Instability of a magnetic fluid jet in the presence of an axial magnetic field

目前磁流體的應用範圍廣泛，諸如醫學、軍事、太空、機械等領域皆佔有一席之地，其特性在於流體具有磁化特性，因此容易受到磁場的影響，達到遠端遙控的主要目的。目前磁噴流主要應用於磁噴墨印表機上（Magnetic ink jet printer），利用磁流體進行噴墨的動作，此過程需要高效率且準確的定位，故使用磁場來控制磁流體再適合不過。磁流體種類繁多，組成率各異且複雜不易分析，為簡化起見，本論文考慮一個較為理想的流場：假設流體為順磁性，然後施加一軸向均勻磁場，接著使用線性穩定性分析來探討磁力對噴流的作用。 在所考慮的物理模型中主要包含主要四種機制：黏滯力、表面張力、空氣壓力以及磁力。黏滯力的效應是穩定機制（Stabilizing mechanism）。表面張力的效應對於m=0軸對稱模態而言是不穩定機制（Destabilizing mechanism），但對於m>0而言為穩定機制。空氣壓力對於噴流則只有不穩定的效應，空氣壓力越大對噴流擾亂的機制越強。磁力效應是絕對穩定機制，尤其對於非軸對稱模態的抑制效果更為顯著，此暗示以磁力控制磁流體噴流之不穩定性將有非常大的效果。本篇論文最主要貢獻在於加入噴流黏滯性以其空氣壓力的影響，並更詳細的探討磁力機制對於流場不穩定性的影響。 最後，吾人在第四章統整分析了許多數據，期望能夠詳盡了解此流場中的各物理機制，並繪製一張磁場參數對韋伯數的參數地圖，以供實驗設計者做定性上的參考，期望實驗能有所依據。Currently, magnetic fluid has been widely utilized in various fields, such as medical, military, space, machinery. It plays an important role in these fields, its unique characteristics is that the fluid has a magnetic nature affected by the magnetic field; further, it achieve the main purpose of remote control. Now magnetic fluids mainly used in magnetic ink jet printer. This process requires efficient and accurate positioning, so it is a good way to control the magnetic fluid by magnetic fields. This study established an ideal flow at first including Newtonian fluid and paramagnetic material, and make assumption under the conditions of an external magnetic field. Next, we use linear perturbation and the temporal instability to simplify and expand the normal mode equation. Finally we obtained dispersion relation matrix and used bisection to attained numerical solutions; therefore, the physical mechanism can be revealed. In this study, the flow field includes the main four mechanisms: viscosity, surface tension, air pressure and magnetic force. Firstly, Viscous force is to inhibit every mode, which m = 1 mode are affected the most. Secondly, The effect of surface tension on each mode is the same as viscous force except for m = 0 mode. When the surface tension is greater than a critical value, this effect contributes to its instability. Thirdly, Air pressure only increase the instability, the greater the air pressure mechanism is, the stronger jet disruption is. Lastly, the effect of magnetic force is opposite to air pressure, which only inhibits the jet, especially for non-axisymmetric modes. Eventually, we analyzed lots of data in the fourth chapter and looked forward to a detailed understanding of the flow field in the physical mechanism; in addition, the parametric diagram magnetic field parameter versus the Weber number presented a qualitative reference to the experiment designer