優化具嵌入擋板之矩形流道的電滲流流量

Abstract

亥姆霍茲-斯莫魯霍夫斯基速率(Helmholtz-Smoluchowski, H-S velocity)能夠精準地預估於電雙層很薄且形狀簡單的流道中其電滲流(electro-osmotic, EO flow)的流量。然而當流道切截面為非均勻的情形，H-S速率便無法做為預測電滲流流量的準則。一典型的例子就是將表面電荷與流道壁面不同的薄板嵌入於流道中或者流道切截面為不規則狀的應用。 本研究於德拜-休克耳近似(Debye Hückel approximation, DHA)之下以半解析解探討電滲流於三種流道結構之流量。第一種是垂直薄板嵌入於矩形流道的設置，簡稱垂直板(Vertical plate, VP)問題；第二種是水平板嵌入於矩形流道中心的設置，簡稱水平板(Horizontal plate, HP)問題；第三種是矩形流道壁面具凹槽結構的設置，簡稱凹槽壁面(Groove wall, GW)問題，其中薄板表面經正規化後的介達電位為α，而流道內壁牆上則為β。以上三種問題都會探討流道外部施加電場方向平行於平板或凹槽延伸的方向，簡稱縱向流(Longitudinal EO pumping, LEOP)，而僅HP和GW問題將延伸探討流道外部施加電場方向垂直於平板或凹槽延伸的方向，簡稱橫向流(Transverse EO pumping, TEOP)。 本研究將闡述上述三種問題在何種情況下仍適用H-S速率，並探討電滲流在各種參數影響下的流量與H-S速率所預估的流量兩者之間的差異。最後，本研究會引入一個α−β平面圖，並於此平面上尋找優化電滲流流量的幾何參數。

The Helmholtz-Smoluchowski (H-S) velocity is known to be an accurate and useful formula for estimating the electro-osmotic (EO) flow rates in a simple micro-channel with a thin electric-double layer. However, in case the channel cross section is not so simple, the usefulness of H-S velocity could be sharply limited. A fundamental interest representing this situation would be a rectangular channel with built-in baffle plates or flow channel with groove walls, where baffle plates may develop a different normalized zeta potential α on the surface other than those on channel walls β. In this study, semi-analytical solutions are pursued under the Debye Hückel approximation (DHA) to obtain EO pumping rates of the three different channel structures. First is EO flow in a rectangular channel with vertical baffle plates, abbreviated as vertical plate (VP) problem; second would be EO flow in a rectangular channel with horizontal baffle plates, abbreviated as horizontal plate (HP) problem; third is EO flow in a rectangular channel with groove walls, abbreviated as groove wall (GW) problem. The three distinguished problem are investigated in a case when EO flow is either driven along or transverse to the plates or grooves, thus distinguishing longitudinal EO pumping (LEOP) and transverse EO pumping (TEOP). In particular, we examine how the EO pumping rates deviate from those predicted by the H-S velocity, and a diagram of optimal EO pumping rates on the α−β plane in introduced that accounts for the general features of the analysis.