容器幾何參數對顆粒鐘現象的影響

Abstract

本文主要探討顆粒氣體在二格非對稱容器中的顆粒振盪現象。我們改變容器參數值（開口大小、區間的寬度、深度、底板傾角），使二格容器產生不對稱性，觀察此改變對顆粒氣體系統造成的影響。 我們在各二格非對稱容器的顆粒配比相圖中發現兩種不同區域的顆粒振盪(granular oscillation，簡寫GO)，其分類如下：GO1 & GO2為非對稱寬度容器中的顆粒振盪；GOM & GOS為非對稱深度容器中的顆粒振盪；GOI & GOO為非對稱傾斜底板容器中的顆粒振盪。其中，GO1的顆粒流動時間特徵為寬區到窄區的時間較長，窄區到寬區的時間較短；GO2則是從窄區道寬區的時間較長，寬區到窄區的時間較短，出現反轉現象。此外GOI & GOO也有與GO1&GO2相似的顆粒流動時間反轉的關係，但是GOM & GOS則無反轉現象發生。 我們將研究的焦點放在二元顆粒氣體系統的顆粒振盪上。我們統計顆粒流動時間(τRL、τLR，其中下標RL代表顆粒從右區流動到左區，LR代表顆粒從左區流動到右區)和高速攝影機對二元顆粒氣體系統的顆粒振盪進行研究。我們發現：容器幾何參數增加將使GO1、GO2、GOM、GOS的兩向顆粒流動時間差值(τRL -τLR )增加。而GOI & GOO之顆粒流動時間則受到顆粒配比影響。 最後，我們嘗試將寬度與深度兩個容器的非對稱參數進行偶合，最後得到容器寬度比與深度比在多顆粒配比下的等效曲線。而容器內顆粒系統則以等效曲線為界分為從淺區到深區的流動時間較長，與從深區到淺區的顆粒流動時間較長兩種趨勢。

This article explores the granular gases in the compartmentalized systems. We try to change the geometry parameters of asymmetric container (width ratio, height ratio, and angle of bottom) in order to study the phenomenon of granular gases. We found two different granular oscillation in each asymmetric container. The phase diagram of granular number has two oscillating areas. They are GO1&GO2 in asymmetric width container, GOM&GOS in asymmetric height container and GOI&GOO in asymmetric slope bottom container. In GO1 state, the granular gases spend longer time moving from the wider compartment to the narrower compartment; However, GO1 and GO2 are the opposite. In addition, GOI & GOO share the same trend with GO1 & GO2, but GOM and GOS are not. . And then, we focus on the granular oscillation. We count the τRL and τLR, and use the high-speed camera to record the movement of particles in the granular oscillation. (τRL -τLR ) are increases when the geometry parameter of asymmetric container is enlarged in GO1, GO2, GOM and GOS state. GOI’s and GOO’s τ are dependent on granular proportion. Finally, we combine the parameters of width ratio and height ratio to get the equivalent curves between the two parameters. The curves is the boundary of the two trend of τ: (1) The granular gases spend longer time moving from the higher compartment to the lower compartment. (2) The granular gases spend longer time moving from the lower compartment to the higher compartment.