Temporal instability of compound threads and jets
Temporal instability of compound threads and jets
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DOI：
10.1017/s0022112000001282
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发表时间：
2000-10
影响因子：
3.7
通讯作者：
A. Chauhan;C. Maldarelli;D. Papageorgiou;D. Rumschitzki
中科院分区：
文献类型：
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作者：
A. Chauhan;C. Maldarelli;D. Papageorgiou;D. Rumschitzki
复合螺纹和射流由被第二不混溶液体的环包围的核心液体组成。来自两个接口的圆周曲率的轴对称扰动的毛细管力使复合螺纹和射流（分别具有内半径R1和外半径aR1）的圆柱形基态不稳定。毛细管的不稳定性导致分裂成液滴;环状相的存在允许环状相和芯相的性质影响液滴尺寸。技术上感兴趣的是核首先断裂，然后是环的断裂。这导致化合物滴。通过喷射，这种模式可以形成复合颗粒，或者如果环形流体被蒸发去除，则可以形成其尺寸由两种流体调制的单滴。本文是一项研究的线性时间不稳定性的复合线程和射流了解环形流体的性能如何控制液滴大小的射流破碎，并确定有利于复合液滴形成的条件。对于无量纲的一阶环厚度a，数值求解了时间色散方程;对于薄环（a-1 = ε [Lt] 1），通过在ε中的渐近展开，解析求解了时间色散方程。有两种时间增长模式：一种是拉伸模式，当波长大于未受干扰的内圆周2 π R1时不稳定，其中两个界面同相增长;另一种是压缩模式，当波长大于2 π aR1时不稳定，它完全异相增长。增长率总是真实的，表明在喷射配置扰动对流下游的基本速度。对于一阶厚度，拉伸模式的增长率较高的系统参数检查的整个范围内。液滴大小与最大增长波的波数（kmax）成比例。我们发现，对于占主导地位的拉伸模式和a = 2，从0.1到10的环芯粘度的比率的变化，或外表面的内界面的张力，可以导致kmax的变化约为2倍。然而，对于系统比率的这些变化，最快增长波的增长率（smax）和外界面与内界面的振幅比（Amax）仅略微变化，Amax接近1。该系统似乎对环空与核心流体的密度比最敏感。对于0.1和10之间的变化，kmax再次变化2倍，但Amax和smax在低密度比的大振幅比下变化更显着。在最大增长波（Amax）处的拉伸模式的振幅比指示膜或芯是否将首先破裂。当该比率接近1时，线性理论预测核心破裂而环空完整，形成化合物滴。除了低的密度比的值，我们的研究结果表明，大多数系统条件促进复合液滴的形成。对于薄环隙，模式之间的增长率差距变得更大。在极限ε → 0时，压缩模增长率与ε 2大致成正比，而拉伸模增长率与ε 0大致成正比，并渐近于一个半径为R1、张力等于两个张力之和的单射流。因此，在此极限下，生长速率和kmax与膜密度和粘度无关。拉伸模式的振幅比对于所有波数都等于1，因此薄膜在化合物滴下时破裂。我们的研究结果与以前发表的测量不稳定波的复合射流。
Compound threads and jets consist of a core liquid surrounded by an annulus of a second immiscible liquid. Capillary forces derived from axisymmetric disturbances in the circumferential curvatures of the two interfaces destabilize cylindrical base states of compound threads and jets (with inner and outer radii R1 and aR1 respectively). The capillary instability causes breakup into drops; the presence of the annular phase allows both the annular- and core-phase properties to influence the drop size. Of technological interest is breakup where the core snaps first, and then the annulus. This results in compound drops. With jets, this pattern can form composite particles, or if the annular fluid is evaporatively removed, single drops whose size is modulated by both fluids. This paper is a study of the linear temporal instability of compound threads and jets to understand how annular fluid properties control drop size in jet breakup, and to determine conditions which favour compound drop formation. The temporal dispersion equation is solved numerically for non-dimensional annular thicknesses a of order one, and analytically for thin annuli (a – 1 = ε [Lt ] 1) by asymptotic expansion in ε. There are two temporally growing modes: a stretching mode, unstable for wavelengths greater than the undisturbed inner circumference 2πR1, in which the two interfaces grow in phase; and a squeezing mode, unstable for wavelengths greater than 2πaR1, which grows exactly out of phase. Growth rates are always real, indicating that in jetting configurations disturbances convect downstream with the base velocity. For order-one thicknesses, the growth rate of the stretching mode is higher for the entire range of system parameters examined. The drop size scales with the wavenumber of the maximally growing wave (kmax). We find that for the dominant stretching mode and a = 2, variations from 0.1 to 10 in the ratios of the annulus to core viscosity, or the tension of the outer surface to that of the inner interface, can result in changes in kmax by a factor of approximately 2. However, for these changes in the system ratios, the growth rate (smax) and the ratio of the amplitude of the outer to the inner interface (Amax) for the fastest growing wave only change marginally, with Amax near one. The system appears most sensitive to the ratio of the density of the annulus to the core fluid. For a variation between 0.1 and 10, kmax again changes by a factor of 2, but Amax and smax vary more significantly with large amplitude ratios for low density ratios. The amplitude ratio of the stretching mode at the maximally growing wave (Amax) indicates whether the film or core will break first. When this ratio is near one, linear theory predicts that the core breaks with the annulus intact, forming compound drops. Except for low values of the density ratio, our results indicate that most system conditions promote compound drop formation. For thin annuli, the growth rate disparity between modes becomes even greater. In the limit ε → 0, the squeezing growth rate is roughly proportional to ε2 while the stretching mode growth rate is roughly proportional to ε0 and asymptotes to a single jet with radius R1 and tension equal to the sum of the two tensions. Thus, in this limit the growth rate and kmax are independent of the film density and viscosity. The amplitude ratio of the stretching mode becomes equal to one for all wavenumbers; so thin films break as compound drops. Our results compare favourably with previously published measurements on unstable waves in compound jets.