Drag force axial

Fig. 9.11 Stationary relative velocity, Vp, of pentachloroethane drops in motionless water is dependent on drop diameter, dp. Very small drops behave bice rigid spheres, as shown. Larger drops have an internal circulation and are bnaUy deformed ebipticaUy. When they have reached a certain diameter, the drops in the end oschlate along and across their major axis. Their axial velocity is nearly independent of the diameter. Once the drop size is higher than a maximum value dp raax., the drop will break, owing to the drag forces. (From Ref. 2.)...

In a spin-filter based stirred bioreactor, there are various forces acting on both the liquid medium and the cell particles gravity force, axial force due to impeller rotation, centrifugal force created by the spin-filter rotation, and radial force (drag) generated by the perfusion flux. 

Fluid-dynamic operating conditions, such as axial or angular velocity (i.e., shear stress that determines drag force value) and transmembrane pressure (that determines disperse-phase flux, for a given disperse-phase viscosity and membrane... 

The axial velocity affects the droplet size by both influencing the surfactant mass transfer to the newly formed interface (that speeds up the reduction of the interfacial tension) and the drag force (that pulls droplets away from the pore mouth). 

The advancement of a flow through the duct is accompanied by its deceleration near the walls and by the EPR drag force, thus displacing the liquid to the center of the duct. This leads to the surprising maxima on the longitudinal velocity profiles, Fig. 3.12. The flow in the middle constantly accelerates, but its value tends to a certain limit reached in the main steady-state region. For this laminar case, v = const, the dimensionless axial velocity is known to reach the value 1.5 irrespective to Re [380], if the EPR is absent. In the case of interest, it depends upon all the parameters A, 6, and Re, can be... 

The steady drag force term in the axial component of the gas momentum equation is treated in the same way as described when considering the liquid momentum equation, as discussed in sect C.4.5. 

It follows from (2.6.14) and (2.6.15) that to calculate the drag force of a body of revolution of any shape with arbitrary orientation in a Stokes flow, it suffices to know the value of this force only for two special positions of the body in space. The axial (Fy) and transversal (Fl) drags can be obtained both theoretically... 

The tensor S is symmetric only at a point O unique for each body, this point is called the center of hydrodynamic reaction. This tensor is called the conjugate tensor and characterizes the crossed reaction of the body under translational and rotational motion (the drag moment in the translational motion and the drag force in the rotational motion). For bodies with orthotropic, axial, or spherical symmetry, the conjugate tensor is zero. However, it is necessary to take this tensor into account for bodies with helicoidal symmetry (propeller-like bodies). 

The axial and transverse motion of two drops close to each other was considered in [525], Some leading terms were obtained in the asymptotic expansion of the drag force with respect to the small dimensionless distance between the drop boundaries. The case of interaction between a solid particle and a drop was also investigated. 

Here, subscripts p and f denote the particle and the fluid respectively, subscripts z, r, q> denote the axial, radial and angular direction resjKctively. In the three equations the first term in R.H.S. is the buroyancy forre and the second term is the drag force. The last terms in Eq. (48-a), Eq. (48-b) and Eq. (48-c) are gravity, centrifugal force and Coriolis force respectively. K appearing in Eq. (48-b) is the curl of the fluid velocity, supposed to be axially oriented. 

Dynamic interfacial effects due to capillary advancement in the presence of electroosmotic flows in hydrophobic circular microchannels have recently been investigated by Yang et al. [8]. In a general sense, their theoretical development is based on the prototype equation of motion of the form of Eq. 1, with an additional term appearing in the right-hand side to model the electroosmotic body force. Not only that, the quantification of the viscous drag force is also adapted to accommodate the influences of electroosmotic slip. To address these issues carefully, one may first derive an expression for electroosmotic flow velocity in presence of an axial electric field strength of Ej in the solution as... 

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