Viscous Drag Force Research Articles

Macroscopic characteristics for direct-injection multi-hole sprays using dimensionless analysis

The macroscopic spray characteristics were quantified using dimensionless analysis by examining the role of the dominating forces associated with liquid-jet breakup. The Weber number, Reynolds number, and air-to-liquid density ratio dimensionless numbers were used to capture the primary forces including the inertia, viscous, surface tension, and aerodynamic drag forces. Planar Mie-scattering technique was applied to generate spray images over a broad range of conditions found in today’s spark-ignition-direct-injection (SIDI) engines, providing a relatively large range of dimensionless numbers. The effect of fuel properties were examined using gasoline, methanol and ethanol fluids. Six regions described on a Weber number versus Reynolds number domain were selected to identify the relative importance of the inertia force, surface tension force, and viscous force on macroscopic spray structure. The effect of aerodynamic drag was individually determined by characterizing the spray over a range of ambient air-to-liquid density ratios. As a result, for the non-flash-boiling multi-hole sprays in this study, the Weber number and air-to-liquid density ratio have much more profound effect on the spray penetration and spray–plume angle compared to the Reynolds number contribution. The inertia force and air drag force are more important factors compared to the viscous force and surface tension force. This analysis yielded dimensionless correlations for spray penetration and spray–plume angle that provided important insight into the spray breakup and atomization processes.

Flow induced particle migration in fresh concrete: Theoretical frame, numerical simulations and experimental results on model fluids

Abstract In this paper, we describe and compare the various physical phenomena which potentially lead to flow induced particle migration in concrete. We show that, in the case of industrial casting of concrete, gravity induced particle migration dominates all other potential sources of heterogeneities induced by flow. We then show, from comparisons between experiments using model materials, dimensional analysis and numerical simulations, that, from a quantitative point of view, the viscous drag force, which prevents particles from migrating during a casting process, shall neither be computed from the apparent viscosity nor from the plastic viscosity of the suspending phase but from its tangential viscosity. Finally, the transfer of this type of numerical prediction tool to real concrete is discussed.

Noncontact Bubble Manipulation in Microchannel by Using Photothermal Marangoni Effect

A noncontact bubble manipulation by an optically induced local surface tension gradient is described in this paper. In microfluidic devices, the effects of interfacial phenomena become dominant with decreasing of the length scale. An appropriate control of the local gradient of the interfacial properties can provide a powerful method for bubble handling in the microfluidic system. Here, the photothermal technique is used to induce the gradient in surface tension around a microbubble. The thermocapillary force around the bubble is induced and controlled by local laser focusing. The bubble in a microchannel filled with silicone oil with varied viscosity was examined to verify experimentally the optical manipulation method of bubbles based on the photothermal Marangoni effect. As a result, three applications of bubble manipulation by using photothermal Marangoni effect are obtained: detachment from channel wall, trapping in liquid phase, and transportation in the channel. Additionally, minimum optical power for the manipulation was evaluated. The effects of bubble size, liquid viscosity, and irradiated optical power on the manipulation characteristics can be summarized by a dimensionless number that is a ratio of the thermocapillary force to viscous drag force for the bubble.

Wet granular rafts: aggregation in two dimensions under shear flow

The aggregation and fragmentation of cohesive granular particles trapped at an air–liquid interface under shear flow are investigated by experiments and compared with numerical simulations. The cohesion owing to the formation of capillary bridges from a thin oil film covering the particles is found to dominate other particle–particle interactions. In the steady state the radius of gyration Rg of an N particle cluster follows a power law Rg ∝ N1/δ. The fractal dimension δ of the clusters lies in the range between 1.5 and 1.6 and depends only weakly on the shear rate . The probability to find a cluster of N particles or larger P(N) displays an exponential tail P(N) ∝ exp(−N/Nc) with a characteristic cluster size Nc. A power law Nc ∝ −β with an exponent β = 0.65 ± 0.06 (β = 0.68 ± 0.02) is found in our experiments (simulations). The fractal dimension of the clusters and the value of β are consistent with an estimate of the largest stable cluster based on the balance between the capillary force and the viscous drag force.

Transport and Deposition of Evaporating Droplets in a Ventilated Environment

In this study, droplet transport, dispersion, and deposition in a ventilated office with two manikins were studied using a computer-modeling approach. Different airflow distribution systems were used, and an Eulerian approach was employed for the airflow simulation. The trajectories of droplets were evaluated using the Lagrangian approach by solving the equation of droplet motion that included the inertial, viscous drag, Brownian, Saffman lift, and gravity forces. Droplet evaporation was also taken into account by solving the droplet heat and mass transfer equations, thus, allowing for the variation of the droplet size. Mixing and displacement air distribution systems were examined, and trajectories of droplets in the range of 1 to 100 microns emitted by one of the manikins were simulated under a range of conditions. The simulation results showed that the chance for small droplets to leave the room through the exhaust is relatively high. When the mixing air distribution system is used, the drop dispersion is higher than with the displacement distribution system. This in turn suggests that the chance of transmission of air borne diseases is relatively higher for the mixing ventilation system.

Numerical study of upward particulate pipe flows at a constant Reynolds number

The method based on 2D Reynolds-averaged Navier-Stokes equations has been employed for the simulation of upward turbulent particulate cylindrical pipe flows of different diameters for a constant flow Reynolds number. This approach was supplied with appropriate closure equations which took into account all pertinent forces and effects that exerted influence on gas and particles: the particle-particle, particle-wall, and particle-turbulence interactions; gravitation, viscous drag, and lift forces; and turbulence modulation. The finite volume technique was applied to the numerical solution of the governing equations. The results show the effect of the mass loading on the radial distributions of the longitudinal velocity lag, the turbulence modulation, and particle concentration. In particular, the two-way coupling of turbulence with the given particles raises simultaneously the velocity lag between gas and particles, originating from direct impact of turbulence on particle motion, and turbulence attenuation by the particles. The radial distributions of longitudinal particle velocity and mass concentration become flatter for higher flow mass loading.

Particle scale modelling of the multiphase flow in a dense medium cyclone: Effect of vortex finder outlet pressure

Dense medium cyclone (DMC) is widely used to upgrade run-of-mine coal in the coal industry. In practice, different designs of the outlet geometry of the vortex finder are used to achieve different purposes. However, the underlying mechanisms are not well understood. In this work, this phenomenon is studied numerically with reference to the effect of the pressure at the vortex finder. The simulation is carried out by use of a combined approach of computational fluid dynamics (CFD) and discrete element method (DEM) (CFD–DEM). In the model, DEM is used to describe the motion of discrete coal particles, and CFD to describe the motion of medium slurry which is a mixture of gas, water and fine magnetite particles. It is shown that a relatively small change of the vortex finder pressure can cause significant variations of both the medium-coal flow and DMC performance. An important finding is that the flow direction of the axial velocity of the air phase in the “air-core” could reverse (changing from upward to downward) as the vortex finder pressure increases, which results in the downward viscous drag force on coal particles and consequently causes some low density coal to be misplaced to the reject/underflow. This work suggests that the control of the pressure at the outlet of the vortex finder is important for DMC performance.

Dissipation of shock wave in a gas-droplet mixture by droplet fragmentation

In this paper, we investigate the shock wave dissipation in a gas-droplet mixture over a wedge. A similar gas-droplet mixture had been considered earlier but this time we take account of breakup of the large droplets and see how the shock wave is affected. We consider a droplet breakup model dependent on the critical Weber number and add the equation of droplet number density evolution to the compressible two-fluid model. The viscous drag force, the heat transfer, and the phase change of the droplets are all included in the present model for interaction between phases. The fractional step method is used to solve the two-fluid governing equations in two parts: the hyperbolic operator is solved by the second-order WAF-HLL scheme and the source operator by the fourth-order Runge–Kutta method. We elaborate how the shock dissipation and pressure distribution is affected by the droplet size and droplet volume fraction.

Dynamical simulation of cornea deformation in laser surgery

A dynamical simulation method is presented to model the cornea deformation in surgery of laser thermokeratoplasty. The virtual cornea is constructed as a mass-spring system. The corneal surface tension is simulated by damping spring stretch between mass points on the cornea model. The aqueous humor in the eyeball is modeled as ideal gas, and the intraocular pressure is simulated by gas pressure. The coagulation force is exerted on each photocoagulation spot to demonstrate its collapse caused by the condensation of corneal soft tissue irradiated by laser. An extra viscous drag force is added to each mass point to weaken the mass point oscillation. The use of the effective time-corrected Verlet integral method brings about flowing and stable dynamic simulation procedures. The simulation results show that, comparing to the undeformed model, the curvature of the region between the optical center and photocoagulation spot increases obviously. Moreover, the shape of the deformed virtual cornea is much similar to that of the real cornea after surgery.

The not-so-simple effects of boundary conditions on models of simple shear

Analog modeling of geological processes, such as folding instabilities or the behavior of inclusions in a matrix, often employs a linear simple-shear rig. In theory, a homogeneous plane-strain flow is prescribed at the boundaries of such deformation rigs but, in practice, the resulting internal deformation of the analog material (commonly paraffin wax or silicone putties) often deviates strongly from the intended homogeneous strain field. This can easily lead to misinterpretation of such analog experiments. We present a numerical finite-element approach to quantify the influence of imperfect simple-shear boundary conditions on the internal deformation of a homogeneous viscous analog material. The results demonstrate that imperfect boundary conditions in the vorticity-normal plane can cause the heterogeneous strain observed in some analog experiments. However, in other experiments, the analog material lies on top of a weak lubricating material or is sandwiched between two such materials. These layers lead to a viscous drag force acting on the analog material, resulting in imperfect simple-shear boundary conditions in the third dimension. For this experimental configuration, the numerical results show that the lubricating layers are responsible for the heterogeneous strain observed in analog models. The resulting errors in internal strain can be as high as 100%, and these difficult-to-avoid boundary effects must be considered when interpreting analog simple-shear experiments.

Surface Potential of Coal Particles in Coal-Oil Mixture and Control of Settling Stability Under Gravity

This work deals with the problem of settling under gravity for coal-oil mixtures when the concentration of particles is large. The repulsive force necessary to ensure stability of coal particle is vital. The net forces acting on the particle include gravity, buoyancy, viscous drag force, and electrostatic repulsive force. Accordingly, the equation at the terminal velocity at settling is obtained along with a critical surface potential to prevent settling under gravity.

Computational study of local and global ECM degradation and the effects on cell speed and cell–matrix tractions

Cell migration is important to biological processes such as wound healing and cancer invasion. Cell movement involves forming bonds between cell surface receptors and ligands present in the extracellular matrix (ECM) in order to generate the necessary forces on the matrix. For three-dimensional cell migration, partial degradation of the adjacent ECM using matrix metalloproteinases is necessary to create a passage with less motion resistance. Our mathematical model takes into consideration cell–ECM tractions needed to drive cell movement, viscous drag forces, and a transient matrix degradation process. Simulations were performed for global and highly localized matrix degradation processes, where the latter occurred at the cell–ECM interface. It was observed that the higher the speed of the cell boundary, the higher the matrix concentration after localized degradation. The results showed that a greater ECM degradation coefficient was needed for optimal cell migration to occur for the local process and that cell–ECM tractions were larger. The results from this investigation complement those obtained by other studies where it has been shown that cell speed is a biphasic function of ligand and matrix metalloproteinase concentration, and would also be of use for research on wound healing, cancer cell invasion, and tissue engineering.

A simple dynamic optical manipulation technique for label-free detection of biological cells

A dynamic optical tweezers system is employed for generation of an optical trap in continuous rotation for manipulating a biological cell in an aqueous solution. When the rotating speed is increased, the trapped cell experiences an augmented viscous drag force, and eventually it escapes from the trap at the critical rotating speed: when the drag force is greater than the trapping force. With experimental verifications, the method can easily be employed to differentiate cells in terms of trapping forces due to different refractive indices. The proposed method is a simple, robust, accurate and noninvasive label-free technique for cell detection.

Numerical simulation of three‐dimensional gas‐solid particle flow in a horizontal pipe

AbstractA three‐dimensional model of particulate flows using the Reynolds Averaged Navier‐Stokes method is presented. The governing equations of the gas–solids flow are supplemented with appropriate closure equations to take into account all the relevant forces exerted on the solid particles, such as particle‐turbulence interactions, turbulence modulation, particle–particle interactions, particle–wall interactions, as well as gravitational, viscous drag, and lift forces. A finite volume numerical technique was implemented for the numerical solution of the problem. The method has been validated by comparing its results with the limited number of available experimental data for the velocity and turbulence intensity of the gas–particle flow. The results show that the presence of particles in the flow has a significant effect on all the flow variables. Most notably, the distribution of all the parameters becomes asymmetric, because of the gravitational effect on the particles and particle sedimentation. © 2011 American Institute of Chemical Engineers AIChE J, 2011

Forces affecting double-stranded DNA translocation through synthetic nanopores

One of the recent applications of nanopores is to use them as detectors/analyzers for bio-molecules and nanopore based sequencing has been studied to quickly sequence DNA. In this paper, three categories of forces proposed in the literature to oppose the electrical driving forces in the DNA translocation process are analyzed, (1) the entropic forces of DNA uncoiling/recoiling at the pore entrance/exits, (2) the viscous drag acting on the blob like DNA outside the nanopore, and (3) the viscous drag acting on the linear DNA inside the nanopore. The magnitudes of these forces are calculated based on the parameters used in experiments and it is shown that the first two of the aforementioned categories of forces are usually small compared to the electrical driving force, while the last one is of the same order as the electrical driving force. To evaluate the viscous drag force acting on the linear DNA inside the nanopore, a hydrodynamic model based on the lubrication approximation is used to calculate the flow field and the viscous drag force acting on a DNA immobilized in a nanopore. This model is validated by good agreement with the experimental data for the tethering force used to immobilize a DNA inside the nanopore.

Analytical model of microfluidic transport of non-magnetic particles in ferrofluids under the influence of a permanent magnet

This study describes an analytical model and experimental verifications of transport of non-magnetic spherical microparticles in ferrofluids in a microfluidic system that consists of a microchannel and a permanent magnet. The permanent magnet produces a spatially non-uniform magnetic field that gives rise to a magnetic buoyancy force on particles within ferrofluid-filled microchannel. We obtained trajectories of particles in the microchannel by (1) calculating magnetic buoyancy force through the use of an analytical expression of magnetic field distributions and a nonlinear magnetization model of ferrofluids, (2) deriving governing equations of motion for particles through the use of analytical expressions of dominant magnetic buoyancy and hydrodynamic viscous drag forces, (3) solving equations of motion for particles in laminar flow conditions. We studied effects of particle size and flow rate in the microchannel on the trajectories of particles. The analysis indicated that particles were increasingly deflected in the direction that was perpendicular to the flow when size of particles increased, or when flow rate in the microchannel decreased. We also studied “wall effect” on the trajectories of particles in the microchannel when surfaces of particles were in contact with channel wall. Experimentally obtained trajectories of particles were used to confirm the validity of our analytical results. We believe this study forms the theoretical foundation for size-based particle (both synthetic and biological) separation in ferrofluids in a microfluidic device. The simplicity and versatility of our analytical model make it useful for quick optimizations of future separation devices as the model takes into account important design parameters including particle size, property of ferrofluids, magnetic field distribution, dimension of microchannel, and fluid flow rate.

A simple control scheme for the manipulation of a particle by means of optical tweezers

AbstractWe present a simple control scheme for changing the position of a microscopic particle immersed in a viscous medium and trapped by optical tweezers. We derive a simple feedback controller under the consideration that the particle mass is so small that it can be discarded from the motion equations. This approximation is well justified in practice, since the inertial force produced by the motion of a micron‐scaled trapped particle is completely dominated by the medium viscous drag force. Finally, we formally prove that the obtained controller is able to globally asymptotically stabilize the system when the particle mass is considered, if some suitable values of some control parameter are used. The stability analysis of the controlled system was carried out by using the standard Lyapunov stability theory. Also, by means of numerical simulations, we show that the obtained closed‐loop system is robust when random thermal noise is presented. Copyright © 2010 John Wiley & Sons, Ltd.

MATHEMATICAL MODEL OF TWO-PHASE FLOWS LOADED WITH LIGHT AND HEAVY PARTICLES TO ANALYZE CFB PROCESSES

Mathematical modeling of polydispersed (gas-solid particles) flow with light (ash) and heavy (corundum) particles is presented to analyze manifold process occurring in circulating fluidized beds (CFB). This study covers the process of turbulent mixing of particle and particle-particle collision, particle-surface collision and pertains the gravitation and viscous drag and lift forces. The 2D RANS (Reynolds Averaged Navier-Stokes) equations are used for numerical modeling of uprising polydispersed turbulent flow with implemented k-Lh model of closure. The flow domain is a round pipe with diameter of 30 mm and height of 100 calibers (pipe diameters). The flow (mean velocity up to 10 m/s) carries two fractions of ash particles (material density of 1020 kg/m 3 and sizes of 0.25 and 0.4 mm) and corundum particles (material density of 4000 kg/m 3 and size 0.4 mm). Two mass loadings – 5 and 10 kg/kg – were considered. The results are presented in the form of distribution of axial and radial velocity components of gaseous and solid phases, particle mass concentration and kinetic turbulent energy along the flow height at steady-state flow cross-sections.

Magnetophoresis of Nanoparticles

Iron oxide cores of 35 nm are coated with gold nanoparticles so that individual particle motion can be tracked in real time through the plasmonic response using dark field optical microscopy. Although Brownian and viscous drag forces are pronounced for nanoparticles, we show that magnetic manipulation is possible using large magnetic field gradients. The trajectories are analyzed to separate contributions from the different types of forces. With field gradients up to 3000 T/m, forces as small as 1.5 fN are detected.

Active Control of Separating Boundary Layer

AbstractFlow control refers to the ability to alter flows with the aim of achieving a desired effect: examples include drag reduction, noise attenuation, improved mixing or increased combustion efficiency among many other industrial applications. The reduction and control of the viscous drag force exerted on bodies moving in a fluid is of great technical interest. Several active and passive methods to achieve a delay of separation in the boundary layer have been developed and are being developed. In this paper we present a new concept for boundary layer separation control that is based on the synthetic jet concept which converts acoustic oscillations into mean fluid motions. We use synthetic jets as methods for Coanda effect's amplification. (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)