Deformation of an oil droplet on a solid substrate in simple shear flow
Introduction
The phenomena of deformation and displacement of immiscible fluids on solid substrate take place in removal of oil droplets from the narrow passage of a porous rock structure in enhanced oil recovery. The ease of oil droplet deformation and displacement determines the efficiency of enhanced oil recovery or the transport of non-aqueous phase liquids through the rock structure via water or surfactant flooding. Apart from enhanced oil recovery, liquid droplets adhering to, moving along, or dislodging from solid surfaces are encountered in several natural and engineering settings and under a wide range of physical conditions such as detergency and cell detachment in human body. The fundamentals of oil droplet deformation and detachment are studied during last decade but most of the studies are restricted to theoretical model development. The experimental work with respect to visual observation of oil droplet deformation and displacement is scanty in openly available literature.
Dussan (1987) theoretically analyzed the phenomenon of a droplet dislodging from a solid surface in the presence of motion of surrounding fluid. Dussan (1987) developed yield criteria for the critical capillary number, Ca, as a function of the advancing and receding contact angles, and , for an oil droplet sliding on a plane. The capillary number, () is a ratio of viscous to surface tension forces, where is the oil–water interfacial tension, is the viscosity of shearing fluid and is the free stream velocity of shearing fluid. The analysis was based on asymptotic theory valid for small contact angle hysteresis . Here, is the advancing contact angle and is the receding contact angle of oil the droplet. Mahe et al. (1988) studied experimentally the attachment and detachment processes of different alkane droplets having different contact angles on glass surface in simple shear flow. They mainly focused on visual observation of detachment of an inverted oil droplet from a solid substrate by viewing the contact area through a microscope. They observed that the oil droplet adhered to the solid substrate having equilibrium contact angle close to deforms and leans in the direction of shear. The contact angle of the advancing edge increases, whereas that for the receding edge decreases. And finally the droplet detaches when the receding edge slides and meets the advancing edge at the downstream side of the droplet. Mahe et al. (1988) presented the data in terms of shear rates required for the detachment of different sizes of oil droplets. Feng and Basaran (1994) theoretically modeled translationally symmetric cylindrical bubble protruding from a slot in a solid wall into liquid undergoing simple shear flow. They solved two-dimensional Navier–Stokes equations by the Galerkin finite element method. The plot of bubble deformation versus Reynolds number is found to exhibit turning points, where Re reaches critical value. Li and Pozrikidis (1996) studied the three-dimensional analogue of the problem of Feng and Basaran (1994) in the limit of low Re using boundary integral method. They computed the shapes of droplets as a function of Ca for different geometries of the contact line. It is concluded that the droplet with elliptical contact line is likely to dislodge or breakup before the droplet with circular contact line. Basu et al. (1997) proposed a mathematical model for the detachment of non-wetting droplet and partially wetting droplet ( based on visual observation described by Mahe et al. (1988). According to Basu et al. (1997), a droplet detaches from solid substrate when the drag on the droplet due to motion of shearing fluid overcomes the retentive force due to the contact angle hysteresis and interfacial tension. However, a droplet having an equilibrium contact angle, , approaching slides on the solid surface and does not detach. With further increase in the shear rate, the sliding droplet detaches from the solid surface when the lift force equals the adhesive, gravitational and buoyancy force of the droplet. The critical shear for the detachment of a pristine droplet, having of , is reasonably predicted by the model where sliding as the mode of detachment is assumed, whereas the experimental data for squalane droplet, having of , is reasonably predicted by the model where lift is considered as the mode of detachment. However, mathematical model developed by Basu et al. (1997) involves assumptions and hence it suffers from accuracy of prediction of oil droplet detachment in shear flow. Dimitrakopoulos and Higdon (1997) studied theoretically two dimensional droplet dislodging from a solid surface in shear field taking into account the gravity. They found critical shear rate of detachment as a function of viscosity ratio of droplet and shear fluids, Bond number and contact angle hysteresis. Schleizer and Bonnecaze (1999) used boundary integral method to determine droplet deformation on a solid surface in a shear field with fixed and mobile contact line for negligible gravity and inertia. The deformation of the droplet increases with the increase in capillary number, viscosity ratio and size of the droplet. They studied the effect of surfactant concentration on deformation of the oil droplet. The dynamics of partial detachment of oil droplet from solid surface is simulated by Jones et al. (1999) using dissipation particle dynamics approach. According to them, at a shear rate exceeding critical value, the oil droplet acquires tendency to lift off the surface leading to its removal.
Most of the studies mentioned above are mathematical models except for the work of Mahe et al. (1988), who observed the detachment process by viewing the contact area through a microscope. The droplet deformation is not visually observed from the side of the droplet. It is noted that contact angle hysteresis plays an important role and droplet tends to slide in the intermediate range of equilibrium contact angle of the oil droplet. Thus it is important to observe the deformation and detachment from the side of the droplet. Further, in most of the mathematical modeling work, experimental verification of the droplet deformation is not carried out. In the present study, the deformation and detachment of two different oil droplets, namely aniline and isoquinoline attached to a solid substrate in simple shear field were visually observed and droplet deformation were quantified. Finally, the droplet deformation in shear field was analyzed using computational fluid mechanics software (Fluent 6.3) and compared with the droplet deformation observed in the experiment.
Section snippets
Material
Oil droplets used in the experiment were analytical grade aniline (E Merck) and isoquinoline (Spectochem). RO water of conductivity obtained from Sartorius de-ionized water purification system (Sartorius, Arium 61315) was used as shearing fluid. The physical properties of the test fluids are given in Table 1.
Setup
Fig. 1 shows the schematic of the experimental setup used in visualization of droplet deformation and detachment in shear field. An overhead tank (a), with an arrangement to
Computational fluid dynamics simulation
A two-dimensional droplet attached to a solid substrate as illustrated in Fig. 2a is considered for modeling purpose. The droplet size is specified by its volume or equivalently by the radius of a spherical cap, , where, is the equilibrium contact angle of the droplet on the solid substrate and r is the contact radius. The shearing fluid (fluid 1) has density and viscosity and the droplet liquid (fluid 2) has density and viscosity . The gravitation is neglected as the
Visual observation
Fig. 3, Fig. 4 show sequence of photographs of aniline and isoquinoline droplets in simple shear flow. Initially, the partially wetting aniline droplet deforms and advancing contact point slightly moves in the down stream side and finally it detaches from the substrate when the receding contact point is about to dislodge. Whereas, isoquinoline droplet having slightly higher wetting characteristics than that of aniline deforms and elongates as the flow rate is increased and
Conclusion
In order to elucidate the mechanism of deformation and detachment of oil droplet adhered to a solid substrate in simple shear flow, experiments were carried out such that the phenomena could be visually observed. As the shearing fluid (aqueous phase) flow rate is increased in quasi-steady manner, the oil droplet (aniline and isoquinoline) deformed and advancing and receding contact angle formed at the upstream and downstream side of the droplet. Finally oil droplet detaches when advancing
Notations
radius of the oil droplet, m bond number , dimensionless capillary number , dimensionless capillary number for the dynamic contact angle as defined in Eq. (8) (, dimensionless equivalent diameter of the channel, m gravity, height of the spherical cap as assumed for stationary oil droplet, m pressure, contact radius of the oil droplet, m radius of the spherical cap as assumed for stationary oil droplet, m Reynolds number, average free
Acknowledgment
Authors acknowledge the funding from department of science and technology, Government of India for executing the project (CE/19/2003-SERC-Engg).
References (12)
- et al.
A model for detachment of a partially wetting drop from solid surface by shear flow
Journal of Colloid and Interface Science
(1997) - et al.
A continuum method for modeling surface tension
Journal of Computational Physics
(1992) - et al.
Retention of liquid drops by solid surfaces
Journal of Colloid and Interface Science
(1990) - et al.
Adhesion of droplets on solid wall and detachment by shear flow
Journal of Colloid and Interface Science
(1988) The dynamics of spreading of liquids on a solid surface I. Viscous flow
Journal of Fluid Mechanics
(1986)- et al.
Displacement of fluid droplets from solid surfaces in low-Reynolds-number shear flows
Journal of Fluid Mechanics
(1997)
Cited by (35)
The shape shapes the interfacial liquid-liquid mass transfer: CFD simulations for single spherical and ellipsoidal drops
2023, Chemical Engineering ScienceCitation Excerpt :For a given liquid–liquid system, Schmidt number is constant and hence as the Reynolds number increases circulation rate inside the drop also increases and thus effect of convective mass transfer on overall mass transfer increases. As conducting highly controlled experiments at droplet level is very difficult, CFD modelling assumes great importance to fundamentally understand various phenomena involving single drops (Gupta & Basu, 2008; Chen, 2001; Wang et al., 2017; Van Baten & Krishna, 2004; Jeon et al., 2009). There are several experimental studies on understanding liquid–liquid mass transfer phenomenon for single droplets (Schröter et al., 1998; Grassia and Ubal, 2018; Henschke and Pfennig, 1999; Ubal et al., 2010; Wegener, 2007).
Observation of water droplet motion in a shear flow
2023, Experimental Thermal and Fluid ScienceRole of surfactant-induced Marangoni effects in droplet dynamics on a solid surface in shear flow
2022, Colloids and Surfaces A: Physicochemical and Engineering AspectsBinary droplet interactions in shear water-in-oil emulsion: A molecular dynamics study
2022, Journal of Molecular LiquidsCitation Excerpt :The critical wind speed for the downstream movement of droplets on a solid surface in a shear flow is experimentally studied [32,33]. Gupta and Basu [34] compared the experiment and volume of fluid method for the deformation of oil droplets on a solid substrate in a water shear flow. Wang et al. [35] studied the dynamics of oil droplet deformation and the start-up process on walls driven by an external shear flow based on the lattice Boltzmann method (LBM).
Dynamic behaviors of water droplet moving on surfaces with different wettability driven by airflow
2022, International Journal of Multiphase FlowCitation Excerpt :They found that the accumulation of the surfactant near the triple line caused by low pressure induced surface tension gradients around the droplet-surface interface and facilitated the droplet depinning. Gupta and Basu (2008) clarified the influence of interfacial tension of different oil droplets on their motions and the droplet deformation increased as the interfacial tension decreased. Milne and Amirfazli (2009) used a corrective factor based on contact angle and the fluid properties to match well with the data of hexadecane droplet motion and water droplet driven by shear flow.
Inner and outer flow of an adhering droplet in shear flow
2022, International Journal of Multiphase Flow