Tension force, internal

Atomization generally refers to a process in which a bulk liquid is disintegrated into small drops or droplets by internal and/or external forces as a result of the interaction between the liquid (dispersed phase) and surrounding medium (continuous phase). The term dispersed phase represents the liquid to be atomized and the atomized drops/droplets, whereas the term continuous phase refers to the medium in which the atomization occurs or by which a liquid is atomized. The disintegration or breakup occurs when the disruptive forces exceed the liquid surface tension force. The consolidating... 

Ohnesorge Number Oh = pL/(pLoD0f5 Compare internal viscosity force to surface tension force Walzel [398]... 

The bed void volume available for flow and for gas and liquid holdup is determined by the particle size distribution and shape, the particle porosity, and the packing effectiveness. The total voidage and the total liquid holdup can be divided into external and internal terms corresponding to interparticle (bed) and intraparticle (porosity) voidage. The external liquid holdup is further subdivided into static holdup eLs (holdup remaining after bed draining due to surface tension forces) and dynamic holdup eLrf. Additional expressions for the liquid holdup are the pore fillup Ft and the liquid saturation SL ... 

The curves for the drag coefficient and the terminal velocity converge for small and large bubbles. This is likely to be because there is always some surface active contaminants present, even in distilled water, that will prevent the internal circulation of the smallest bubbles. For the large bubbles the surface tension forces are not important. Several different drag formulations are given based on the Reynolds number and the density ratio of the gas and liquid [54, 163, 78]. 

Tomiyama, A., Celata, G. R, Hosokawa, S. Yoshida, S. 2002a Terminal velocity of single bubbles in surface tension force dominant regime. International Journal of Multiphase Flow 28, 1497-1519. 

If both internal and external liquids happen to be ideal dielectrics and there are no free charges at the interface, or if liquid inside the drop is highly conductive and the external liquid is an isolator, the external electric field leads to the appearance of a force distributed over the surface of drop. This phenomenon is caused by the discontinuity of the electric field at the interface [55]. The force is perpendicular to the interface and is directed from the liquid with higher dielectric permittivity (or from the conducting liquid) toward the liquid with lower dielectric permittivity (or toward the isolator). For the equilibrium shape of a motionless drop in a quiescent liquid to be conserved, the condition of equality of the surface electric force and the surface tension force must be satisfied. As a result, at static conditions, the drop assumes the shape of an ellipsoid extended along the direction of the external electric field. 

The propensity for stretch is evident in most types of filter and may arise as a result of cloth tensioning mechanisms, internal pressures, or other forces, such as the mass of the filter cake and the gravitational pull that it exerts on the fabric. In the case of filter belts, excessive force from the filter s tensioning mechanism may, in extreme cases, cause the belt to extend to the maximum length that the machine can handle. This in turn could lead to drive problems and hence the need to shorten the belt or even replace it. This will be discussed further in Section 3.9.1. 

As in gas-liquid systems, this flow is formed based on the type of microchannel geometry used flow symmetric geometry forms annular flow, while flow asymmetric forms parallel flow. This flow regime is observed at elevated flow rates in the microchannel without static internals - the higher the flow velocity, the better the stability. The shear force of the continuous phase is dominant over the surface tension force and, therefore, the dispersed phase flows straight forming annular or parallel flow. 

Hirai T, Program control system for winding tension force to obtain a uniform residual stress distribution in material. Proceedings of the 7 International Conference on Composite Materials, 1 Manufacture, Guangzhou, 101-106, 22-24 Nov 1989. 

In multiphase flows in microchannels, the importance of the surface tension force is much greater than in large-scale systems. This is easily understood, as the internal pressure increase across a bubble is... 

Lagisetty et al, describe the deformation of the droplet by a scalar strain measure z that we shall deem to be the additional internal coordinate. The physical process involves the drop being entrained in a turbulent eddy in which the drop is subject to deformation by viscous forces and restoration by surface tension forces. Their analysis shows that z, starting from zero, is always positive and that breakage occurs if and when it reaches the value of unity. The uncertainty of breakage arises from two sources. First, the deforming viscous force (available in the eddy) may only deform the droplet... 

In a product load analysis the structure as a whole and each of its elements together are in a state of equilibrium. There are no unbalanced forces of tension, compression, flexure, or shear acting on the structure at any point. All the forces counteract one another, which results m equilibrium. When all the forces acting on a given element in the same direction are summed up algebraically, the net effect is no load. However the product does respond to the various forces internally. 

Figure 5.6. (a) Small cylindrical liquid particle, and (b) free body diagram of portion of particle at (a) showing surface tension forces and internal pressure ip) that will be greater than atmospheric pressure for the curvature shown. 

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