scholarly journals Sedimentation of a surfactant-laden drop under the influence of an electric field

2018 ◽  
Vol 849 ◽  
pp. 277-311 ◽  
Author(s):  
Antarip Poddar ◽  
Shubhadeep Mandal ◽  
Aditya Bandopadhyay ◽  
Suman Chakraborty
Keyword(s):  
Surface Tension ◽  
Electric Field ◽  
Surfactant Concentration ◽  
Perturbation Technique ◽  
Internal Flow ◽  
Dielectric Fluid ◽  
Regular Perturbation ◽  
Spherical Drop ◽  
Leaky Dielectric ◽  
Marangoni Stress

The sedimentation of a surfactant-laden deformable viscous drop acted upon by an electric field is considered theoretically. The convection of surfactants in conjunction with the combined effect of electrohydrodynamic flow and sedimentation leads to a locally varying surface tension, which subsequently alters the drop dynamics via the interplay of Marangoni, Maxwell and hydrodynamic stresses. Assuming small capillary number and small electric Reynolds number, we employ a regular perturbation technique to solve the coupled system of governing equations. It is shown that when a leaky dielectric drop is sedimenting in another leaky dielectric fluid, the Marangoni stress can oppose the electrohydrodynamic motion severely, thereby causing corresponding changes in the internal flow pattern. Such effects further result in retardation of the drop settling velocity, which would have otherwise increased due to the influence of charge convection. For non-spherical drop shapes, the effect of Marangoni stress is overcome by the ‘tip-stretching’ effect on the flow field. As a result, the drop deformation gets intensified with an increase in sensitivity of the surface tension to the local surfactant concentration. Consequently, for an oblate type of deformation the elevated drag force causes a further reduction in velocity. For similar reasons, prolate drops experience less drag and settle faster than the surfactant-free case. In addition to this, with increased sensitivity of the interfacial tension to the surfactant concentration, the asymmetric deformation about the equator gets suppressed. These findings may turn out to be of fundamental significance towards designing electrohydrodynamically actuated droplet-based microfluidic systems that are intrinsically tunable by varying the surfactant concentration.

scholarly journals Liquid toroidal drop under uniform electric field

2017 ◽  
Vol 473 (2202) ◽  
pp. 20160633 ◽  
Author(s):  
Michael Zabarankin
Keyword(s):  
Surface Tension ◽  
Electric Field ◽  
Dielectric Constants ◽  
Uniform Electric Field ◽  
Normal Velocity ◽  
Spherical Drop ◽  
Electric Stress ◽  
Freely Suspended ◽  
Major Radius ◽  
External Forces

The problem of a stationary liquid toroidal drop freely suspended in another fluid and subjected to an electric field uniform at infinity is addressed analytically. Taylor’s discriminating function implies that, when the phases have equal viscosities and are assumed to be slightly conducting (leaky dielectrics), a spherical drop is stationary when Q =(2 R 2 +3 R +2)/(7 R 2 ), where R and Q are ratios of the phases’ electric conductivities and dielectric constants, respectively. This condition holds for any electric capillary number, Ca E , that defines the ratio of electric stress to surface tension. Pairam and Fernández-Nieves showed experimentally that, in the absence of external forces (Ca E =0), a toroidal drop shrinks towards its centre, and, consequently, the drop can be stationary only for some Ca E >0. This work finds Q and Ca E such that, under the presence of an electric field and with equal viscosities of the phases, a toroidal drop having major radius ρ and volume 4 π /3 is qualitatively stationary—the normal velocity of the drop’s interface is minute and the interface coincides visually with a streamline. The found Q and Ca E depend on R and ρ , and for large ρ , e.g. ρ ≥3, they have simple approximations: Q ∼( R 2 + R +1)/(3 R 2 ) and Ca E ∼ 3 3 π ρ / 2   ( 6  ln  ⁡ ρ + 2  ln ⁡ [ 96 π ] − 9 ) / ( 12  ln  ⁡ ρ + 4  ln ⁡ [ 96 π ] − 17 )   ( R + 1 ) 2 / ( R − 1 ) 2 .

The effect of surfactants on drop deformation and on the rheology of dilute emulsions in Stokes flow

1997 ◽  
Vol 341 ◽  
pp. 165-194 ◽  
Author(s):  
XIAOFAN LI ◽  
C. POZRIKIDIS
Keyword(s):  
Surface Tension ◽  
Stokes Flow ◽  
Capillary Number ◽  
Surfactant Concentration ◽  
Drop Deformation ◽  
Main Body ◽  
Incident Flow ◽  
Spherical Drop ◽  
Convection Diffusion ◽  
Elasticity Number

The effect of an insoluble surfactant on the transient deformation and asymptotic shape of a spherical drop that is subjected to a linear shear or extensional flow at vanishing Reynolds number is studied using a numerical method. The viscosity of the drop is equal to that of the ambient fluid, and the interfacial tension is assumed to depend linearly on the local surfactant concentration. The drop deformation is affected by non-uniformities in the surface tension due to the surfactant molecules convection–diffusion. The numerical procedure combines the boundary-integral method for solving the equations of Stokes flow, and a finite-difference method for solving the unsteady convection–diffusion equation for the surfactant concentration over the evolving interface. The parametric investigations address the effect of the ratio of the vorticity to the rate of strain of the incident flow, the Péclet number expressing the ability of the surfactant to diffuse, the elasticity number expressing the sensitivity of the surface tension to variations in surfactant concentration, and the capillary number expressing the strength of the incident flow. At small and moderate capillary numbers, the effect of a surfactant in a non-axisymmetric flow is found to be similar to that in axisymmetric straining flow studied by previous authors. The accumulation of surfactant molecules at the tips of an elongated drop decreases the surface tension locally and promotes the deformation, whereas the dilution of the surfactant over the main body of the drop increases the surface tension and restrains the deformation. At large capillary numbers, the dilution of the surfactant and the rotational motion associated with the vorticity of the incident flow work synergistically to increase the critical capillary number beyond which the drop exhibits continuous elongation. The numerical results establish the regions of validity of the small-deformation theory developed by previous authors, and illustrate the influence of the surfactant on the flow kinematics and on the rheological properties of a dilute suspension. Surfactants have a stronger effect on the rheology of a suspension than on the deformation of the individual drops.

Effect of Gravity Modulation on Electrothermal Convection in a Dielectric Fluid Saturated Anisotropic Porous Layer

2013 ◽  
Vol 136 (3) ◽  
Author(s):  
Mahantesh S. Swamy ◽  
I. S. Shivakumara ◽  
N. B. Naduvinamani
Keyword(s):  
Heat Transfer ◽  
Electric Field ◽  
Porous Layer ◽  
Initial Conditions ◽  
Low Frequency ◽  
Dielectric Fluid ◽  
Gravity Modulation ◽  
Regular Perturbation ◽  
Stability Parameters ◽  
Ac Electric Field

This paper deals with linear and nonlinear stability analyses of thermal convection in a dielectric fluid saturated anisotropic Brinkman porous layer subject to the combined effect of AC electric field and time-periodic gravity modulation (GM). In the realm of linear theory, the critical stability parameters are computed by regular perturbation method. The local nonlinear theory based on truncated Fourier series method gives the information of convection amplitudes and heat transfer. Principle of exchange of stabilities is found to be valid and subcritical instability is ruled out. Based on the governing linear autonomous system several qualitative results on stability are discussed. The sensitive dependence of the solution of Lorenz system of electrothermal convection to the choice of initial conditions points to the possibility of chaos. Low frequency g-jitter is found to have significant stabilizing influence which is in turn diminished by an imposed AC electric field. The role of other governing parameters on the stability threshold and on transient heat transfer is determined.

Surfactant-induced retardation of the thermocapillary migration of a droplet

1997 ◽  
Vol 340 ◽  
pp. 35-59 ◽  
Author(s):  
JINNAN CHEN ◽  
KATHLEEN J. STEBE
Keyword(s):  
Surface Tension ◽  
Surfactant Concentration ◽  
Surface Concentration ◽  
Terminal Velocity ◽  
Control Surface ◽  
Surfactant Adsorption ◽  
Thermocapillary Migration ◽  
Marangoni Stress ◽  
Surface Convection ◽  
The Impact

A neutrally buoyant droplet in a fluid possessing a temperature gradient migrates under the action of thermocapillarity. The drop pole in the high-temperature region has a reduced surface tension. The surface pulls away from this low-tension region, establishing a Marangoni stress which propels the droplet into the warmer fluid. Thermocapillary migration is retarded by the adsorption of surfactant: surfactant is swept to the trailing pole by surface convection, establishing a surfactant-induced Marangoni stress resisting the flow (Barton & Subramanian 1990).The impact of surfactant adsorption on drop thermocapillary motion is studied for two nonlinear adsorption frameworks in the sorption-controlled limit. The Langmuir adsorption framework accounts for the maximum surface concentration Γ′∞ that can be attained for monolayer adsorption; the Frumkin adsorption framework accounts for Γ′∞ and for non-ideal surfactant interactions. The compositional dependence of the surface tension alters both the thermocapillary stress which drives the flow and the surfactant-induced Marangoni stress which retards it. The competition between these stresses determines the terminal velocity U′, which is given by Young's velocity U′0 in the absence of surfactant adsorption. In the regime where adsorption–desorption and surface convection are of the same order, U′ initially decreases with surfactant concentration for the Langmuir model. A minimum is then attained, and U′ subsequently increases slightly with bulk concentration, but remains significantly less than U′0. For cohesive interactions in the Frumkin model, U′ decreases monotonically with surfactant concentration, asymptoting to a value less than the Langmuir velocity. For repulsive interactions, U′ is non-monotonic, initially decreasing with concentration, subsequently increasing for elevated concentrations. The implications of these results for using surfactants to control surface mobilities in thermocapillary migration are discussed.

Stability of an elastico-viscous liquid film flowing down an inclined plane

1967 ◽  
Vol 63 (2) ◽  
pp. 527-536 ◽  
Author(s):  
A. S. Gupta ◽  
Lajpat Rai
Keyword(s):  
Surface Tension ◽  
Stress Relaxation ◽  
Viscous Liquid ◽  
Perturbation Technique ◽  
Two Dimensional ◽  
Regular Perturbation ◽  
Inclined Plane ◽  
Viscous Liquid Film ◽  
The Stability ◽  
Sommerfeld Equation

AbstractAn analysis is made of the stability of a layer of an elastico-viscous liquid flowing down an inclined plane in the presence of two-dimensional disturbances. The modified Orr-Sommerfeld equation is solved by a regular perturbation technique for disturbances of large wavelengths. It is shown that in the absence of surface tension, the layer is more unstable as compared with that for an ordinary viscous liquid if Q1 > Q2, Q1 and Q2 being stress relaxation and strain retardation parameters respectively.

Flows Inside and Around a Vaporizing/Condensing Drop Translating in an Electric Field

1990 ◽  
Vol 57 (4) ◽  
pp. 1044-1055 ◽  
Author(s):  
H. D. Nguyen ◽  
J. N. Chung
Keyword(s):  
Electric Field ◽  
Drag Force ◽  
Mass Flux ◽  
Flow Behavior ◽  
Perturbation Technique ◽  
Internal Flow ◽  
Uniform Electric Field ◽  
State Equations ◽  
Total Drag ◽  
Linear Partial Differential Equations

The flow behavior inside and around a translating liquid drop that simultaneously experiences a large interfacial radial mass flux as a result of evaporation or condensation, and the influence of a uniform electric field is analyzed in this paper. The steady-state equations of continuity and momentum of both continuous and drop phases are transformed, by a perturbation technique, into a series of systems of linear partial differential equations which are then solved analytically. The flow structure and the drag force are computed to the first order in ε( =U∞R/ν), the perturbed parameter. Interfacial velocity profiles are represented by Legendre polynomials up to second order to accommodate the electric-field-induced shear stress. It is found that the presence of an electric field does not contribute to the total drag force, but greatly modifies the flow patterns. The droplet internal flow is dominated by the electric field such that the double loop Taylor flow appears at relatively high field strength. The outside flow is dominated by the interfacial mass flux and the recirculation zone only shows up for an evaporating drop under a negative electric field. The electric field also moves the dividing streamline toward to or away from the surface depending on the direction of the electric field and the velocity direction at the interface. Also the effects of an electric field on the flow field are more pronounced for a drop with outward interfacial mass flux because the electric field helps restore the strength of internal circulation weakened by the outward interfacial mass flux.

scholarly journals The Changing Shape of a Liquid Drop in an Electric Field

2013 ◽  
Vol 3 ◽  
pp. 24-40
Author(s):  
A.A.S.N. Jayalal ◽  
K.A.I.L. Wijewardena Gamalath
Keyword(s):  
Surface Tension ◽  
Dielectric Constant ◽  
Aspect Ratio ◽  
Electric Field ◽  
Applied Electric Field ◽  
Applied Field ◽  
Cone Angle ◽  
Constant Ratio ◽  
Spherical Drop ◽  
Fluid Drop

An approximate extension of the slender body theory was used to determine the static shape of a conically ended dielectric fluid drop in an electric field. Using induced surface charge density, hydrostatic pressure and the surface tension of the liquid with interfacial tension stresses and Maxwell electric stresses, a governing equation was obtained for slender geometries for the equilibrium configuration and numerically solved for 3D. For an applied electric field, the electric energy on a spherical drop can be maximized in a weak dielectric by increasing the applied electric field. The minimum dielectric constant ratio needed to produce a conical end is 14.5 corresponding to a cone angle 31.25° .There is a sharp increment of the aspect ratio after reaching the threshold value of the applied field strength and the deformation of the fluid drop increases with the increase in dielectric constant of the fluid drop. For a particular dielectric constant ratio, the threshold electric field producing conical interface increases with the increased surface tension of the liquid. The threshold electric field for a water drop is 1.0854×104 units and the corresponding aspect ratio is 15. For the minimum dielectric ratio the cone angle of the drop decreases with applied field making the drop more stable at higher fields.

scholarly journals Laminar condensation on a moving drop. Part 1. Singular perturbation technique

1984 ◽  
Vol 139 ◽  
pp. 105-130 ◽  
Author(s):  
J. N. Chung ◽  
P. S. Ayyaswamy ◽  
S. S. Sadhal
Keyword(s):  
Singular Perturbation ◽  
Perturbation Technique ◽  
Continuous Phase ◽  
Transport Processes ◽  
Forced Flow ◽  
Saturated Steam ◽  
Singular Perturbation Technique ◽  
Spherical Drop ◽  
Coupled Equations ◽  
Induced Velocity

In this paper, laminar condensation on a spherical drop in a forced flow is investigated. The drop experiences a strong, radial, condensation-induced velocity while undergoing slow translation. In view of the high condensation velocity, the flow field, although the drop experiences slow translation, is not in the Stokes-flow regime. The drop environment is assumed to consist of a mixture of saturated steam (condensable) and air (non-condensable). The study has been carried out in two different ways. In Part 1 the continuous phase is treated as quasi-steady and the governing equations for this phase are solved through a singular perturbation technique. The transient heat-up of the drop interior is solved by the series-truncation numerical method. The solution for the total problem is obtained by matching the results for the continuous and dispersed phases. In Part 2 both the phases are treated as fully transient and the entire set of coupled equations are solved by numerical means. Validity of the quasi-steady assumption of Part 1 is discussed. Effects due to the presence of the non-condensable component and of the drop surface temperature on transport processes are discussed in both parts. A significant contribution of the present study is the inclusion of the roles played by both the viscous and the inertial effects in the problem treatment.

Sign in / Sign up

Export Citation Format

Share Document