在傳統的布朗運動中，物體都是從環境中的熱擾動所得到動能以及被驅動，被動粒子與水分子都是被動的型態而兩者的大小大約差了〖10〗^4；本篇論文主要探討主動粒子與被動粒子之間的交互作用利用實驗以及數值模擬的方法來研究，藉由主動粒子來提升被動粒子的擴散率在低雷諾數的環境中，而細菌是一種良好方便的方法建立自我推進粒子系統。 我們選擇了溶藻弧菌作為實驗中的自我推進粒子，它利用單一鞭毛馬達來做為運動的動力來源，而溶藻弧菌的鞭毛馬達利用鈉離子濃度差來獲取能量，所以調控環境中不同的鈉離子濃度來控制自我推進粒子的運動速度；此外，我們利用兩種不同的品種:VIO5(前進和後退)以及NMB136(直游)。實驗上，將聚苯乙烯的粒子混入自我推進粒子中在二維薄膜系統，並調控了自我推進粒子的特性、速度、濃度，以及被動粒子的大小。 我們主要關注在短時間尺度下被動粒子的行為，利用了Mean Square Displacement、Particle Image Velocimetry (PIV)、Power spectra 和 Probability density function (PDF)，我們觀察到在短時間內不同的主動粒子給予被動粒子相同的影響，但在時間大於0.3秒以後直游的主動粒子可以造成長時間的影響，而從不同濃度中可以發現隨著直游的主動粒子濃度增加被動粒子所受到影響也隨之增加，但增加前進和後退的主動粒子濃度所受的影響卻達到飽和；從PDF中，我們也觀察到被動粒子主要受到兩種影響，一個為布朗運動，另一個則是主動粒子所帶來的碰撞；從改變不同被動粒子大小中，觀察到在前進和後退的主動粒子溶液中，某特地大小的被動粒子會受到較大的影響。 此外，為了進一步了解主動粒子所帶來的影響，我們利用數值模擬的方法來探討直游的主動粒子與被動粒子之間碰撞所帶來的影響，改變不同的情況去比較實驗與模擬兩著的差異，發現群體運動和碰撞在主動粒子與被動粒子之間是很重要的。 ;In the classical picture of Brownian motion, both the particles and fluid molecules are passive, driven by thermal fluctuations and the size of particle is larger than fluid molecules. In this thesis, we present both the experimental and computational studies of passive particle motions in active particle which size similar to passive particle. The bacteria are ideal candidates for building experimental active particle systems. We use polar single-flagellated bacteria, Vibrio alginolyticus, as controllable straight-swimming (NMB136) and reversal (VIO5) particles. Passive micron-size particles are mixed with active bacteria in free-standing films as quasi-two-dimensional systems. We control bacterial swimming speed (active particle speed), cell concentration and size of passive particle. By analyzing the mean square displacements (MSD) of passive particles, we study the motional behavior at short time scales. When the passive particles interact with straight and reversal swimmer, it both shows ballistic behavior in short time scale. The straight swimmer can enhance the diffusion to a longer time scale indicating the different swimming pattern have strong influence on the passive particle behavior. We found that there are two kinds of mechanisms of passive particles motion, one is ordinary Brownian motion and the other is the collisions by active particle. In the reverse particle, the size of passive particle has favorite dimension by the collective motion. In order to learn the mechanism of the enhanced diffusion in our experimental system, we build up Brownian dynamic simulation to study the interaction between the passive and active particles. The behavior of passive particle is effective by increasing the bacterial swimming speed (active particle speed) and cell concentration which increase frequency of collision. Therefore, collision rate and collective motion are both important in active suspension bath.
