterns are based on concepts of dynamic immobility (when the distribution of surfactant along the interface gives an interfacial tension gradient that every-where balances the interfacial shear stress) and of steric immobility. The mechanisms include rapid approach (when both interfaces are mobile), dimple formation (when the interfacial tension gradient exceeds the interfacial shear stress), even drainage (when the interfaces are dynamically or sterically immobile) and uneven drainage (when there is local mobility). Reasons for uneven drainage are discussed. The different theoretical models developed to describe film thinning are reviewed. The emphasis is on the assumptions and the relationship between the equations describing flow in the film and those describing surface behavior. The predictions of the different models are compared but the emphasis is on the success of more recent models based on the above mentioned mechanisms to describe symmetrical film drainage.

The effect of surfactants on the coalescence of a drop at an interface. II

The effect of additions of sodium lauryl sulfate (10 −6 to 10 −4 gm/l) and the effect of the age of the interface and drop size on the rate and pattern of coalescence were investigated for toluene drops and anisole drops in water. Color movies (at 16 and 32 frames/sec) were taken of the light interference patterns produced by the changing thickness of the film of water trapped between the oil droplet and the layer of oil. The work indicates that in the trapped film there exists a complex pattern of flow behavior that is strongly influenced by the surfactant concentration. In particular, a bulk flow of fluid into the film occurs for concentrations of sodium lauryl sulfate of 10 −6 gm/l. This could be caused by a momentum effect or by interfacial tension gradients that exist because the bulk flow of fluid sweeps surfactant from sections of the film. This work extends the observations of Hodgson and Lee made for the rest times of the toluene-water system by presenting the behavior of the trapped film of fluid. In addition the effect of surfactants on the rest times and the film behavior is given for the low-density difference system of anisole and water. For relatively high concentrations of surfactant (10 −4 gm/l) the controlling mechanism is the expulsion of the fluid from beyond the barrier ring and not of the fluid from within the barrier ring, as has been suggested by the parallel plate model. A simple, two-dimensional model based on this observation is compared with the observed rate of drainage for separations less than 6000 A. The effect of van der Waals attraction was included in this model. A mathematical model is presented for the prediction of the diameter of the barrier ring as a function of elapsed time.

Film flow and coalescence-I Basic relations, film shape and criteria for interface mobility

The basic hydrodynamic equations determining flow at an interface are reviewed. An equation relating the profile of a thin film formed between a drop and an interface, or between two drops, to the pressure drop due to flow is derived. For the case of a small drop radius b coalescing at an interface, the radius of the film R 1 = 2 b 2(Δπ g/3γ) 1 2 , but the position of minimum thickness is shown to occur at R 1/√2 in agreement with experiment. The influence of interfacial tension gradients on tangential movement of the interface itself is examined in detail. It is shown that the interfaces of the film in the case of a small drop are partly or completely mobile unless the interfacial tension difference between the centre and the periphery Δγ 0=γ h/ b, assuming the film approximates to the plane disc model. Equations showing how interface mobility is controlled by mass transfer of a third component are considered and the effect of mobility on drop coalescence times in dispersions is discussed.

Binary liquid flow in micropores

Experimental values of phenomenological coefficients for liquid flow through porous (Vycor) glass are presented at two or more compositions for each of the binary systems: I, C6H6(1)+CCl4;II, C6H6(1)+C6H12; III, CCl4(1)+C6H12. Hydrodynamic flow and ordinary diffusion in pores of about 26 Å radius are described approximately by the usual macroscopic equations; discrepancies may be interpreted by means of a micropore model in terms of frictional and adsorption effects in a slipping monolayer film at the pore surface. The increase which occurs in the Staverman reflection coefficient 12σ with decreasing volume fraction of the selectively adsorbed component (1), especially in system II, are explained in terms of a net volume flow due to an interfacial tension gradient which arises when selective adsorption occurs in the presence of a concentration gradient. A contribution to σ also results from a difference in friction coefficients per unit volume for the two solution components in the surface film. An apparent experimental discrepancy (system I) between the cross-coefficients for volume and relative velocity flow is not explained by the theory.

Some effects of interfacial diffusion on the gravity coalescence of liquid drops

The rate of thinning of the Phase 2 film separating a drop (Phase 1) from a Phase 1/ Phase 2 interface was found to increase with diffusion from, and decrease with diffusion into, the drop. The film thickness at rupture appeared to be unaffected. The results provide direct confirmation of the mechanism proposed by Groothius and Zuiderweg, based on the Marangoni effect whereby changes in the rate of film thinning arise from interfacial flow as a result of gradients in interfacial tension produced by unequal distribution of the diffusing component over the drop surface.

Protoplasmic streaming as a process of jet propulsion

Protoplasmic streaming is proposed to be generally a countercurrent process in which tubular and vesicular membranous elements of the endoplasm jet-propel themselves in the direction of streaming by a pumping action in which the cytoplasmic matrix is ejected in the opposite direction. Movement of inclusions with the jet-propelled membranous elements apparently depends upon the fact that they are membrane encapsulated and enmeshed in a dense network of these elements, for which they have a high affinity. Circulation of matrix between massive lamellar elements of the endoplasmic reticulum also seems to be accomplished by a pumping action of the constituent double-membrane lamellae. The recoil of these massive elements and of membrane-encapsulated organelles may be the basis for their translational and rotational movements. The pumping of matrix by membranous elements is suggested to be an accompaniment of metabolic activity at their surfaces and the primitive basis for cell circulations. In this view, the very elements responsible for syntheses and other metabolic reactions, also provide the channels and motive force for partitioning, exposing, circulating, and transporting both the substrates upon which they act and the products of their actions. When protoplasmic streaming in various forms is analyzed as a countercurrent process involving jet propulsion, its many manifestations can be formulated as mere variations on a common theme, as postulated in the following: 1. 1. Cyclosis of plant-cell protoplasm reflects the continuous countercurrent circulation of matrix through the lumina of counter-moving membranous elements. 2. 2. Asters form by jet propulsion of membranous elements inward along the rays to the clear hyaline central region where they accumulate as a gelled mass. 3. 3. “Peristaltic” flow of axoplasm and “damming up” of constricted neurons occur as a result of the temporary “pile up” of jet-propelled elements of the axonal endoplasmic reticulum (and accompanying inclusions) at the nodes of Ranvier and other constricted regions. 4. 4. Myxomycete shuttle streaming primarily reflects the back-and-forth countercurrent circulation of matrix through the lumina of elements of the endoplasmic reticulum. The matrix and jet-propelled elements alternately accumulate in greater amounts at opposite ends of the stream. 5. 5. Protoplasmic streaming in fungal hyphae, viewed as a process of mass exchange rather than of bulk transfer, resolves the long-standing enigma of where the streaming protoplasm goes to. Membranous elements and inclusions make headway to certain regions at the expense of matrix which, being retrojected in tandem, accumulates at other regions. The cycles of waxing and waning of vacuolar size at opposite extremities of hyphae in which reversals of streaming occur, reflect the accumulation and evacuation of matrix retrojected from one end to the other by the jet-propelled elements. 6. 6. The countercurrent basis of protoplasmic streaming is revealed in organisms which feed by filament streaming. When only an interfacial film separates the protoplasm from the medium, as in a foraminiferan reticulopod, the movement of retrojected matrix is manifested because it carries the film and adhering particulate matter back to the cell body with it by adhesive drag. A gradient of dynamic interfacial tension probably promotes the flow of the film.

Countercurrent Streaming in Liquid Surfaces and Its Relevance to Protoplasmic Movements

Movements of surface films counter to the interior stream are brought about by film pressure generated by surface tension gradients. In a similar process, the formation of new interfaces during protoplasmic syntheses could sustain gradients of interfacial tension with resulting protoplasmic movements.

The Marangoni Effect and Liquid/Liquid Coalescence

THE rate of coalescence of liquid drops (phase 1) suspended in an immiscible liquid (phase 2) has been shown to increase when a third component, soluble in both phases, diffuses out of the drop1–5, and vice versa. This behaviour has been attributed to the Marangoni effect6, whereby interfacial flow is established by gradients in interfacial tension causing an increase in one case, and a decrease in the other, of the rate of thinning of the phase-2 film separating the coalescing interfaces.

Surface Renewal and Molecular Diffusion in Interphase Mass Transfer

IN 1953 Lewis and Pratt1 described violent spontaneous movements of the liquid-liquid interface which they observed during measurements of interfacial tension in the presence of mass transfer by the drop-weight method. These phenomena have since been investigated more fully2–5. It is now generally accepted that they are due to the formation of local gradients of interfacial tension caused by local variations of solute concentration at the interface as the result of mass transfer.