1試體Specimen
所有顆粒同一粒徑 (預設 5 µm)All particles have the same diameter (default 5 µm)
截尾對數常態分佈 (預設 2 / 5 / 12 µm)；1 µm = 10⁻⁶ mTruncated log-normal distribution (default 2 / 5 / 12 µm); 1 µm = 10⁻⁶ m
2D 模型顯示片狀顆粒的 L × T 剖面The 2D model shows the L × T section of each plate
網格數越多，影像越細緻、可解析的最小孔徑越小，但產生試體與計算時間越長。More grid cells give a finer image and resolve smaller pores, but building and computing take longer.
預設值：間隙比 0.15 (2D) / 0.08 (3D)，亂數種子 1。間隙比 = 相鄰顆粒最小間距 / 粒徑，數值越大孔隙越大。Defaults: gap ratio 0.15 (2D) / 0.08 (3D), random seed 1. Gap ratio = minimum clearance / particle size; larger values give larger pores.
亂數種子決定隨機堆積中顆粒的位置、粒徑抽樣與方向：相同種子必定產生相同試體 (可重現，方便全班比對)；更換種子即得到另一個統計上等效、但排列不同的試體，可用來觀察試體變異對結果的影響。The random seed fixes particle positions, sampled sizes and orientations in random packing: the same seed always rebuilds the identical specimen (reproducible, so the whole class can compare results); a new seed gives a statistically equivalent specimen with a different arrangement, showing specimen-to-specimen variability.
2D 規則堆積取 3D 晶格的 (100) 或基面剖面。2D lattices are (100) or basal-plane sections of the 3D lattice.
裂縫為自顆粒表面向內收窄的 V 形開口 (2D 為楔形，3D 為平面狀裂隙)，開口寬度在最小–最大值間呈三角分布 (峰值 = 開口大小)，開裂深度：「深度」為平均開口裂縫的深度，各裂縫依其開口寬度等比例調整，但不超過「最大值」且不超過顆粒半徑的 90%。auto：平均開口 = max(2.5 格點, 0.06 × 粒徑)，最小 = 0.5 倍、最大 = 1.6 倍平均開口；數量 2D 為 2–4 條、3D 為 3–5 條；深度 = max(4 格點, 2.5 × 平均開口)，最大值 = 0.25 × 粒徑 (即半徑的一半)。預設 (2D, 5 µm 顆粒)：深度 0.75 µm、最大 1.25 µm。開口小於約 2 個格點時無法解析，可提高影像網格數。Cracks are V-shaped notches that open at the particle surface and narrow inwards (a wedge in 2D, a planar slit in 3D). Opening widths follow a triangular distribution between min and max, peaking at the opening size; Crack depth: “depth” applies to a crack of the mean opening; each crack scales with its own opening, capped by the maximum and by 90 % of the particle radius. Auto: mean opening = max(2.5 cells, 0.06 × particle size), min = 0.5 ×, max = 1.6 × the mean opening; 2–4 cracks per particle in 2D, 3–5 in 3D; depth = max(4 cells, 2.5 × mean opening), maximum = 0.25 × particle size (half the radius). Defaults (2D, 5 µm particles): depth 0.75 µm, maximum 1.25 µm. Openings narrower than about 2 grid cells cannot be resolved — increase the grid resolution if needed.
「重新配置顆粒」以新的隨機種子重新堆積顆粒 (種子欄會顯示新值，輸入同一種子即可重現)。規則堆積 (SC/FCC/BCC/HCP) 的位置固定，只有不規則顆粒外形會改變。“Re-arrange particles” re-packs the particles with a new random seed (shown in the seed box; enter the same seed to reproduce it). Regular lattices (SC/FCC/BCC/HCP) have fixed positions — only irregular particle outlines change.
2灌入液體Intrusion liquid
1 mPa·s = 10⁻³ Pa·s。水銀為非潤濕液體 (θ > 90°)，需加壓才能進入孔隙。1 mPa·s = 10⁻³ Pa·s. Mercury is non-wetting (θ > 90°) and must be forced into pores.
3灌入條件Intrusion settings
1 MPa = 10⁶ Pa。商用儀器約 0.0035–414 MPa。1 MPa = 10⁶ Pa. Commercial porosimeters span about 0.0035–414 MPa.
變速升/降壓：量測點集中在高壓段 (約 900 點)，每點停留時間隨壓力增加，升/降壓速率由程式自動決定 (auto)，可精細解析小孔。升壓預設為線性 2 MPa/s；降壓預設為「不降壓」：只做 Pmin → Pmax 灌入。選擇降壓方式後，一個循環 = 升壓灌入 + 降壓退出 (Pmax → Pmin)。dec/min：每分鐘壓力改變一個數量級 (十倍)；MPa/s：每秒改變的壓力。Variable rate: measurement points (about 900) crowd into the high-pressure range and each is held longer as pressure rises, so the rate is set automatically (auto) and fine pores are resolved in detail. Pressurization defaults to linear, 2 MPa/s; depressurization defaults to “None”: intrusion only (Pmin → Pmax). With a depressurization mode, one cycle = intrusion + extrusion (Pmax → Pmin). dec/min = pressure decades per minute; MPa/s = pressure change per second.
預設 0：只做一次升降壓。輸入 n 則共做 1 + n 次循環 (需選擇降壓方式才可設定)。Default 0: a single pressure cycle. Entering n gives 1 + n cycles in total (requires a depressurization mode).
4動畫設定Animation settings
預設：播完後停留 2 秒，自動從頭重播 1 次；勾選「無限次」則一直重播到按「暫停」。「直接完成」立即算出最終結果、不重播。Default: after the run ends, hold for 2 s and replay once from the start; tick “Unlimited” to keep replaying until Pause. Finish computes the final result at once, without replay.
52D 灌入影像2D intrusion image3D 灌入影像3D intrusion image
滑鼠：滾輪縮放、拖曳平移。Mouse: wheel = zoom, drag = pan.座標軸：Z 軸朝上，X、Y、Z 符合右手定則。滑鼠：滾輪縮放、左鍵拖曳旋轉、Shift 或右鍵拖曳平移。Axes: Z up; X, Y, Z form a right-handed system. Mouse: wheel = zoom, drag = rotate, Shift/right-drag = pan.
顆粒Solid 灌入液體Intruded liquid 滯留液體 (退出時被截斷)Trapped liquid 空孔隙Empty pore 灌入面 (外側為液體槽)Inlet face (liquid reservoir outside)
6灌入面積 vs. 灌入時間Intruded area vs. time灌入體積 vs. 灌入時間Intruded volume vs. time
7灌入 / 退出面積 vs. 孔徑Intrusion / extrusion area vs. pore diameter灌入 / 退出體積 vs. 孔徑Intrusion / extrusion volume vs. pore diameter
圖 7 的圓點為量測點 (每個壓力步一點；實心 = 灌入、空心 = 退出)。每條曲線標示循環編號 #n；圖例「#n: a% → b%」= 該循環最大灌入量 → 降壓後殘留量 (實線灌入、虛線退出)。Dots in chart 7 are measurement points (one per pressure step; filled = intrusion, open = extrusion). Each curve is tagged with its cycle #n; legend “#n: a% → b%” = maximum intrusion → residual after depressurization (solid = intrusion, dashed = extrusion).
圖表：滾輪縮放、拖曳平移、雙擊恢復自動範圍。孔徑 D 由 Washburn 方程式 D = −4γcosθ / P 換算。Charts: wheel = zoom, drag = pan, double-click = auto range. Pore diameter from the Washburn equation D = −4γcosθ / P.
8試驗結果Test results
滲流判定：單向灌入時液體連通至對面；四周灌入時任一灌入簇連通兩相對面。臨界孔徑取累積灌入曲線斜率最大處 (Katz–Thompson 概念)。Percolation: for one-way intrusion the liquid reaches the opposite face; for all-side intrusion one connected cluster spans two opposite faces. Dcrit = steepest slope of the cumulative curve (Katz–Thompson concept).
模型說明（點擊展開）About the model (click to expand)
- 試體由顆粒堆積後離散為像素 (2D) 或體素 (3D)；每個孔隙格點的「局部孔徑」取可容納之最大內切圓／球直徑 (local thickness)。Particles are packed and discretised into pixels (2D) or voxels (3D). Each pore cell is assigned a local pore diameter = diameter of the largest inscribed circle/sphere covering it (local thickness).
- 非潤濕液體在壓力 P 下只能進入 D ≥ −4γcosθ/P 的孔，且必須經由已灌入區域與灌入面相連 —— 大孔若只經由小喉道相通，須等到小喉道被打開才會被灌入，即「墨水瓶效應」。圖 7 虛線為不考慮連通性的幾何孔徑分佈，可與模擬灌入曲線比較。A non-wetting liquid at pressure P enters only pores with D ≥ −4γcosθ/P that are connected to the inlet through already-filled space. A large pore behind a narrow throat fills only when the throat opens — the ink-bottle effect. The dashed line in chart 7 is the geometric pore-size distribution without connectivity, for comparison.
- 灌入動力學以 Hagen–Poiseuille / Washburn 流動估算：前進速度 v = D²ΔP / (32 μ L)，因此黏度會影響灌入時間；對水銀而言此延遲極短，量測可視為準靜態。Filling kinetics follow Hagen–Poiseuille / Washburn flow, v = D²ΔP / (32 μ L), so viscosity affects the time response; for mercury the lag is tiny and the test is quasi-static.
- 降壓退出：壓力降到 P < −4γcosθr/D 時，孔徑 D 內的液體被拉回，因此由最小的孔 (喉道) 先排空；但液體必須仍與灌入面 (外部液體) 連通才能離開。喉道排空時液柱在喉道斷裂 (snap-off)，後方較大孔體中的液體失去與外部的連通而被截留 (墨水瓶效應) —— 因此退出曲線無法回到零。又因 θr < θa，同一孔要在較低壓力才退出，退出曲線位在灌入曲線之上，形成遲滯迴圈。圖 7 的孔徑依儀器慣例一律以 θa 換算。Extrusion: on depressurization, liquid in a pore of diameter D is withdrawn once P < −4γcosθr/D, so the smallest pores (necks) empty first — but only liquid still connected to the inlet (the external liquid) can leave. When a neck empties, the liquid thread breaks there (snap-off) and liquid in the larger pore bodies behind it is cut off and trapped (ink-bottle effect), so the extrusion curve does not return to zero. Because θr < θa, each pore empties at a lower pressure than it filled, so the extrusion curve lies above the intrusion curve — a hysteresis loop. As in instrument software, chart 7 converts pressure to D with θa for both branches.
- 多次循環：再次升壓時，被截留的液體在灌入前沿碰到它時重新與外部連通。第 2 次以後的循環很快達到穩定迴圈，第 1 次與第 2 次灌入曲線的差即為「截留孔隙量」。Repeated cycles: on re-pressurization, trapped liquid reconnects when the advancing front reaches it. Loops from cycle 2 onward quickly become stable; the gap between the 1st and 2nd intrusion curves equals the trapped pore volume.
- 試體邊界以外假設全部為液體 (液體槽)：灌入面上的孔隙直接與外部液體接觸，影像中以液體色帶 (2D) 或著色的灌入面 (3D) 表示；非灌入面視為封閉。3D 影像的液體預設為半透明，完全灌入後仍可看見內部顆粒。Outside the specimen boundary there is only liquid (a reservoir): pores on the inlet faces touch the external liquid directly, shown as a liquid band (2D) or tinted inlet faces (3D); non-inlet faces are sealed. In 3D the liquid is translucent by default, so particles remain visible after full intrusion.
- 表面開裂：模擬天然顆粒 (如骨材、礦物粉體) 表面的微裂縫。裂縫開口在顆粒表面、與顆粒間孔隙相連，但寬度遠小於顆粒間孔隙，因此需要較高壓力才能灌入，使孔徑分佈出現第二個 (較小孔徑的) 峰值 —— 雙峰孔徑分佈。塑膠與鐵氟龍對水的接觸角大於 90°，水在這兩種材料中也會表現為非潤濕液體。Surface cracks mimic micro-cracks on natural particles (aggregates, mineral powders). They open at the particle surface into the inter-particle pores but are much narrower, so they fill only at higher pressure, adding a second, small-pore peak to the pore-size distribution (bimodal). On plastic and Teflon the water contact angle exceeds 90°, so water also behaves as a non-wetting liquid.
- 小於約 2 個格點的孔無法解析；2D 平面模型的孔隙連通性遠低於 3D，較不易滲流。本模擬為教學用途，不取代實際儀器量測。Pores smaller than about two cells are not resolved. Pore connectivity in a 2D plane is much lower than in 3D, so 2D models percolate less readily. This simulator is for teaching and does not replace instrument measurements.
No comments:
Post a Comment